relude-0.7.0.0: Safe, performant, user-friendly and lightweight Haskell Standard Library
Copyright(c) 2018-2020 Kowainik
LicenseMIT
MaintainerKowainik <xrom.xkov@gmail.com>
StabilityStable
PortabilityPortable
Safe HaskellTrustworthy
LanguageHaskell2010

Relude.Numeric

Description

Provides numerical data types and functions.

Since: 0.5.0

Synopsis

Reexports

toIntegralSized :: (Integral a, Integral b, Bits a, Bits b) => a -> Maybe b #

Attempt to convert an Integral type a to an Integral type b using the size of the types as measured by Bits methods.

A simpler version of this function is:

toIntegral :: (Integral a, Integral b) => a -> Maybe b
toIntegral x
  | toInteger x == y = Just (fromInteger y)
  | otherwise        = Nothing
  where
    y = toInteger x

This version requires going through Integer, which can be inefficient. However, toIntegralSized is optimized to allow GHC to statically determine the relative type sizes (as measured by bitSizeMaybe and isSigned) and avoid going through Integer for many types. (The implementation uses fromIntegral, which is itself optimized with rules for base types but may go through Integer for some type pairs.)

Since: base-4.8.0.0

xor :: Bits a => a -> a -> a infixl 6 #

Bitwise "xor"

data Int #

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances

Instances details
Bounded Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: Int #

maxBound :: Int #

Enum Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Int -> Int #

pred :: Int -> Int #

toEnum :: Int -> Int #

fromEnum :: Int -> Int #

enumFrom :: Int -> [Int] #

enumFromThen :: Int -> Int -> [Int] #

enumFromTo :: Int -> Int -> [Int] #

enumFromThenTo :: Int -> Int -> Int -> [Int] #

Eq Int 
Instance details

Defined in GHC.Classes

Methods

(==) :: Int -> Int -> Bool #

(/=) :: Int -> Int -> Bool #

Integral Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

quot :: Int -> Int -> Int #

rem :: Int -> Int -> Int #

div :: Int -> Int -> Int #

mod :: Int -> Int -> Int #

quotRem :: Int -> Int -> (Int, Int) #

divMod :: Int -> Int -> (Int, Int) #

toInteger :: Int -> Integer #

Data Int

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int -> c Int #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int #

toConstr :: Int -> Constr #

dataTypeOf :: Int -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int) #

gmapT :: (forall b. Data b => b -> b) -> Int -> Int #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r #

gmapQ :: (forall d. Data d => d -> u) -> Int -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Int -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int -> m Int #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int #

Num Int

Since: base-2.1

Instance details

Defined in GHC.Num

Methods

(+) :: Int -> Int -> Int #

(-) :: Int -> Int -> Int #

(*) :: Int -> Int -> Int #

negate :: Int -> Int #

abs :: Int -> Int #

signum :: Int -> Int #

fromInteger :: Integer -> Int #

Ord Int 
Instance details

Defined in GHC.Classes

Methods

compare :: Int -> Int -> Ordering #

(<) :: Int -> Int -> Bool #

(<=) :: Int -> Int -> Bool #

(>) :: Int -> Int -> Bool #

(>=) :: Int -> Int -> Bool #

max :: Int -> Int -> Int #

min :: Int -> Int -> Int #

Read Int

Since: base-2.1

Instance details

Defined in GHC.Read

Real Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

toRational :: Int -> Rational #

Show Int

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Int -> ShowS #

show :: Int -> String #

showList :: [Int] -> ShowS #

Ix Int

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

range :: (Int, Int) -> [Int] #

index :: (Int, Int) -> Int -> Int #

unsafeIndex :: (Int, Int) -> Int -> Int #

inRange :: (Int, Int) -> Int -> Bool #

rangeSize :: (Int, Int) -> Int #

unsafeRangeSize :: (Int, Int) -> Int #

Lift Int 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Int -> Q Exp #

Bits Int

Since: base-2.1

Instance details

Defined in Data.Bits

Methods

(.&.) :: Int -> Int -> Int #

(.|.) :: Int -> Int -> Int #

xor :: Int -> Int -> Int #

complement :: Int -> Int #

shift :: Int -> Int -> Int #

rotate :: Int -> Int -> Int #

zeroBits :: Int #

bit :: Int -> Int #

setBit :: Int -> Int -> Int #

clearBit :: Int -> Int -> Int #

complementBit :: Int -> Int -> Int #

testBit :: Int -> Int -> Bool #

bitSizeMaybe :: Int -> Maybe Int #

bitSize :: Int -> Int #

isSigned :: Int -> Bool #

shiftL :: Int -> Int -> Int #

unsafeShiftL :: Int -> Int -> Int #

shiftR :: Int -> Int -> Int #

unsafeShiftR :: Int -> Int -> Int #

rotateL :: Int -> Int -> Int #

rotateR :: Int -> Int -> Int #

popCount :: Int -> Int #

FiniteBits Int

Since: base-4.6.0.0

Instance details

Defined in Data.Bits

NFData Int 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Int -> () #

Hashable Int 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int -> Int #

hash :: Int -> Int #

Generic1 (URec Int :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Int) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Int a -> Rep1 (URec Int) a #

to1 :: forall (a :: k0). Rep1 (URec Int) a -> URec Int a #

Functor (URec Int :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b #

(<$) :: a -> URec Int b -> URec Int a #

Foldable (URec Int :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Int m -> m #

foldMap :: Monoid m => (a -> m) -> URec Int a -> m #

foldMap' :: Monoid m => (a -> m) -> URec Int a -> m #

foldr :: (a -> b -> b) -> b -> URec Int a -> b #

foldr' :: (a -> b -> b) -> b -> URec Int a -> b #

foldl :: (b -> a -> b) -> b -> URec Int a -> b #

foldl' :: (b -> a -> b) -> b -> URec Int a -> b #

foldr1 :: (a -> a -> a) -> URec Int a -> a #

foldl1 :: (a -> a -> a) -> URec Int a -> a #

toList :: URec Int a -> [a] #

null :: URec Int a -> Bool #

length :: URec Int a -> Int #

elem :: Eq a => a -> URec Int a -> Bool #

maximum :: Ord a => URec Int a -> a #

minimum :: Ord a => URec Int a -> a #

sum :: Num a => URec Int a -> a #

product :: Num a => URec Int a -> a #

Traversable (URec Int :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) #

sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) #

mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) #

sequence :: Monad m => URec Int (m a) -> m (URec Int a) #

Eq (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Int p -> URec Int p -> Bool #

(/=) :: URec Int p -> URec Int p -> Bool #

Ord (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Int p -> URec Int p -> Ordering #

(<) :: URec Int p -> URec Int p -> Bool #

(<=) :: URec Int p -> URec Int p -> Bool #

(>) :: URec Int p -> URec Int p -> Bool #

(>=) :: URec Int p -> URec Int p -> Bool #

max :: URec Int p -> URec Int p -> URec Int p #

min :: URec Int p -> URec Int p -> URec Int p #

Show (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Int p -> ShowS #

show :: URec Int p -> String #

showList :: [URec Int p] -> ShowS #

Generic (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Int p) :: Type -> Type #

Methods

from :: URec Int p -> Rep (URec Int p) x #

to :: Rep (URec Int p) x -> URec Int p #

data URec Int (p :: k)

Used for marking occurrences of Int#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Int (p :: k) = UInt {}
type Rep1 (URec Int :: k -> Type) 
Instance details

Defined in GHC.Generics

type Rep1 (URec Int :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: k -> Type)))
type Rep (URec Int p) 
Instance details

Defined in GHC.Generics

type Rep (URec Int p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UInt" 'PrefixI 'True) (S1 ('MetaSel ('Just "uInt#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UInt :: Type -> Type)))

data Int8 #

8-bit signed integer type

Instances

Instances details
Bounded Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

succ :: Int8 -> Int8 #

pred :: Int8 -> Int8 #

toEnum :: Int -> Int8 #

fromEnum :: Int8 -> Int #

enumFrom :: Int8 -> [Int8] #

enumFromThen :: Int8 -> Int8 -> [Int8] #

enumFromTo :: Int8 -> Int8 -> [Int8] #

enumFromThenTo :: Int8 -> Int8 -> Int8 -> [Int8] #

Eq Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int8 -> Int8 -> Bool #

(/=) :: Int8 -> Int8 -> Bool #

Integral Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

quot :: Int8 -> Int8 -> Int8 #

rem :: Int8 -> Int8 -> Int8 #

div :: Int8 -> Int8 -> Int8 #

mod :: Int8 -> Int8 -> Int8 #

quotRem :: Int8 -> Int8 -> (Int8, Int8) #

divMod :: Int8 -> Int8 -> (Int8, Int8) #

toInteger :: Int8 -> Integer #

Data Int8

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int8 -> c Int8 #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int8 #

toConstr :: Int8 -> Constr #

dataTypeOf :: Int8 -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int8) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int8) #

gmapT :: (forall b. Data b => b -> b) -> Int8 -> Int8 #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int8 -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int8 -> r #

gmapQ :: (forall d. Data d => d -> u) -> Int8 -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Int8 -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int8 -> m Int8 #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int8 -> m Int8 #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int8 -> m Int8 #

Num Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(+) :: Int8 -> Int8 -> Int8 #

(-) :: Int8 -> Int8 -> Int8 #

(*) :: Int8 -> Int8 -> Int8 #

negate :: Int8 -> Int8 #

abs :: Int8 -> Int8 #

signum :: Int8 -> Int8 #

fromInteger :: Integer -> Int8 #

Ord Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

compare :: Int8 -> Int8 -> Ordering #

(<) :: Int8 -> Int8 -> Bool #

(<=) :: Int8 -> Int8 -> Bool #

(>) :: Int8 -> Int8 -> Bool #

(>=) :: Int8 -> Int8 -> Bool #

max :: Int8 -> Int8 -> Int8 #

min :: Int8 -> Int8 -> Int8 #

Read Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Real Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

toRational :: Int8 -> Rational #

Show Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

showsPrec :: Int -> Int8 -> ShowS #

show :: Int8 -> String #

showList :: [Int8] -> ShowS #

Ix Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

range :: (Int8, Int8) -> [Int8] #

index :: (Int8, Int8) -> Int8 -> Int #

unsafeIndex :: (Int8, Int8) -> Int8 -> Int #

inRange :: (Int8, Int8) -> Int8 -> Bool #

rangeSize :: (Int8, Int8) -> Int #

unsafeRangeSize :: (Int8, Int8) -> Int #

Lift Int8 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Int8 -> Q Exp #

Bits Int8

Since: base-2.1

Instance details

Defined in GHC.Int

FiniteBits Int8

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

NFData Int8 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Int8 -> () #

Hashable Int8 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int8 -> Int #

hash :: Int8 -> Int #

data Int16 #

16-bit signed integer type

Instances

Instances details
Bounded Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Eq Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int16 -> Int16 -> Bool #

(/=) :: Int16 -> Int16 -> Bool #

Integral Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Data Int16

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int16 -> c Int16 #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int16 #

toConstr :: Int16 -> Constr #

dataTypeOf :: Int16 -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int16) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int16) #

gmapT :: (forall b. Data b => b -> b) -> Int16 -> Int16 #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int16 -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int16 -> r #

gmapQ :: (forall d. Data d => d -> u) -> Int16 -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Int16 -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int16 -> m Int16 #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int16 -> m Int16 #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int16 -> m Int16 #

Num Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Ord Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

compare :: Int16 -> Int16 -> Ordering #

(<) :: Int16 -> Int16 -> Bool #

(<=) :: Int16 -> Int16 -> Bool #

(>) :: Int16 -> Int16 -> Bool #

(>=) :: Int16 -> Int16 -> Bool #

max :: Int16 -> Int16 -> Int16 #

min :: Int16 -> Int16 -> Int16 #

Read Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Real Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

toRational :: Int16 -> Rational #

Show Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

showsPrec :: Int -> Int16 -> ShowS #

show :: Int16 -> String #

showList :: [Int16] -> ShowS #

Ix Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Lift Int16 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Int16 -> Q Exp #

Bits Int16

Since: base-2.1

Instance details

Defined in GHC.Int

FiniteBits Int16

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

NFData Int16 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Int16 -> () #

Hashable Int16 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int16 -> Int #

hash :: Int16 -> Int #

data Int32 #

32-bit signed integer type

Instances

Instances details
Bounded Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Eq Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int32 -> Int32 -> Bool #

(/=) :: Int32 -> Int32 -> Bool #

Integral Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Data Int32

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int32 -> c Int32 #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int32 #

toConstr :: Int32 -> Constr #

dataTypeOf :: Int32 -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int32) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int32) #

gmapT :: (forall b. Data b => b -> b) -> Int32 -> Int32 #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int32 -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int32 -> r #

gmapQ :: (forall d. Data d => d -> u) -> Int32 -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Int32 -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int32 -> m Int32 #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int32 -> m Int32 #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int32 -> m Int32 #

Num Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Ord Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

compare :: Int32 -> Int32 -> Ordering #

(<) :: Int32 -> Int32 -> Bool #

(<=) :: Int32 -> Int32 -> Bool #

(>) :: Int32 -> Int32 -> Bool #

(>=) :: Int32 -> Int32 -> Bool #

max :: Int32 -> Int32 -> Int32 #

min :: Int32 -> Int32 -> Int32 #

Read Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Real Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

toRational :: Int32 -> Rational #

Show Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

showsPrec :: Int -> Int32 -> ShowS #

show :: Int32 -> String #

showList :: [Int32] -> ShowS #

Ix Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Lift Int32 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Int32 -> Q Exp #

Bits Int32

Since: base-2.1

Instance details

Defined in GHC.Int

FiniteBits Int32

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

NFData Int32 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Int32 -> () #

Hashable Int32 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int32 -> Int #

hash :: Int32 -> Int #

data Int64 #

64-bit signed integer type

Instances

Instances details
Bounded Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Eq Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int64 -> Int64 -> Bool #

(/=) :: Int64 -> Int64 -> Bool #

Integral Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Data Int64

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int64 -> c Int64 #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int64 #

toConstr :: Int64 -> Constr #

dataTypeOf :: Int64 -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int64) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int64) #

gmapT :: (forall b. Data b => b -> b) -> Int64 -> Int64 #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int64 -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int64 -> r #

gmapQ :: (forall d. Data d => d -> u) -> Int64 -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Int64 -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int64 -> m Int64 #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int64 -> m Int64 #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int64 -> m Int64 #

Num Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Ord Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

compare :: Int64 -> Int64 -> Ordering #

(<) :: Int64 -> Int64 -> Bool #

(<=) :: Int64 -> Int64 -> Bool #

(>) :: Int64 -> Int64 -> Bool #

(>=) :: Int64 -> Int64 -> Bool #

max :: Int64 -> Int64 -> Int64 #

min :: Int64 -> Int64 -> Int64 #

Read Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Real Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

toRational :: Int64 -> Rational #

Show Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

showsPrec :: Int -> Int64 -> ShowS #

show :: Int64 -> String #

showList :: [Int64] -> ShowS #

Ix Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Lift Int64 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Int64 -> Q Exp #

Bits Int64

Since: base-2.1

Instance details

Defined in GHC.Int

FiniteBits Int64

Since: base-4.6.0.0

Instance details

Defined in GHC.Int

NFData Int64 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Int64 -> () #

Hashable Int64 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int64 -> Int #

hash :: Int64 -> Int #

data Word #

A Word is an unsigned integral type, with the same size as Int.

Instances

Instances details
Bounded Word

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Word

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Word -> Word #

pred :: Word -> Word #

toEnum :: Int -> Word #

fromEnum :: Word -> Int #

enumFrom :: Word -> [Word] #

enumFromThen :: Word -> Word -> [Word] #

enumFromTo :: Word -> Word -> [Word] #

enumFromThenTo :: Word -> Word -> Word -> [Word] #

Eq Word 
Instance details

Defined in GHC.Classes

Methods

(==) :: Word -> Word -> Bool #

(/=) :: Word -> Word -> Bool #

Integral Word

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

quot :: Word -> Word -> Word #

rem :: Word -> Word -> Word #

div :: Word -> Word -> Word #

mod :: Word -> Word -> Word #

quotRem :: Word -> Word -> (Word, Word) #

divMod :: Word -> Word -> (Word, Word) #

toInteger :: Word -> Integer #

Data Word

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word -> c Word #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word #

toConstr :: Word -> Constr #

dataTypeOf :: Word -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word) #

gmapT :: (forall b. Data b => b -> b) -> Word -> Word #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r #

gmapQ :: (forall d. Data d => d -> u) -> Word -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Word -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word -> m Word #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word #

Num Word

Since: base-2.1

Instance details

Defined in GHC.Num

Methods

(+) :: Word -> Word -> Word #

(-) :: Word -> Word -> Word #

(*) :: Word -> Word -> Word #

negate :: Word -> Word #

abs :: Word -> Word #

signum :: Word -> Word #

fromInteger :: Integer -> Word #

Ord Word 
Instance details

Defined in GHC.Classes

Methods

compare :: Word -> Word -> Ordering #

(<) :: Word -> Word -> Bool #

(<=) :: Word -> Word -> Bool #

(>) :: Word -> Word -> Bool #

(>=) :: Word -> Word -> Bool #

max :: Word -> Word -> Word #

min :: Word -> Word -> Word #

Read Word

Since: base-4.5.0.0

Instance details

Defined in GHC.Read

Real Word

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

toRational :: Word -> Rational #

Show Word

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Word -> ShowS #

show :: Word -> String #

showList :: [Word] -> ShowS #

Ix Word

Since: base-4.6.0.0

Instance details

Defined in GHC.Arr

Methods

range :: (Word, Word) -> [Word] #

index :: (Word, Word) -> Word -> Int #

unsafeIndex :: (Word, Word) -> Word -> Int #

inRange :: (Word, Word) -> Word -> Bool #

rangeSize :: (Word, Word) -> Int #

unsafeRangeSize :: (Word, Word) -> Int #

Lift Word 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Word -> Q Exp #

Bits Word

Since: base-2.1

Instance details

Defined in Data.Bits

FiniteBits Word

Since: base-4.6.0.0

Instance details

Defined in Data.Bits

NFData Word 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Word -> () #

Hashable Word 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word -> Int #

hash :: Word -> Int #

Generic1 (URec Word :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Word) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Word a -> Rep1 (URec Word) a #

to1 :: forall (a :: k0). Rep1 (URec Word) a -> URec Word a #

Functor (URec Word :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b #

(<$) :: a -> URec Word b -> URec Word a #

Foldable (URec Word :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Word m -> m #

foldMap :: Monoid m => (a -> m) -> URec Word a -> m #

foldMap' :: Monoid m => (a -> m) -> URec Word a -> m #

foldr :: (a -> b -> b) -> b -> URec Word a -> b #

foldr' :: (a -> b -> b) -> b -> URec Word a -> b #

foldl :: (b -> a -> b) -> b -> URec Word a -> b #

foldl' :: (b -> a -> b) -> b -> URec Word a -> b #

foldr1 :: (a -> a -> a) -> URec Word a -> a #

foldl1 :: (a -> a -> a) -> URec Word a -> a #

toList :: URec Word a -> [a] #

null :: URec Word a -> Bool #

length :: URec Word a -> Int #

elem :: Eq a => a -> URec Word a -> Bool #

maximum :: Ord a => URec Word a -> a #

minimum :: Ord a => URec Word a -> a #

sum :: Num a => URec Word a -> a #

product :: Num a => URec Word a -> a #

Traversable (URec Word :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) #

sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) #

mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) #

sequence :: Monad m => URec Word (m a) -> m (URec Word a) #

Eq (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Word p -> URec Word p -> Bool #

(/=) :: URec Word p -> URec Word p -> Bool #

Ord (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Word p -> URec Word p -> Ordering #

(<) :: URec Word p -> URec Word p -> Bool #

(<=) :: URec Word p -> URec Word p -> Bool #

(>) :: URec Word p -> URec Word p -> Bool #

(>=) :: URec Word p -> URec Word p -> Bool #

max :: URec Word p -> URec Word p -> URec Word p #

min :: URec Word p -> URec Word p -> URec Word p #

Show (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Word p -> ShowS #

show :: URec Word p -> String #

showList :: [URec Word p] -> ShowS #

Generic (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Word p) :: Type -> Type #

Methods

from :: URec Word p -> Rep (URec Word p) x #

to :: Rep (URec Word p) x -> URec Word p #

data URec Word (p :: k)

Used for marking occurrences of Word#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Word (p :: k) = UWord {}
type Rep1 (URec Word :: k -> Type) 
Instance details

Defined in GHC.Generics

type Rep1 (URec Word :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: k -> Type)))
type Rep (URec Word p) 
Instance details

Defined in GHC.Generics

type Rep (URec Word p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: Type -> Type)))

data Word8 #

8-bit unsigned integer type

Instances

Instances details
Bounded Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Eq Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word8 -> Word8 -> Bool #

(/=) :: Word8 -> Word8 -> Bool #

Integral Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Data Word8

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word8 -> c Word8 #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word8 #

toConstr :: Word8 -> Constr #

dataTypeOf :: Word8 -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word8) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word8) #

gmapT :: (forall b. Data b => b -> b) -> Word8 -> Word8 #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word8 -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word8 -> r #

gmapQ :: (forall d. Data d => d -> u) -> Word8 -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Word8 -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word8 -> m Word8 #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word8 -> m Word8 #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word8 -> m Word8 #

Num Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Ord Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

compare :: Word8 -> Word8 -> Ordering #

(<) :: Word8 -> Word8 -> Bool #

(<=) :: Word8 -> Word8 -> Bool #

(>) :: Word8 -> Word8 -> Bool #

(>=) :: Word8 -> Word8 -> Bool #

max :: Word8 -> Word8 -> Word8 #

min :: Word8 -> Word8 -> Word8 #

Read Word8

Since: base-2.1

Instance details

Defined in GHC.Read

Real Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

toRational :: Word8 -> Rational #

Show Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

showsPrec :: Int -> Word8 -> ShowS #

show :: Word8 -> String #

showList :: [Word8] -> ShowS #

Ix Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Lift Word8 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Word8 -> Q Exp #

Bits Word8

Since: base-2.1

Instance details

Defined in GHC.Word

FiniteBits Word8

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

NFData Word8 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Word8 -> () #

Hashable Word8 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word8 -> Int #

hash :: Word8 -> Int #

data Word16 #

16-bit unsigned integer type

Instances

Instances details
Bounded Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Eq Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word16 -> Word16 -> Bool #

(/=) :: Word16 -> Word16 -> Bool #

Integral Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Data Word16

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word16 -> c Word16 #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word16 #

toConstr :: Word16 -> Constr #

dataTypeOf :: Word16 -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word16) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word16) #

gmapT :: (forall b. Data b => b -> b) -> Word16 -> Word16 #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word16 -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word16 -> r #

gmapQ :: (forall d. Data d => d -> u) -> Word16 -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Word16 -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word16 -> m Word16 #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word16 -> m Word16 #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word16 -> m Word16 #

Num Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Ord Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Read Word16

Since: base-2.1

Instance details

Defined in GHC.Read

Real Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Show Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Ix Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Lift Word16 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Word16 -> Q Exp #

Bits Word16

Since: base-2.1

Instance details

Defined in GHC.Word

FiniteBits Word16

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

NFData Word16 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Word16 -> () #

Hashable Word16 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word16 -> Int #

hash :: Word16 -> Int #

data Word32 #

32-bit unsigned integer type

Instances

Instances details
Bounded Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Eq Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word32 -> Word32 -> Bool #

(/=) :: Word32 -> Word32 -> Bool #

Integral Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Data Word32

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word32 -> c Word32 #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word32 #

toConstr :: Word32 -> Constr #

dataTypeOf :: Word32 -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word32) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word32) #

gmapT :: (forall b. Data b => b -> b) -> Word32 -> Word32 #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word32 -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word32 -> r #

gmapQ :: (forall d. Data d => d -> u) -> Word32 -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Word32 -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word32 -> m Word32 #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word32 -> m Word32 #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word32 -> m Word32 #

Num Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Ord Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Read Word32

Since: base-2.1

Instance details

Defined in GHC.Read

Real Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Show Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Ix Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Lift Word32 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Word32 -> Q Exp #

Bits Word32

Since: base-2.1

Instance details

Defined in GHC.Word

FiniteBits Word32

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

NFData Word32 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Word32 -> () #

Hashable Word32 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word32 -> Int #

hash :: Word32 -> Int #

data Word64 #

64-bit unsigned integer type

Instances

Instances details
Bounded Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Eq Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word64 -> Word64 -> Bool #

(/=) :: Word64 -> Word64 -> Bool #

Integral Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Data Word64

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word64 -> c Word64 #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word64 #

toConstr :: Word64 -> Constr #

dataTypeOf :: Word64 -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word64) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word64) #

gmapT :: (forall b. Data b => b -> b) -> Word64 -> Word64 #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word64 -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word64 -> r #

gmapQ :: (forall d. Data d => d -> u) -> Word64 -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Word64 -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word64 -> m Word64 #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word64 -> m Word64 #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word64 -> m Word64 #

Num Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Ord Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Read Word64

Since: base-2.1

Instance details

Defined in GHC.Read

Real Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Show Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Ix Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Lift Word64 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Word64 -> Q Exp #

Bits Word64

Since: base-2.1

Instance details

Defined in GHC.Word

FiniteBits Word64

Since: base-4.6.0.0

Instance details

Defined in GHC.Word

NFData Word64 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Word64 -> () #

Hashable Word64 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word64 -> Int #

hash :: Word64 -> Int #

byteSwap64 :: Word64 -> Word64 #

Reverse order of bytes in Word64.

Since: base-4.7.0.0

byteSwap32 :: Word32 -> Word32 #

Reverse order of bytes in Word32.

Since: base-4.7.0.0

byteSwap16 :: Word16 -> Word16 #

Swap bytes in Word16.

Since: base-4.7.0.0

class Fractional a => Floating a where #

Trigonometric and hyperbolic functions and related functions.

The Haskell Report defines no laws for Floating. However, (+), (*) and exp are customarily expected to define an exponential field and have the following properties:

  • exp (a + b) = exp a * exp b
  • exp (fromInteger 0) = fromInteger 1

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a #

exp :: a -> a #

sqrt :: a -> a #

(**) :: a -> a -> a infixr 8 #

logBase :: a -> a -> a #

sin :: a -> a #

cos :: a -> a #

tan :: a -> a #

asin :: a -> a #

acos :: a -> a #

atan :: a -> a #

sinh :: a -> a #

cosh :: a -> a #

tanh :: a -> a #

asinh :: a -> a #

acosh :: a -> a #

atanh :: a -> a #

Instances

Instances details
Floating Double

Since: base-2.1

Instance details

Defined in GHC.Float

Floating Float

Since: base-2.1

Instance details

Defined in GHC.Float

Floating CFloat 
Instance details

Defined in Foreign.C.Types

Floating CDouble 
Instance details

Defined in Foreign.C.Types

RealFloat a => Floating (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Methods

pi :: Complex a #

exp :: Complex a -> Complex a #

log :: Complex a -> Complex a #

sqrt :: Complex a -> Complex a #

(**) :: Complex a -> Complex a -> Complex a #

logBase :: Complex a -> Complex a -> Complex a #

sin :: Complex a -> Complex a #

cos :: Complex a -> Complex a #

tan :: Complex a -> Complex a #

asin :: Complex a -> Complex a #

acos :: Complex a -> Complex a #

atan :: Complex a -> Complex a #

sinh :: Complex a -> Complex a #

cosh :: Complex a -> Complex a #

tanh :: Complex a -> Complex a #

asinh :: Complex a -> Complex a #

acosh :: Complex a -> Complex a #

atanh :: Complex a -> Complex a #

log1p :: Complex a -> Complex a #

expm1 :: Complex a -> Complex a #

log1pexp :: Complex a -> Complex a #

log1mexp :: Complex a -> Complex a #

Floating a => Floating (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Floating a => Floating (Op a b) 
Instance details

Defined in Data.Functor.Contravariant

Methods

pi :: Op a b #

exp :: Op a b -> Op a b #

log :: Op a b -> Op a b #

sqrt :: Op a b -> Op a b #

(**) :: Op a b -> Op a b -> Op a b #

logBase :: Op a b -> Op a b -> Op a b #

sin :: Op a b -> Op a b #

cos :: Op a b -> Op a b #

tan :: Op a b -> Op a b #

asin :: Op a b -> Op a b #

acos :: Op a b -> Op a b #

atan :: Op a b -> Op a b #

sinh :: Op a b -> Op a b #

cosh :: Op a b -> Op a b #

tanh :: Op a b -> Op a b #

asinh :: Op a b -> Op a b #

acosh :: Op a b -> Op a b #

atanh :: Op a b -> Op a b #

log1p :: Op a b -> Op a b #

expm1 :: Op a b -> Op a b #

log1pexp :: Op a b -> Op a b #

log1mexp :: Op a b -> Op a b #

Floating a => Floating (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

pi :: Const a b #

exp :: Const a b -> Const a b #

log :: Const a b -> Const a b #

sqrt :: Const a b -> Const a b #

(**) :: Const a b -> Const a b -> Const a b #

logBase :: Const a b -> Const a b -> Const a b #

sin :: Const a b -> Const a b #

cos :: Const a b -> Const a b #

tan :: Const a b -> Const a b #

asin :: Const a b -> Const a b #

acos :: Const a b -> Const a b #

atan :: Const a b -> Const a b #

sinh :: Const a b -> Const a b #

cosh :: Const a b -> Const a b #

tanh :: Const a b -> Const a b #

asinh :: Const a b -> Const a b #

acosh :: Const a b -> Const a b #

atanh :: Const a b -> Const a b #

log1p :: Const a b -> Const a b #

expm1 :: Const a b -> Const a b #

log1pexp :: Const a b -> Const a b #

log1mexp :: Const a b -> Const a b #

class (RealFrac a, Floating a) => RealFloat a where #

Efficient, machine-independent access to the components of a floating-point number.

Methods

floatRadix :: a -> Integer #

a constant function, returning the radix of the representation (often 2)

floatDigits :: a -> Int #

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: a -> (Int, Int) #

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int) #

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: Integer -> Int -> a #

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

isNaN :: a -> Bool #

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool #

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool #

True if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool #

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool #

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a #

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Instances

Instances details
RealFloat Double

Since: base-2.1

Instance details

Defined in GHC.Float

RealFloat Float

Since: base-2.1

Instance details

Defined in GHC.Float

RealFloat CFloat 
Instance details

Defined in Foreign.C.Types

RealFloat CDouble 
Instance details

Defined in Foreign.C.Types

RealFloat a => RealFloat (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

RealFloat a => RealFloat (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

floatRadix :: Const a b -> Integer #

floatDigits :: Const a b -> Int #

floatRange :: Const a b -> (Int, Int) #

decodeFloat :: Const a b -> (Integer, Int) #

encodeFloat :: Integer -> Int -> Const a b #

exponent :: Const a b -> Int #

significand :: Const a b -> Const a b #

scaleFloat :: Int -> Const a b -> Const a b #

isNaN :: Const a b -> Bool #

isInfinite :: Const a b -> Bool #

isDenormalized :: Const a b -> Bool #

isNegativeZero :: Const a b -> Bool #

isIEEE :: Const a b -> Bool #

atan2 :: Const a b -> Const a b -> Const a b #

data Double #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Constructors

D# Double# 

Instances

Instances details
Eq Double

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Double -> Double -> Bool #

(/=) :: Double -> Double -> Bool #

Floating Double

Since: base-2.1

Instance details

Defined in GHC.Float

Data Double

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double #

toConstr :: Double -> Constr #

dataTypeOf :: Double -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Double) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) #

gmapT :: (forall b. Data b => b -> b) -> Double -> Double #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r #

gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double #

Ord Double

Note that due to the presence of NaN, Double's Ord instance does not satisfy reflexivity.

>>> 0/0 <= (0/0 :: Double)
False

Also note that, due to the same, Ord's operator interactions are not respected by Double's instance:

>>> (0/0 :: Double) > 1
False
>>> compare (0/0 :: Double) 1
GT
Instance details

Defined in GHC.Classes

Read Double

Since: base-2.1

Instance details

Defined in GHC.Read

RealFloat Double

Since: base-2.1

Instance details

Defined in GHC.Float

Lift Double 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Double -> Q Exp #

NFData Double 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Double -> () #

Hashable Double

Note: prior to hashable-1.3.0.0, hash 0.0 /= hash (-0.0)

The hash of NaN is not well defined.

Since: hashable-1.3.0.0

Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Double -> Int #

hash :: Double -> Int #

Generic1 (URec Double :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Double) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Double a -> Rep1 (URec Double) a #

to1 :: forall (a :: k0). Rep1 (URec Double) a -> URec Double a #

Functor (URec Double :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b #

(<$) :: a -> URec Double b -> URec Double a #

Foldable (URec Double :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Double m -> m #

foldMap :: Monoid m => (a -> m) -> URec Double a -> m #

foldMap' :: Monoid m => (a -> m) -> URec Double a -> m #

foldr :: (a -> b -> b) -> b -> URec Double a -> b #

foldr' :: (a -> b -> b) -> b -> URec Double a -> b #

foldl :: (b -> a -> b) -> b -> URec Double a -> b #

foldl' :: (b -> a -> b) -> b -> URec Double a -> b #

foldr1 :: (a -> a -> a) -> URec Double a -> a #

foldl1 :: (a -> a -> a) -> URec Double a -> a #

toList :: URec Double a -> [a] #

null :: URec Double a -> Bool #

length :: URec Double a -> Int #

elem :: Eq a => a -> URec Double a -> Bool #

maximum :: Ord a => URec Double a -> a #

minimum :: Ord a => URec Double a -> a #

sum :: Num a => URec Double a -> a #

product :: Num a => URec Double a -> a #

Traversable (URec Double :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) #

sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) #

mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) #

sequence :: Monad m => URec Double (m a) -> m (URec Double a) #

Eq (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Double p -> URec Double p -> Bool #

(/=) :: URec Double p -> URec Double p -> Bool #

Ord (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Double p -> URec Double p -> Ordering #

(<) :: URec Double p -> URec Double p -> Bool #

(<=) :: URec Double p -> URec Double p -> Bool #

(>) :: URec Double p -> URec Double p -> Bool #

(>=) :: URec Double p -> URec Double p -> Bool #

max :: URec Double p -> URec Double p -> URec Double p #

min :: URec Double p -> URec Double p -> URec Double p #

Show (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Double p -> ShowS #

show :: URec Double p -> String #

showList :: [URec Double p] -> ShowS #

Generic (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Double p) :: Type -> Type #

Methods

from :: URec Double p -> Rep (URec Double p) x #

to :: Rep (URec Double p) x -> URec Double p #

data URec Double (p :: k)

Used for marking occurrences of Double#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Double (p :: k) = UDouble {}
type Rep1 (URec Double :: k -> Type) 
Instance details

Defined in GHC.Generics

type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))
type Rep (URec Double p) 
Instance details

Defined in GHC.Generics

type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

data Float #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Constructors

F# Float# 

Instances

Instances details
Eq Float

Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Float)
False

Also note that Float's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Float -> Float -> Bool #

(/=) :: Float -> Float -> Bool #

Floating Float

Since: base-2.1

Instance details

Defined in GHC.Float

Data Float

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float #

toConstr :: Float -> Constr #

dataTypeOf :: Float -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) #

gmapT :: (forall b. Data b => b -> b) -> Float -> Float #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r #

gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float #

Ord Float

Note that due to the presence of NaN, Float's Ord instance does not satisfy reflexivity.

>>> 0/0 <= (0/0 :: Float)
False

Also note that, due to the same, Ord's operator interactions are not respected by Float's instance:

>>> (0/0 :: Float) > 1
False
>>> compare (0/0 :: Float) 1
GT
Instance details

Defined in GHC.Classes

Methods

compare :: Float -> Float -> Ordering #

(<) :: Float -> Float -> Bool #

(<=) :: Float -> Float -> Bool #

(>) :: Float -> Float -> Bool #

(>=) :: Float -> Float -> Bool #

max :: Float -> Float -> Float #

min :: Float -> Float -> Float #

Read Float

Since: base-2.1

Instance details

Defined in GHC.Read

RealFloat Float

Since: base-2.1

Instance details

Defined in GHC.Float

Lift Float 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Float -> Q Exp #

NFData Float 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Float -> () #

Hashable Float

Note: prior to hashable-1.3.0.0, hash 0.0 /= hash (-0.0)

The hash of NaN is not well defined.

Since: hashable-1.3.0.0

Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Float -> Int #

hash :: Float -> Int #

Generic1 (URec Float :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Float) :: k -> Type #

Methods

from1 :: forall (a :: k0). URec Float a -> Rep1 (URec Float) a #

to1 :: forall (a :: k0). Rep1 (URec Float) a -> URec Float a #

Functor (URec Float :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b #

(<$) :: a -> URec Float b -> URec Float a #

Foldable (URec Float :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Float m -> m #

foldMap :: Monoid m => (a -> m) -> URec Float a -> m #

foldMap' :: Monoid m => (a -> m) -> URec Float a -> m #

foldr :: (a -> b -> b) -> b -> URec Float a -> b #

foldr' :: (a -> b -> b) -> b -> URec Float a -> b #

foldl :: (b -> a -> b) -> b -> URec Float a -> b #

foldl' :: (b -> a -> b) -> b -> URec Float a -> b #

foldr1 :: (a -> a -> a) -> URec Float a -> a #

foldl1 :: (a -> a -> a) -> URec Float a -> a #

toList :: URec Float a -> [a] #

null :: URec Float a -> Bool #

length :: URec Float a -> Int #

elem :: Eq a => a -> URec Float a -> Bool #

maximum :: Ord a => URec Float a -> a #

minimum :: Ord a => URec Float a -> a #

sum :: Num a => URec Float a -> a #

product :: Num a => URec Float a -> a #

Traversable (URec Float :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) #

sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) #

mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) #

sequence :: Monad m => URec Float (m a) -> m (URec Float a) #

Eq (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

(==) :: URec Float p -> URec Float p -> Bool #

(/=) :: URec Float p -> URec Float p -> Bool #

Ord (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

compare :: URec Float p -> URec Float p -> Ordering #

(<) :: URec Float p -> URec Float p -> Bool #

(<=) :: URec Float p -> URec Float p -> Bool #

(>) :: URec Float p -> URec Float p -> Bool #

(>=) :: URec Float p -> URec Float p -> Bool #

max :: URec Float p -> URec Float p -> URec Float p #

min :: URec Float p -> URec Float p -> URec Float p #

Show (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Float p -> ShowS #

show :: URec Float p -> String #

showList :: [URec Float p] -> ShowS #

Generic (URec Float p) 
Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Float p) :: Type -> Type #

Methods

from :: URec Float p -> Rep (URec Float p) x #

to :: Rep (URec Float p) x -> URec Float p #

data URec Float (p :: k)

Used for marking occurrences of Float#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Float (p :: k) = UFloat {}
type Rep1 (URec Float :: k -> Type) 
Instance details

Defined in GHC.Generics

type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))
type Rep (URec Float p) 
Instance details

Defined in GHC.Generics

type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

class Num a where #

Basic numeric class.

The Haskell Report defines no laws for Num. However, (+) and (*) are customarily expected to define a ring and have the following properties:

Associativity of (+)
(x + y) + z = x + (y + z)
Commutativity of (+)
x + y = y + x
fromInteger 0 is the additive identity
x + fromInteger 0 = x
negate gives the additive inverse
x + negate x = fromInteger 0
Associativity of (*)
(x * y) * z = x * (y * z)
fromInteger 1 is the multiplicative identity
x * fromInteger 1 = x and fromInteger 1 * x = x
Distributivity of (*) with respect to (+)
a * (b + c) = (a * b) + (a * c) and (b + c) * a = (b * a) + (c * a)

Note that it isn't customarily expected that a type instance of both Num and Ord implement an ordered ring. Indeed, in base only Integer and Rational do.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+) :: a -> a -> a infixl 6 #

(-) :: a -> a -> a infixl 6 #

(*) :: a -> a -> a infixl 7 #

negate :: a -> a #

Unary negation.

abs :: a -> a #

Absolute value.

signum :: a -> a #

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Integer -> a #

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances

Instances details
Num Int

Since: base-2.1

Instance details

Defined in GHC.Num

Methods

(+) :: Int -> Int -> Int #

(-) :: Int -> Int -> Int #

(*) :: Int -> Int -> Int #

negate :: Int -> Int #

abs :: Int -> Int #

signum :: Int -> Int #

fromInteger :: Integer -> Int #

Num Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(+) :: Int8 -> Int8 -> Int8 #

(-) :: Int8 -> Int8 -> Int8 #

(*) :: Int8 -> Int8 -> Int8 #

negate :: Int8 -> Int8 #

abs :: Int8 -> Int8 #

signum :: Int8 -> Int8 #

fromInteger :: Integer -> Int8 #

Num Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Num Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Num Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Num Integer

Since: base-2.1

Instance details

Defined in GHC.Num

Num Natural

Note that Natural's Num instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though.

Since: base-4.8.0.0

Instance details

Defined in GHC.Num

Num Word

Since: base-2.1

Instance details

Defined in GHC.Num

Methods

(+) :: Word -> Word -> Word #

(-) :: Word -> Word -> Word #

(*) :: Word -> Word -> Word #

negate :: Word -> Word #

abs :: Word -> Word #

signum :: Word -> Word #

fromInteger :: Integer -> Word #

Num Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Num Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Num Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Num Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Num CChar 
Instance details

Defined in Foreign.C.Types

Num CSChar 
Instance details

Defined in Foreign.C.Types

Num CUChar 
Instance details

Defined in Foreign.C.Types

Num CShort 
Instance details

Defined in Foreign.C.Types

Num CUShort 
Instance details

Defined in Foreign.C.Types

Num CInt 
Instance details

Defined in Foreign.C.Types

Methods

(+) :: CInt -> CInt -> CInt #

(-) :: CInt -> CInt -> CInt #

(*) :: CInt -> CInt -> CInt #

negate :: CInt -> CInt #

abs :: CInt -> CInt #

signum :: CInt -> CInt #

fromInteger :: Integer -> CInt #

Num CUInt 
Instance details

Defined in Foreign.C.Types

Num CLong 
Instance details

Defined in Foreign.C.Types

Num CULong 
Instance details

Defined in Foreign.C.Types

Num CLLong 
Instance details

Defined in Foreign.C.Types

Num CULLong 
Instance details

Defined in Foreign.C.Types

Num CBool 
Instance details

Defined in Foreign.C.Types

Num CFloat 
Instance details

Defined in Foreign.C.Types

Num CDouble 
Instance details

Defined in Foreign.C.Types

Num CPtrdiff 
Instance details

Defined in Foreign.C.Types

Num CSize 
Instance details

Defined in Foreign.C.Types

Num CWchar 
Instance details

Defined in Foreign.C.Types

Num CSigAtomic 
Instance details

Defined in Foreign.C.Types

Num CClock 
Instance details

Defined in Foreign.C.Types

Num CTime 
Instance details

Defined in Foreign.C.Types

Num CUSeconds 
Instance details

Defined in Foreign.C.Types

Num CSUSeconds 
Instance details

Defined in Foreign.C.Types

Num CIntPtr 
Instance details

Defined in Foreign.C.Types

Num CUIntPtr 
Instance details

Defined in Foreign.C.Types

Num CIntMax 
Instance details

Defined in Foreign.C.Types

Num CUIntMax 
Instance details

Defined in Foreign.C.Types

Num WordPtr 
Instance details

Defined in Foreign.Ptr

Num IntPtr 
Instance details

Defined in Foreign.Ptr

Num CodePoint 
Instance details

Defined in Data.Text.Encoding

Methods

(+) :: CodePoint -> CodePoint -> CodePoint #

(-) :: CodePoint -> CodePoint -> CodePoint #

(*) :: CodePoint -> CodePoint -> CodePoint #

negate :: CodePoint -> CodePoint #

abs :: CodePoint -> CodePoint #

signum :: CodePoint -> CodePoint #

fromInteger :: Integer -> CodePoint #

Num DecoderState 
Instance details

Defined in Data.Text.Encoding

Methods

(+) :: DecoderState -> DecoderState -> DecoderState #

(-) :: DecoderState -> DecoderState -> DecoderState #

(*) :: DecoderState -> DecoderState -> DecoderState #

negate :: DecoderState -> DecoderState #

abs :: DecoderState -> DecoderState #

signum :: DecoderState -> DecoderState #

fromInteger :: Integer -> DecoderState #

Integral a => Num (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

(+) :: Ratio a -> Ratio a -> Ratio a #

(-) :: Ratio a -> Ratio a -> Ratio a #

(*) :: Ratio a -> Ratio a -> Ratio a #

negate :: Ratio a -> Ratio a #

abs :: Ratio a -> Ratio a #

signum :: Ratio a -> Ratio a #

fromInteger :: Integer -> Ratio a #

RealFloat a => Num (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Methods

(+) :: Complex a -> Complex a -> Complex a #

(-) :: Complex a -> Complex a -> Complex a #

(*) :: Complex a -> Complex a -> Complex a #

negate :: Complex a -> Complex a #

abs :: Complex a -> Complex a #

signum :: Complex a -> Complex a #

fromInteger :: Integer -> Complex a #

HasResolution a => Num (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

(+) :: Fixed a -> Fixed a -> Fixed a #

(-) :: Fixed a -> Fixed a -> Fixed a #

(*) :: Fixed a -> Fixed a -> Fixed a #

negate :: Fixed a -> Fixed a #

abs :: Fixed a -> Fixed a #

signum :: Fixed a -> Fixed a #

fromInteger :: Integer -> Fixed a #

Num a => Num (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(+) :: Min a -> Min a -> Min a #

(-) :: Min a -> Min a -> Min a #

(*) :: Min a -> Min a -> Min a #

negate :: Min a -> Min a #

abs :: Min a -> Min a #

signum :: Min a -> Min a #

fromInteger :: Integer -> Min a #

Num a => Num (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(+) :: Max a -> Max a -> Max a #

(-) :: Max a -> Max a -> Max a #

(*) :: Max a -> Max a -> Max a #

negate :: Max a -> Max a #

abs :: Max a -> Max a #

signum :: Max a -> Max a #

fromInteger :: Integer -> Max a #

Num a => Num (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Num a => Num (Sum a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Sum a -> Sum a -> Sum a #

(-) :: Sum a -> Sum a -> Sum a #

(*) :: Sum a -> Sum a -> Sum a #

negate :: Sum a -> Sum a #

abs :: Sum a -> Sum a #

signum :: Sum a -> Sum a #

fromInteger :: Integer -> Sum a #

Num a => Num (Product a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Product a -> Product a -> Product a #

(-) :: Product a -> Product a -> Product a #

(*) :: Product a -> Product a -> Product a #

negate :: Product a -> Product a #

abs :: Product a -> Product a #

signum :: Product a -> Product a #

fromInteger :: Integer -> Product a #

Num a => Num (Down a)

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

(+) :: Down a -> Down a -> Down a #

(-) :: Down a -> Down a -> Down a #

(*) :: Down a -> Down a -> Down a #

negate :: Down a -> Down a #

abs :: Down a -> Down a #

signum :: Down a -> Down a #

fromInteger :: Integer -> Down a #

Num a => Num (Op a b) 
Instance details

Defined in Data.Functor.Contravariant

Methods

(+) :: Op a b -> Op a b -> Op a b #

(-) :: Op a b -> Op a b -> Op a b #

(*) :: Op a b -> Op a b -> Op a b #

negate :: Op a b -> Op a b #

abs :: Op a b -> Op a b #

signum :: Op a b -> Op a b #

fromInteger :: Integer -> Op a b #

Num a => Num (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

(+) :: Const a b -> Const a b -> Const a b #

(-) :: Const a b -> Const a b -> Const a b #

(*) :: Const a b -> Const a b -> Const a b #

negate :: Const a b -> Const a b #

abs :: Const a b -> Const a b #

signum :: Const a b -> Const a b #

fromInteger :: Integer -> Const a b #

(Applicative f, Num a) => Num (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(+) :: Ap f a -> Ap f a -> Ap f a #

(-) :: Ap f a -> Ap f a -> Ap f a #

(*) :: Ap f a -> Ap f a -> Ap f a #

negate :: Ap f a -> Ap f a #

abs :: Ap f a -> Ap f a #

signum :: Ap f a -> Ap f a #

fromInteger :: Integer -> Ap f a #

Num (f a) => Num (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(+) :: Alt f a -> Alt f a -> Alt f a #

(-) :: Alt f a -> Alt f a -> Alt f a #

(*) :: Alt f a -> Alt f a -> Alt f a #

negate :: Alt f a -> Alt f a #

abs :: Alt f a -> Alt f a #

signum :: Alt f a -> Alt f a #

fromInteger :: Integer -> Alt f a #

data Integer #

Invariant: Jn# and Jp# are used iff value doesn't fit in S#

Useful properties resulting from the invariants:

Instances

Instances details
Enum Integer

Since: base-2.1

Instance details

Defined in GHC.Enum

Eq Integer 
Instance details

Defined in GHC.Integer.Type

Methods

(==) :: Integer -> Integer -> Bool #

(/=) :: Integer -> Integer -> Bool #

Integral Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Data Integer

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer #

toConstr :: Integer -> Constr #

dataTypeOf :: Integer -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) #

gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r #

gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer #

Num Integer

Since: base-2.1

Instance details

Defined in GHC.Num

Ord Integer 
Instance details

Defined in GHC.Integer.Type

Read Integer

Since: base-2.1

Instance details

Defined in GHC.Read

Real Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Show Integer

Since: base-2.1

Instance details

Defined in GHC.Show

Ix Integer

Since: base-2.1

Instance details

Defined in GHC.Arr

Lift Integer 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Integer -> Q Exp #

Bits Integer

Since: base-2.1

Instance details

Defined in Data.Bits

NFData Integer 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Integer -> () #

Hashable Integer 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Integer -> Int #

hash :: Integer -> Int #

subtract :: Num a => a -> a -> a #

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

fromIntegral :: (Integral a, Num b) => a -> b #

general coercion from integral types

realToFrac :: (Real a, Fractional b) => a -> b #

general coercion to fractional types

class Num a => Fractional a where #

Fractional numbers, supporting real division.

The Haskell Report defines no laws for Fractional. However, (+) and (*) are customarily expected to define a division ring and have the following properties:

recip gives the multiplicative inverse
x * recip x = recip x * x = fromInteger 1

Note that it isn't customarily expected that a type instance of Fractional implement a field. However, all instances in base do.

Minimal complete definition

fromRational, (recip | (/))

Methods

(/) :: a -> a -> a infixl 7 #

Fractional division.

recip :: a -> a #

Reciprocal fraction.

fromRational :: Rational -> a #

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

Instances

Instances details
Fractional CFloat 
Instance details

Defined in Foreign.C.Types

Fractional CDouble 
Instance details

Defined in Foreign.C.Types

Integral a => Fractional (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

(/) :: Ratio a -> Ratio a -> Ratio a #

recip :: Ratio a -> Ratio a #

fromRational :: Rational -> Ratio a #

RealFloat a => Fractional (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Methods

(/) :: Complex a -> Complex a -> Complex a #

recip :: Complex a -> Complex a #

fromRational :: Rational -> Complex a #

HasResolution a => Fractional (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

(/) :: Fixed a -> Fixed a -> Fixed a #

recip :: Fixed a -> Fixed a #

fromRational :: Rational -> Fixed a #

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Fractional a => Fractional (Op a b) 
Instance details

Defined in Data.Functor.Contravariant

Methods

(/) :: Op a b -> Op a b -> Op a b #

recip :: Op a b -> Op a b #

fromRational :: Rational -> Op a b #

Fractional a => Fractional (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

(/) :: Const a b -> Const a b -> Const a b #

recip :: Const a b -> Const a b #

fromRational :: Rational -> Const a b #

class (Real a, Enum a) => Integral a where #

Integral numbers, supporting integer division.

The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the div/mod and quot/rem pairs, given suitable Euclidean functions f and g:

  • x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
  • x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs.

Minimal complete definition

quotRem, toInteger

Methods

quot :: a -> a -> a infixl 7 #

integer division truncated toward zero

rem :: a -> a -> a infixl 7 #

integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

div :: a -> a -> a infixl 7 #

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7 #

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

quotRem :: a -> a -> (a, a) #

simultaneous quot and rem

divMod :: a -> a -> (a, a) #

simultaneous div and mod

toInteger :: a -> Integer #

conversion to Integer

Instances

Instances details
Integral Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

quot :: Int -> Int -> Int #

rem :: Int -> Int -> Int #

div :: Int -> Int -> Int #

mod :: Int -> Int -> Int #

quotRem :: Int -> Int -> (Int, Int) #

divMod :: Int -> Int -> (Int, Int) #

toInteger :: Int -> Integer #

Integral Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

quot :: Int8 -> Int8 -> Int8 #

rem :: Int8 -> Int8 -> Int8 #

div :: Int8 -> Int8 -> Int8 #

mod :: Int8 -> Int8 -> Int8 #

quotRem :: Int8 -> Int8 -> (Int8, Int8) #

divMod :: Int8 -> Int8 -> (Int8, Int8) #

toInteger :: Int8 -> Integer #

Integral Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Integral Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Integral Word

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

quot :: Word -> Word -> Word #

rem :: Word -> Word -> Word #

div :: Word -> Word -> Word #

mod :: Word -> Word -> Word #

quotRem :: Word -> Word -> (Word, Word) #

divMod :: Word -> Word -> (Word, Word) #

toInteger :: Word -> Integer #

Integral Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Integral CChar 
Instance details

Defined in Foreign.C.Types

Integral CSChar 
Instance details

Defined in Foreign.C.Types

Integral CUChar 
Instance details

Defined in Foreign.C.Types

Integral CShort 
Instance details

Defined in Foreign.C.Types

Integral CUShort 
Instance details

Defined in Foreign.C.Types

Integral CInt 
Instance details

Defined in Foreign.C.Types

Methods

quot :: CInt -> CInt -> CInt #

rem :: CInt -> CInt -> CInt #

div :: CInt -> CInt -> CInt #

mod :: CInt -> CInt -> CInt #

quotRem :: CInt -> CInt -> (CInt, CInt) #

divMod :: CInt -> CInt -> (CInt, CInt) #

toInteger :: CInt -> Integer #

Integral CUInt 
Instance details

Defined in Foreign.C.Types

Integral CLong 
Instance details

Defined in Foreign.C.Types

Integral CULong 
Instance details

Defined in Foreign.C.Types

Integral CLLong 
Instance details

Defined in Foreign.C.Types

Integral CULLong 
Instance details

Defined in Foreign.C.Types

Integral CBool 
Instance details

Defined in Foreign.C.Types

Integral CPtrdiff 
Instance details

Defined in Foreign.C.Types

Integral CSize 
Instance details

Defined in Foreign.C.Types

Integral CWchar 
Instance details

Defined in Foreign.C.Types

Integral CSigAtomic 
Instance details

Defined in Foreign.C.Types

Integral CIntPtr 
Instance details

Defined in Foreign.C.Types

Integral CUIntPtr 
Instance details

Defined in Foreign.C.Types

Integral CIntMax 
Instance details

Defined in Foreign.C.Types

Integral CUIntMax 
Instance details

Defined in Foreign.C.Types

Integral WordPtr 
Instance details

Defined in Foreign.Ptr

Integral IntPtr 
Instance details

Defined in Foreign.Ptr

Integral a => Integral (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

quot :: Identity a -> Identity a -> Identity a #

rem :: Identity a -> Identity a -> Identity a #

div :: Identity a -> Identity a -> Identity a #

mod :: Identity a -> Identity a -> Identity a #

quotRem :: Identity a ->