Relude.Numeric

Provides numerical data types and functions.

Since: 0.5.0

Reexports

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

Bitwise "xor"

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 == toInteger y = Just y
  | otherwise                  = Nothing
  where
    y = fromIntegral 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

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

Data Int

Since: base-4.0.0.0

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

Bits Int

Since: base-2.1

Defined in GHC.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

Defined in GHC.Bits

Methods

finiteBitSize :: Int -> Int

countLeadingZeros :: Int -> Int

countTrailingZeros :: Int -> Int

Bounded Int

Since: base-2.1

Defined in GHC.Enum

Methods

minBound :: Int

maxBound :: Int

Enum Int

Since: base-2.1

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]

Num Int

Since: base-2.1

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

Read Int

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Int

readList :: ReadS [Int]

readPrec :: ReadPrec Int

readListPrec :: ReadPrec [Int]

Integral Int

Since: base-2.0.1

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

Real Int

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Int -> Rational

Show Int

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Int -> ShowS

show :: Int -> String

showList :: [Int] -> ShowS

NFData Int

Defined in Control.DeepSeq

Methods

rnf :: Int -> ()

Eq Int

Defined in GHC.Classes

Methods

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

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

Ord Int

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

Hashable Int

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int -> Int

hash :: Int -> Int

Lift Int

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Int -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Int -> Code m Int

Generic1 (URec Int :: k -> Type)

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

Foldable (UInt :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => UInt m -> m

foldMap :: Monoid m => (a -> m) -> UInt a -> m

foldMap' :: Monoid m => (a -> m) -> UInt a -> m

foldr :: (a -> b -> b) -> b -> UInt a -> b

foldr' :: (a -> b -> b) -> b -> UInt a -> b

foldl :: (b -> a -> b) -> b -> UInt a -> b

foldl' :: (b -> a -> b) -> b -> UInt a -> b

foldr1 :: (a -> a -> a) -> UInt a -> a

foldl1 :: (a -> a -> a) -> UInt a -> a

toList :: UInt a -> [a]

null :: UInt a -> Bool

length :: UInt a -> Int

elem :: Eq a => a -> UInt a -> Bool

maximum :: Ord a => UInt a -> a

minimum :: Ord a => UInt a -> a

sum :: Num a => UInt a -> a

product :: Num a => UInt a -> a

Traversable (UInt :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UInt a -> f (UInt b)

sequenceA :: Applicative f => UInt (f a) -> f (UInt a)

mapM :: Monad m => (a -> m b) -> UInt a -> m (UInt b)

sequence :: Monad m => UInt (m a) -> m (UInt a)

Functor (URec Int :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

Generic (URec Int p)

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

Show (URec Int p)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

show :: URec Int p -> String

showList :: [URec Int p] -> ShowS

Eq (URec Int p)

Since: base-4.9.0.0

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

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

data URec Int (p :: k)

Used for marking occurrences of Int#

Since: base-4.9.0.0

Defined in GHC.Generics

data URec Int (p :: k) = UInt {

• uInt# :: Int#

}

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

Since: base-4.9.0.0

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)

Since: base-4.9.0.0

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

Data Int8

Since: base-4.0.0.0

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

Bits Int8

Since: base-2.1

Defined in GHC.Int

Methods

(.&.) :: Int8 -> Int8 -> Int8

(.|.) :: Int8 -> Int8 -> Int8

xor :: Int8 -> Int8 -> Int8

complement :: Int8 -> Int8

shift :: Int8 -> Int -> Int8

rotate :: Int8 -> Int -> Int8

zeroBits :: Int8

bit :: Int -> Int8

setBit :: Int8 -> Int -> Int8

clearBit :: Int8 -> Int -> Int8

complementBit :: Int8 -> Int -> Int8

testBit :: Int8 -> Int -> Bool

bitSizeMaybe :: Int8 -> Maybe Int

bitSize :: Int8 -> Int

isSigned :: Int8 -> Bool

shiftL :: Int8 -> Int -> Int8

unsafeShiftL :: Int8 -> Int -> Int8

shiftR :: Int8 -> Int -> Int8

unsafeShiftR :: Int8 -> Int -> Int8

rotateL :: Int8 -> Int -> Int8

rotateR :: Int8 -> Int -> Int8

popCount :: Int8 -> Int

FiniteBits Int8

Since: base-4.6.0.0

Defined in GHC.Int

Methods

finiteBitSize :: Int8 -> Int

countLeadingZeros :: Int8 -> Int

countTrailingZeros :: Int8 -> Int

Bounded Int8

Since: base-2.1

Defined in GHC.Int

Methods

minBound :: Int8

maxBound :: Int8

Enum Int8

Since: base-2.1

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]

Ix Int8

Since: base-2.1

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

Num Int8

Since: base-2.1

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

Read Int8

Since: base-2.1

Defined in GHC.Int

Methods

readsPrec :: Int -> ReadS Int8

readList :: ReadS [Int8]

readPrec :: ReadPrec Int8

readListPrec :: ReadPrec [Int8]

Integral Int8

Since: base-2.1

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

Real Int8

Since: base-2.1

Defined in GHC.Int

Methods

toRational :: Int8 -> Rational

Show Int8

Since: base-2.1

Defined in GHC.Int

Methods

showsPrec :: Int -> Int8 -> ShowS

show :: Int8 -> String

showList :: [Int8] -> ShowS

NFData Int8

Defined in Control.DeepSeq

Methods

rnf :: Int8 -> ()

Eq Int8

Since: base-2.1

Defined in GHC.Int

Methods

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

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

Ord Int8

Since: base-2.1

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

Hashable Int8

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int8 -> Int

hash :: Int8 -> Int

Lift Int8

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Int8 -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Int8 -> Code m Int8

data Int16

16-bit signed integer type

Instances

Data Int16

Since: base-4.0.0.0

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

Bits Int16

Since: base-2.1

Defined in GHC.Int

Methods

(.&.) :: Int16 -> Int16 -> Int16

(.|.) :: Int16 -> Int16 -> Int16

xor :: Int16 -> Int16 -> Int16

complement :: Int16 -> Int16

shift :: Int16 -> Int -> Int16

rotate :: Int16 -> Int -> Int16

zeroBits :: Int16

bit :: Int -> Int16

setBit :: Int16 -> Int -> Int16

clearBit :: Int16 -> Int -> Int16

complementBit :: Int16 -> Int -> Int16

testBit :: Int16 -> Int -> Bool

bitSizeMaybe :: Int16 -> Maybe Int

bitSize :: Int16 -> Int

isSigned :: Int16 -> Bool

shiftL :: Int16 -> Int -> Int16

unsafeShiftL :: Int16 -> Int -> Int16

shiftR :: Int16 -> Int -> Int16

unsafeShiftR :: Int16 -> Int -> Int16

rotateL :: Int16 -> Int -> Int16

rotateR :: Int16 -> Int -> Int16

popCount :: Int16 -> Int

FiniteBits Int16

Since: base-4.6.0.0

Defined in GHC.Int

Methods

finiteBitSize :: Int16 -> Int

countLeadingZeros :: Int16 -> Int

countTrailingZeros :: Int16 -> Int

Bounded Int16

Since: base-2.1

Defined in GHC.Int

Methods

minBound :: Int16

maxBound :: Int16

Enum Int16

Since: base-2.1

Defined in GHC.Int

Methods

succ :: Int16 -> Int16

pred :: Int16 -> Int16

toEnum :: Int -> Int16

fromEnum :: Int16 -> Int

enumFrom :: Int16 -> [Int16]

enumFromThen :: Int16 -> Int16 -> [Int16]

enumFromTo :: Int16 -> Int16 -> [Int16]

enumFromThenTo :: Int16 -> Int16 -> Int16 -> [Int16]

Ix Int16

Since: base-2.1

Defined in GHC.Int

Methods

range :: (Int16, Int16) -> [Int16]

index :: (Int16, Int16) -> Int16 -> Int

unsafeIndex :: (Int16, Int16) -> Int16 -> Int

inRange :: (Int16, Int16) -> Int16 -> Bool

rangeSize :: (Int16, Int16) -> Int

unsafeRangeSize :: (Int16, Int16) -> Int

Num Int16

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int16 -> Int16 -> Int16

(-) :: Int16 -> Int16 -> Int16

(*) :: Int16 -> Int16 -> Int16

negate :: Int16 -> Int16

abs :: Int16 -> Int16

signum :: Int16 -> Int16

fromInteger :: Integer -> Int16

Read Int16

Since: base-2.1

Defined in GHC.Int

Methods

readsPrec :: Int -> ReadS Int16

readList :: ReadS [Int16]

readPrec :: ReadPrec Int16

readListPrec :: ReadPrec [Int16]

Integral Int16

Since: base-2.1

Defined in GHC.Int

Methods

quot :: Int16 -> Int16 -> Int16

rem :: Int16 -> Int16 -> Int16

div :: Int16 -> Int16 -> Int16

mod :: Int16 -> Int16 -> Int16

quotRem :: Int16 -> Int16 -> (Int16, Int16)

divMod :: Int16 -> Int16 -> (Int16, Int16)

toInteger :: Int16 -> Integer

Real Int16

Since: base-2.1

Defined in GHC.Int

Methods

toRational :: Int16 -> Rational

Show Int16

Since: base-2.1

Defined in GHC.Int

Methods

showsPrec :: Int -> Int16 -> ShowS

show :: Int16 -> String

showList :: [Int16] -> ShowS

NFData Int16

Defined in Control.DeepSeq

Methods

rnf :: Int16 -> ()

Eq Int16

Since: base-2.1

Defined in GHC.Int

Methods

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

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

Ord Int16

Since: base-2.1

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

Hashable Int16

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int16 -> Int

hash :: Int16 -> Int

Lift Int16

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Int16 -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Int16 -> Code m Int16

data Int32

32-bit signed integer type

Instances

Data Int32

Since: base-4.0.0.0

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

Bits Int32

Since: base-2.1

Defined in GHC.Int

Methods

(.&.) :: Int32 -> Int32 -> Int32

(.|.) :: Int32 -> Int32 -> Int32

xor :: Int32 -> Int32 -> Int32

complement :: Int32 -> Int32

shift :: Int32 -> Int -> Int32

rotate :: Int32 -> Int -> Int32

zeroBits :: Int32

bit :: Int -> Int32

setBit :: Int32 -> Int -> Int32

clearBit :: Int32 -> Int -> Int32

complementBit :: Int32 -> Int -> Int32

testBit :: Int32 -> Int -> Bool

bitSizeMaybe :: Int32 -> Maybe Int

bitSize :: Int32 -> Int

isSigned :: Int32 -> Bool

shiftL :: Int32 -> Int -> Int32

unsafeShiftL :: Int32 -> Int -> Int32

shiftR :: Int32 -> Int -> Int32

unsafeShiftR :: Int32 -> Int -> Int32

rotateL :: Int32 -> Int -> Int32

rotateR :: Int32 -> Int -> Int32

popCount :: Int32 -> Int

FiniteBits Int32

Since: base-4.6.0.0

Defined in GHC.Int

Methods

finiteBitSize :: Int32 -> Int

countLeadingZeros :: Int32 -> Int

countTrailingZeros :: Int32 -> Int

Bounded Int32

Since: base-2.1

Defined in GHC.Int

Methods

minBound :: Int32

maxBound :: Int32

Enum Int32

Since: base-2.1

Defined in GHC.Int

Methods

succ :: Int32 -> Int32

pred :: Int32 -> Int32

toEnum :: Int -> Int32

fromEnum :: Int32 -> Int

enumFrom :: Int32 -> [Int32]

enumFromThen :: Int32 -> Int32 -> [Int32]

enumFromTo :: Int32 -> Int32 -> [Int32]

enumFromThenTo :: Int32 -> Int32 -> Int32 -> [Int32]

Ix Int32

Since: base-2.1

Defined in GHC.Int

Methods

range :: (Int32, Int32) -> [Int32]

index :: (Int32, Int32) -> Int32 -> Int

unsafeIndex :: (Int32, Int32) -> Int32 -> Int

inRange :: (Int32, Int32) -> Int32 -> Bool

rangeSize :: (Int32, Int32) -> Int

unsafeRangeSize :: (Int32, Int32) -> Int

Num Int32

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int32 -> Int32 -> Int32

(-) :: Int32 -> Int32 -> Int32

(*) :: Int32 -> Int32 -> Int32

negate :: Int32 -> Int32

abs :: Int32 -> Int32

signum :: Int32 -> Int32

fromInteger :: Integer -> Int32

Read Int32

Since: base-2.1

Defined in GHC.Int

Methods

readsPrec :: Int -> ReadS Int32

readList :: ReadS [Int32]

readPrec :: ReadPrec Int32

readListPrec :: ReadPrec [Int32]

Integral Int32

Since: base-2.1

Defined in GHC.Int

Methods

quot :: Int32 -> Int32 -> Int32

rem :: Int32 -> Int32 -> Int32

div :: Int32 -> Int32 -> Int32

mod :: Int32 -> Int32 -> Int32

quotRem :: Int32 -> Int32 -> (Int32, Int32)

divMod :: Int32 -> Int32 -> (Int32, Int32)

toInteger :: Int32 -> Integer

Real Int32

Since: base-2.1

Defined in GHC.Int

Methods

toRational :: Int32 -> Rational

Show Int32

Since: base-2.1

Defined in GHC.Int

Methods

showsPrec :: Int -> Int32 -> ShowS

show :: Int32 -> String

showList :: [Int32] -> ShowS

NFData Int32

Defined in Control.DeepSeq

Methods

rnf :: Int32 -> ()

Eq Int32

Since: base-2.1

Defined in GHC.Int

Methods

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

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

Ord Int32

Since: base-2.1

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

Hashable Int32

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int32 -> Int

hash :: Int32 -> Int

Lift Int32

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Int32 -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Int32 -> Code m Int32

data Int64

64-bit signed integer type

Instances

Data Int64

Since: base-4.0.0.0

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

Bits Int64

Since: base-2.1

Defined in GHC.Int

Methods

(.&.) :: Int64 -> Int64 -> Int64

(.|.) :: Int64 -> Int64 -> Int64

xor :: Int64 -> Int64 -> Int64

complement :: Int64 -> Int64

shift :: Int64 -> Int -> Int64

rotate :: Int64 -> Int -> Int64

zeroBits :: Int64

bit :: Int -> Int64

setBit :: Int64 -> Int -> Int64

clearBit :: Int64 -> Int -> Int64

complementBit :: Int64 -> Int -> Int64

testBit :: Int64 -> Int -> Bool

bitSizeMaybe :: Int64 -> Maybe Int

bitSize :: Int64 -> Int

isSigned :: Int64 -> Bool

shiftL :: Int64 -> Int -> Int64

unsafeShiftL :: Int64 -> Int -> Int64

shiftR :: Int64 -> Int -> Int64

unsafeShiftR :: Int64 -> Int -> Int64

rotateL :: Int64 -> Int -> Int64

rotateR :: Int64 -> Int -> Int64

popCount :: Int64 -> Int

FiniteBits Int64

Since: base-4.6.0.0

Defined in GHC.Int

Methods

finiteBitSize :: Int64 -> Int

countLeadingZeros :: Int64 -> Int

countTrailingZeros :: Int64 -> Int

Bounded Int64

Since: base-2.1

Defined in GHC.Int

Methods

minBound :: Int64

maxBound :: Int64

Enum Int64

Since: base-2.1

Defined in GHC.Int

Methods

succ :: Int64 -> Int64

pred :: Int64 -> Int64

toEnum :: Int -> Int64

fromEnum :: Int64 -> Int

enumFrom :: Int64 -> [Int64]

enumFromThen :: Int64 -> Int64 -> [Int64]

enumFromTo :: Int64 -> Int64 -> [Int64]

enumFromThenTo :: Int64 -> Int64 -> Int64 -> [Int64]

Ix Int64

Since: base-2.1

Defined in GHC.Int

Methods

range :: (Int64, Int64) -> [Int64]

index :: (Int64, Int64) -> Int64 -> Int

unsafeIndex :: (Int64, Int64) -> Int64 -> Int

inRange :: (Int64, Int64) -> Int64 -> Bool

rangeSize :: (Int64, Int64) -> Int

unsafeRangeSize :: (Int64, Int64) -> Int

Num Int64

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int64 -> Int64 -> Int64

(-) :: Int64 -> Int64 -> Int64

(*) :: Int64 -> Int64 -> Int64

negate :: Int64 -> Int64

abs :: Int64 -> Int64

signum :: Int64 -> Int64

fromInteger :: Integer -> Int64

Read Int64

Since: base-2.1

Defined in GHC.Int

Methods

readsPrec :: Int -> ReadS Int64

readList :: ReadS [Int64]

readPrec :: ReadPrec Int64

readListPrec :: ReadPrec [Int64]

Integral Int64

Since: base-2.1

Defined in GHC.Int

Methods

quot :: Int64 -> Int64 -> Int64

rem :: Int64 -> Int64 -> Int64

div :: Int64 -> Int64 -> Int64

mod :: Int64 -> Int64 -> Int64

quotRem :: Int64 -> Int64 -> (Int64, Int64)

divMod :: Int64 -> Int64 -> (Int64, Int64)

toInteger :: Int64 -> Integer

Real Int64

Since: base-2.1

Defined in GHC.Int

Methods

toRational :: Int64 -> Rational

Show Int64

Since: base-2.1

Defined in GHC.Int

Methods

showsPrec :: Int -> Int64 -> ShowS

show :: Int64 -> String

showList :: [Int64] -> ShowS

NFData Int64

Defined in Control.DeepSeq

Methods

rnf :: Int64 -> ()

Eq Int64

Since: base-2.1

Defined in GHC.Int

Methods

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

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

Ord Int64

Since: base-2.1

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

Hashable Int64

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int64 -> Int

hash :: Int64 -> Int

Lift Int64

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Int64 -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Int64 -> Code m Int64

data Word8

8-bit unsigned integer type

Instances

Data Word8

Since: base-4.0.0.0

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

Bits Word8

Since: base-2.1

Defined in GHC.Word

Methods

(.&.) :: Word8 -> Word8 -> Word8

(.|.) :: Word8 -> Word8 -> Word8

xor :: Word8 -> Word8 -> Word8

complement :: Word8 -> Word8

shift :: Word8 -> Int -> Word8

rotate :: Word8 -> Int -> Word8

zeroBits :: Word8

bit :: Int -> Word8

setBit :: Word8 -> Int -> Word8

clearBit :: Word8 -> Int -> Word8

complementBit :: Word8 -> Int -> Word8

testBit :: Word8 -> Int -> Bool

bitSizeMaybe :: Word8 -> Maybe Int

bitSize :: Word8 -> Int

isSigned :: Word8 -> Bool

shiftL :: Word8 -> Int -> Word8

unsafeShiftL :: Word8 -> Int -> Word8

shiftR :: Word8 -> Int -> Word8

unsafeShiftR :: Word8 -> Int -> Word8

rotateL :: Word8 -> Int -> Word8

rotateR :: Word8 -> Int -> Word8

popCount :: Word8 -> Int

FiniteBits Word8

Since: base-4.6.0.0

Defined in GHC.Word

Methods

finiteBitSize :: Word8 -> Int

countLeadingZeros :: Word8 -> Int

countTrailingZeros :: Word8 -> Int

Bounded Word8

Since: base-2.1

Defined in GHC.Word

Methods

minBound :: Word8

maxBound :: Word8

Enum Word8

Since: base-2.1

Defined in GHC.Word

Methods

succ :: Word8 -> Word8

pred :: Word8 -> Word8

toEnum :: Int -> Word8

fromEnum :: Word8 -> Int

enumFrom :: Word8 -> [Word8]

enumFromThen :: Word8 -> Word8 -> [Word8]

enumFromTo :: Word8 -> Word8 -> [Word8]

enumFromThenTo :: Word8 -> Word8 -> Word8 -> [Word8]

Ix Word8

Since: base-2.1

Defined in GHC.Word

Methods

range :: (Word8, Word8) -> [Word8]

index :: (Word8, Word8) -> Word8 -> Int

unsafeIndex :: (Word8, Word8) -> Word8 -> Int

inRange :: (Word8, Word8) -> Word8 -> Bool

rangeSize :: (Word8, Word8) -> Int

unsafeRangeSize :: (Word8, Word8) -> Int

Num Word8

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word8 -> Word8 -> Word8

(-) :: Word8 -> Word8 -> Word8

(*) :: Word8 -> Word8 -> Word8

negate :: Word8 -> Word8

abs :: Word8 -> Word8

signum :: Word8 -> Word8

fromInteger :: Integer -> Word8

Read Word8

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word8

readList :: ReadS [Word8]

readPrec :: ReadPrec Word8

readListPrec :: ReadPrec [Word8]

Integral Word8

Since: base-2.1

Defined in GHC.Word

Methods

quot :: Word8 -> Word8 -> Word8

rem :: Word8 -> Word8 -> Word8

div :: Word8 -> Word8 -> Word8

mod :: Word8 -> Word8 -> Word8

quotRem :: Word8 -> Word8 -> (Word8, Word8)

divMod :: Word8 -> Word8 -> (Word8, Word8)

toInteger :: Word8 -> Integer

Real Word8

Since: base-2.1

Defined in GHC.Word

Methods

toRational :: Word8 -> Rational

Show Word8

Since: base-2.1

Defined in GHC.Word

Methods

showsPrec :: Int -> Word8 -> ShowS

show :: Word8 -> String

showList :: [Word8] -> ShowS

NFData Word8

Defined in Control.DeepSeq

Methods

rnf :: Word8 -> ()

Eq Word8

Since: base-2.1

Defined in GHC.Word

Methods

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

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

Ord Word8

Since: base-2.1

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

Hashable Word8

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word8 -> Int

hash :: Word8 -> Int

Lift Word8

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Word8 -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Word8 -> Code m Word8

data Word

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

Instances

Data Word

Since: base-4.0.0.0

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

Bits Word

Since: base-2.1

Defined in GHC.Bits

Methods

(.&.) :: Word -> Word -> Word

(.|.) :: Word -> Word -> Word

xor :: Word -> Word -> Word

complement :: Word -> Word

shift :: Word -> Int -> Word

rotate :: Word -> Int -> Word

zeroBits :: Word

bit :: Int -> Word

setBit :: Word -> Int -> Word

clearBit :: Word -> Int -> Word

complementBit :: Word -> Int -> Word

testBit :: Word -> Int -> Bool

bitSizeMaybe :: Word -> Maybe Int

bitSize :: Word -> Int

isSigned :: Word -> Bool

shiftL :: Word -> Int -> Word

unsafeShiftL :: Word -> Int -> Word

shiftR :: Word -> Int -> Word

unsafeShiftR :: Word -> Int -> Word

rotateL :: Word -> Int -> Word

rotateR :: Word -> Int -> Word

popCount :: Word -> Int

FiniteBits Word

Since: base-4.6.0.0

Defined in GHC.Bits

Methods

finiteBitSize :: Word -> Int

countLeadingZeros :: Word -> Int

countTrailingZeros :: Word -> Int

Bounded Word

Since: base-2.1

Defined in GHC.Enum

Methods

minBound :: Word

maxBound :: Word

Enum Word

Since: base-2.1

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]

Num Word

Since: base-2.1

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

Read Word

Since: base-4.5.0.0

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word

readList :: ReadS [Word]

readPrec :: ReadPrec Word

readListPrec :: ReadPrec [Word]

Integral Word

Since: base-2.1

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

Real Word

Since: base-2.1

Defined in GHC.Real

Methods

toRational :: Word -> Rational

Show Word

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Word -> ShowS

show :: Word -> String

showList :: [Word] -> ShowS

NFData Word

Defined in Control.DeepSeq

Methods

rnf :: Word -> ()

Eq Word

Defined in GHC.Classes

Methods

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

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

Ord Word

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

Hashable Word

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word -> Int

hash :: Word -> Int

Lift Word

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Word -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Word -> Code m Word

Generic1 (URec Word :: k -> Type)

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

Foldable (UWord :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => UWord m -> m

foldMap :: Monoid m => (a -> m) -> UWord a -> m

foldMap' :: Monoid m => (a -> m) -> UWord a -> m

foldr :: (a -> b -> b) -> b -> UWord a -> b

foldr' :: (a -> b -> b) -> b -> UWord a -> b

foldl :: (b -> a -> b) -> b -> UWord a -> b

foldl' :: (b -> a -> b) -> b -> UWord a -> b

foldr1 :: (a -> a -> a) -> UWord a -> a

foldl1 :: (a -> a -> a) -> UWord a -> a

toList :: UWord a -> [a]

null :: UWord a -> Bool

length :: UWord a -> Int

elem :: Eq a => a -> UWord a -> Bool

maximum :: Ord a => UWord a -> a

minimum :: Ord a => UWord a -> a

sum :: Num a => UWord a -> a

product :: Num a => UWord a -> a

Traversable (UWord :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UWord a -> f (UWord b)

sequenceA :: Applicative f => UWord (f a) -> f (UWord a)

mapM :: Monad m => (a -> m b) -> UWord a -> m (UWord b)

sequence :: Monad m => UWord (m a) -> m (UWord a)

Functor (URec Word :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

Generic (URec Word p)

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

Show (URec Word p)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

show :: URec Word p -> String

showList :: [URec Word p] -> ShowS

Eq (URec Word p)

Since: base-4.9.0.0

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

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

data URec Word (p :: k)

Used for marking occurrences of Word#

Since: base-4.9.0.0

Defined in GHC.Generics

data URec Word (p :: k) = UWord {

• uWord# :: Word#

}

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

Since: base-4.9.0.0

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)

Since: base-4.9.0.0

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 Word64

64-bit unsigned integer type

Instances

Data Word64

Since: base-4.0.0.0

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

Bits Word64

Since: base-2.1

Defined in GHC.Word

Methods

(.&.) :: Word64 -> Word64 -> Word64

(.|.) :: Word64 -> Word64 -> Word64

xor :: Word64 -> Word64 -> Word64

complement :: Word64 -> Word64

shift :: Word64 -> Int -> Word64

rotate :: Word64 -> Int -> Word64

zeroBits :: Word64

bit :: Int -> Word64

setBit :: Word64 -> Int -> Word64

clearBit :: Word64 -> Int -> Word64

complementBit :: Word64 -> Int -> Word64

testBit :: Word64 -> Int -> Bool

bitSizeMaybe :: Word64 -> Maybe Int

bitSize :: Word64 -> Int

isSigned :: Word64 -> Bool

shiftL :: Word64 -> Int -> Word64

unsafeShiftL :: Word64 -> Int -> Word64

shiftR :: Word64 -> Int -> Word64

unsafeShiftR :: Word64 -> Int -> Word64

rotateL :: Word64 -> Int -> Word64

rotateR :: Word64 -> Int -> Word64

popCount :: Word64 -> Int

FiniteBits Word64

Since: base-4.6.0.0

Defined in GHC.Word

Methods

finiteBitSize :: Word64 -> Int

countLeadingZeros :: Word64 -> Int

countTrailingZeros :: Word64 -> Int

Bounded Word64

Since: base-2.1

Defined in GHC.Word

Methods

minBound :: Word64

maxBound :: Word64

Enum Word64

Since: base-2.1

Defined in GHC.Word

Methods

succ :: Word64 -> Word64

pred :: Word64 -> Word64

toEnum :: Int -> Word64

fromEnum :: Word64 -> Int

enumFrom :: Word64 -> [Word64]

enumFromThen :: Word64 -> Word64 -> [Word64]

enumFromTo :: Word64 -> Word64 -> [Word64]

enumFromThenTo :: Word64 -> Word64 -> Word64 -> [Word64]

Ix Word64

Since: base-2.1

Defined in GHC.Word

Methods

range :: (Word64, Word64) -> [Word64]

index :: (Word64, Word64) -> Word64 -> Int

unsafeIndex :: (Word64, Word64) -> Word64 -> Int

inRange :: (Word64, Word64) -> Word64 -> Bool

rangeSize :: (Word64, Word64) -> Int

unsafeRangeSize :: (Word64, Word64) -> Int

Num Word64

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word64 -> Word64 -> Word64

(-) :: Word64 -> Word64 -> Word64

(*) :: Word64 -> Word64 -> Word64

negate :: Word64 -> Word64

abs :: Word64 -> Word64

signum :: Word64 -> Word64

fromInteger :: Integer -> Word64

Read Word64

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word64

readList :: ReadS [Word64]

readPrec :: ReadPrec Word64

readListPrec :: ReadPrec [Word64]

Integral Word64

Since: base-2.1

Defined in GHC.Word

Methods

quot :: Word64 -> Word64 -> Word64

rem :: Word64 -> Word64 -> Word64

div :: Word64 -> Word64 -> Word64

mod :: Word64 -> Word64 -> Word64

quotRem :: Word64 -> Word64 -> (Word64, Word64)

divMod :: Word64 -> Word64 -> (Word64, Word64)

toInteger :: Word64 -> Integer

Real Word64

Since: base-2.1

Defined in GHC.Word

Methods

toRational :: Word64 -> Rational

Show Word64

Since: base-2.1

Defined in GHC.Word

Methods

showsPrec :: Int -> Word64 -> ShowS

show :: Word64 -> String

showList :: [Word64] -> ShowS

NFData Word64

Defined in Control.DeepSeq

Methods

rnf :: Word64 -> ()

Eq Word64

Since: base-2.1

Defined in GHC.Word

Methods

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

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

Ord Word64

Since: base-2.1

Defined in GHC.Word

Methods

compare :: Word64 -> Word64 -> Ordering

(<) :: Word64 -> Word64 -> Bool

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

(>) :: Word64 -> Word64 -> Bool

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

max :: Word64 -> Word64 -> Word64

min :: Word64 -> Word64 -> Word64

Hashable Word64

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word64 -> Int

hash :: Word64 -> Int

Lift Word64

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Word64 -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Word64 -> Code m Word64

data Word32

32-bit unsigned integer type

Instances

Data Word32

Since: base-4.0.0.0

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

Bits Word32

Since: base-2.1

Defined in GHC.Word

Methods

(.&.) :: Word32 -> Word32 -> Word32

(.|.) :: Word32 -> Word32 -> Word32

xor :: Word32 -> Word32 -> Word32

complement :: Word32 -> Word32

shift :: Word32 -> Int -> Word32

rotate :: Word32 -> Int -> Word32

zeroBits :: Word32

bit :: Int -> Word32

setBit :: Word32 -> Int -> Word32

clearBit :: Word32 -> Int -> Word32

complementBit :: Word32 -> Int -> Word32

testBit :: Word32 -> Int -> Bool

bitSizeMaybe :: Word32 -> Maybe Int

bitSize :: Word32 -> Int

isSigned :: Word32 -> Bool

shiftL :: Word32 -> Int -> Word32

unsafeShiftL :: Word32 -> Int -> Word32

shiftR :: Word32 -> Int -> Word32

unsafeShiftR :: Word32 -> Int -> Word32

rotateL :: Word32 -> Int -> Word32

rotateR :: Word32 -> Int -> Word32

popCount :: Word32 -> Int

FiniteBits Word32

Since: base-4.6.0.0

Defined in GHC.Word

Methods

finiteBitSize :: Word32 -> Int

countLeadingZeros :: Word32 -> Int

countTrailingZeros :: Word32 -> Int

Bounded Word32

Since: base-2.1

Defined in GHC.Word

Methods

minBound :: Word32

maxBound :: Word32

Enum Word32

Since: base-2.1

Defined in GHC.Word

Methods

succ :: Word32 -> Word32

pred :: Word32 -> Word32

toEnum :: Int -> Word32

fromEnum :: Word32 -> Int

enumFrom :: Word32 -> [Word32]

enumFromThen :: Word32 -> Word32 -> [Word32]

enumFromTo :: Word32 -> Word32 -> [Word32]

enumFromThenTo :: Word32 -> Word32 -> Word32 -> [Word32]

Ix Word32

Since: base-2.1

Defined in GHC.Word

Methods

range :: (Word32, Word32) -> [Word32]

index :: (Word32, Word32) -> Word32 -> Int

unsafeIndex :: (Word32, Word32) -> Word32 -> Int

inRange :: (Word32, Word32) -> Word32 -> Bool

rangeSize :: (Word32, Word32) -> Int

unsafeRangeSize :: (Word32, Word32) -> Int

Num Word32

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word32 -> Word32 -> Word32

(-) :: Word32 -> Word32 -> Word32

(*) :: Word32 -> Word32 -> Word32

negate :: Word32 -> Word32

abs :: Word32 -> Word32

signum :: Word32 -> Word32

fromInteger :: Integer -> Word32

Read Word32

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word32

readList :: ReadS [Word32]

readPrec :: ReadPrec Word32

readListPrec :: ReadPrec [Word32]

Integral Word32

Since: base-2.1

Defined in GHC.Word

Methods

quot :: Word32 -> Word32 -> Word32

rem :: Word32 -> Word32 -> Word32

div :: Word32 -> Word32 -> Word32

mod :: Word32 -> Word32 -> Word32

quotRem :: Word32 -> Word32 -> (Word32, Word32)

divMod :: Word32 -> Word32 -> (Word32, Word32)

toInteger :: Word32 -> Integer

Real Word32

Since: base-2.1

Defined in GHC.Word

Methods

toRational :: Word32 -> Rational

Show Word32

Since: base-2.1

Defined in GHC.Word

Methods

showsPrec :: Int -> Word32 -> ShowS

show :: Word32 -> String

showList :: [Word32] -> ShowS

NFData Word32

Defined in Control.DeepSeq

Methods

rnf :: Word32 -> ()

Eq Word32

Since: base-2.1

Defined in GHC.Word

Methods

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

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

Ord Word32

Since: base-2.1

Defined in GHC.Word

Methods

compare :: Word32 -> Word32 -> Ordering

(<) :: Word32 -> Word32 -> Bool

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

(>) :: Word32 -> Word32 -> Bool

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

max :: Word32 -> Word32 -> Word32

min :: Word32 -> Word32 -> Word32

Hashable Word32

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word32 -> Int

hash :: Word32 -> Int

Lift Word32

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Word32 -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Word32 -> Code m Word32

data Word16

16-bit unsigned integer type

Instances

Data Word16

Since: base-4.0.0.0

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

Bits Word16

Since: base-2.1

Defined in GHC.Word

Methods

(.&.) :: Word16 -> Word16 -> Word16

(.|.) :: Word16 -> Word16 -> Word16

xor :: Word16 -> Word16 -> Word16

complement :: Word16 -> Word16

shift :: Word16 -> Int -> Word16

rotate :: Word16 -> Int -> Word16

zeroBits :: Word16

bit :: Int -> Word16

setBit :: Word16 -> Int -> Word16

clearBit :: Word16 -> Int -> Word16

complementBit :: Word16 -> Int -> Word16

testBit :: Word16 -> Int -> Bool

bitSizeMaybe :: Word16 -> Maybe Int

bitSize :: Word16 -> Int

isSigned :: Word16 -> Bool

shiftL :: Word16 -> Int -> Word16

unsafeShiftL :: Word16 -> Int -> Word16

shiftR :: Word16 -> Int -> Word16

unsafeShiftR :: Word16 -> Int -> Word16

rotateL :: Word16 -> Int -> Word16

rotateR :: Word16 -> Int -> Word16

popCount :: Word16 -> Int

FiniteBits Word16

Since: base-4.6.0.0

Defined in GHC.Word

Methods

finiteBitSize :: Word16 -> Int

countLeadingZeros :: Word16 -> Int

countTrailingZeros :: Word16 -> Int

Bounded Word16

Since: base-2.1

Defined in GHC.Word

Methods

minBound :: Word16

maxBound :: Word16

Enum Word16

Since: base-2.1

Defined in GHC.Word

Methods

succ :: Word16 -> Word16

pred :: Word16 -> Word16

toEnum :: Int -> Word16

fromEnum :: Word16 -> Int

enumFrom :: Word16 -> [Word16]

enumFromThen :: Word16 -> Word16 -> [Word16]

enumFromTo :: Word16 -> Word16 -> [Word16]

enumFromThenTo :: Word16 -> Word16 -> Word16 -> [Word16]

Ix Word16

Since: base-2.1

Defined in GHC.Word

Methods

range :: (Word16, Word16) -> [Word16]

index :: (Word16, Word16) -> Word16 -> Int

unsafeIndex :: (Word16, Word16) -> Word16 -> Int

inRange :: (Word16, Word16) -> Word16 -> Bool

rangeSize :: (Word16, Word16) -> Int

unsafeRangeSize :: (Word16, Word16) -> Int

Num Word16

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word16 -> Word16 -> Word16

(-) :: Word16 -> Word16 -> Word16

(*) :: Word16 -> Word16 -> Word16

negate :: Word16 -> Word16

abs :: Word16 -> Word16

signum :: Word16 -> Word16

fromInteger :: Integer -> Word16

Read Word16

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word16

readList :: ReadS [Word16]

readPrec :: ReadPrec Word16

readListPrec :: ReadPrec [Word16]

Integral Word16

Since: base-2.1

Defined in GHC.Word

Methods

quot :: Word16 -> Word16 -> Word16

rem :: Word16 -> Word16 -> Word16

div :: Word16 -> Word16 -> Word16

mod :: Word16 -> Word16 -> Word16

quotRem :: Word16 -> Word16 -> (Word16, Word16)

divMod :: Word16 -> Word16 -> (Word16, Word16)

toInteger :: Word16 -> Integer

Real Word16

Since: base-2.1

Defined in GHC.Word

Methods

toRational :: Word16 -> Rational

Show Word16

Since: base-2.1

Defined in GHC.Word

Methods

showsPrec :: Int -> Word16 -> ShowS

show :: Word16 -> String

showList :: [Word16] -> ShowS

NFData Word16

Defined in Control.DeepSeq

Methods

rnf :: Word16 -> ()

Eq Word16

Since: base-2.1

Defined in GHC.Word

Methods

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

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

Ord Word16

Since: base-2.1

Defined in GHC.Word

Methods

compare :: Word16 -> Word16 -> Ordering

(<) :: Word16 -> Word16 -> Bool

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

(>) :: Word16 -> Word16 -> Bool

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

max :: Word16 -> Word16 -> Word16

min :: Word16 -> Word16 -> Word16

Hashable Word16

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word16 -> Int

hash :: Word16 -> Int

Lift Word16

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Word16 -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Word16 -> Code m Word16

byteSwap16 :: Word16 -> Word16

Reverse order of bytes in Word16.

Since: base-4.7.0.0

byteSwap32 :: Word32 -> Word32

Reverse order of bytes in Word32.

Since: base-4.7.0.0

byteSwap64 :: Word64 -> Word64

Reverse order of bytes in Word64.

Since: base-4.7.0.0

minInt :: Int

maxInt :: Int

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

Data Float

Since: base-4.0.0.0

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

Floating Float

Since: base-2.1

Defined in GHC.Float

Methods

pi :: Float

exp :: Float -> Float

log :: Float -> Float

sqrt :: Float -> Float

(**) :: Float -> Float -> Float

logBase :: Float -> Float -> Float

sin :: Float -> Float

cos :: Float -> Float

tan :: Float -> Float

asin :: Float -> Float

acos :: Float -> Float

atan :: Float -> Float

sinh :: Float -> Float

cosh :: Float -> Float

tanh :: Float -> Float

asinh :: Float -> Float

acosh :: Float -> Float

atanh :: Float -> Float

log1p :: Float -> Float

expm1 :: Float -> Float

log1pexp :: Float -> Float

log1mexp :: Float -> Float

RealFloat Float

Since: base-2.1

Defined in GHC.Float

Methods

floatRadix :: Float -> Integer

floatDigits :: Float -> Int

floatRange :: Float -> (Int, Int)

decodeFloat :: Float -> (Integer, Int)

encodeFloat :: Integer -> Int -> Float

exponent :: Float -> Int

significand :: Float -> Float

scaleFloat :: Int -> Float -> Float

isNaN :: Float -> Bool

isInfinite :: Float -> Bool

isDenormalized :: Float -> Bool

isNegativeZero :: Float -> Bool

isIEEE :: Float -> Bool

atan2 :: Float -> Float -> Float

Read Float

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Float

readList :: ReadS [Float]

readPrec :: ReadPrec Float

readListPrec :: ReadPrec [Float]

NFData Float

Defined in Control.DeepSeq

Methods

rnf :: Float -> ()

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 extensionality:

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

Defined in GHC.Classes

Methods

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

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

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

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

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

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Float -> Int

hash :: Float -> Int

Lift Float

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Float -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Float -> Code m Float

Generic1 (URec Float :: k -> Type)

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

Foldable (UFloat :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => UFloat m -> m

foldMap :: Monoid m => (a -> m) -> UFloat a -> m

foldMap' :: Monoid m => (a -> m) -> UFloat a -> m

foldr :: (a -> b -> b) -> b -> UFloat a -> b

foldr' :: (a -> b -> b) -> b -> UFloat a -> b

foldl :: (b -> a -> b) -> b -> UFloat a -> b

foldl' :: (b -> a -> b) -> b -> UFloat a -> b

foldr1 :: (a -> a -> a) -> UFloat a -> a

foldl1 :: (a -> a -> a) -> UFloat a -> a

toList :: UFloat a -> [a]

null :: UFloat a -> Bool

length :: UFloat a -> Int

elem :: Eq a => a -> UFloat a -> Bool

maximum :: Ord a => UFloat a -> a

minimum :: Ord a => UFloat a -> a

sum :: Num a => UFloat a -> a

product :: Num a => UFloat a -> a

Traversable (UFloat :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b)

sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a)

mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b)

sequence :: Monad m => UFloat (m a) -> m (UFloat a)

Functor (URec Float :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

Generic (URec Float p)

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

Show (URec Float p)

Defined in GHC.Generics

Methods

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

show :: URec Float p -> String

showList :: [URec Float p] -> ShowS

Eq (URec Float p)

Defined in GHC.Generics

Methods

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

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

Ord (URec Float p)

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

data URec Float (p :: k)

Used for marking occurrences of Float#

Since: base-4.9.0.0

Defined in GHC.Generics

data URec Float (p :: k) = UFloat {

• uFloat# :: Float#

}

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

Since: base-4.9.0.0

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)

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)))

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

Data Double

Since: base-4.0.0.0

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

Floating Double

Since: base-2.1

Defined in GHC.Float

Methods

pi :: Double

exp :: Double -> Double

log :: Double -> Double

sqrt :: Double -> Double

(**) :: Double -> Double -> Double

logBase :: Double -> Double -> Double

sin :: Double -> Double

cos :: Double -> Double

tan :: Double -> Double

asin :: Double -> Double

acos :: Double -> Double

atan :: Double -> Double

sinh :: Double -> Double

cosh :: Double -> Double

tanh :: Double -> Double

asinh :: Double -> Double

acosh :: Double -> Double

atanh :: Double -> Double

log1p :: Double -> Double

expm1 :: Double -> Double

log1pexp :: Double -> Double

log1mexp :: Double -> Double

RealFloat Double

Since: base-2.1

Defined in GHC.Float

Methods

floatRadix :: Double -> Integer

floatDigits :: Double -> Int

floatRange :: Double -> (Int, Int)

decodeFloat :: Double -> (Integer, Int)

encodeFloat :: Integer -> Int -> Double

exponent :: Double -> Int

significand :: Double -> Double

scaleFloat :: Int -> Double -> Double

isNaN :: Double -> Bool

isInfinite :: Double -> Bool

isDenormalized :: Double -> Bool

isNegativeZero :: Double -> Bool

isIEEE :: Double -> Bool

atan2 :: Double -> Double -> Double

Read Double

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Double

readList :: ReadS [Double]

readPrec :: ReadPrec Double

readListPrec :: ReadPrec [Double]

NFData Double

Defined in Control.DeepSeq

Methods

rnf :: Double -> ()

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

compare :: Double -> Double -> Ordering

(<) :: Double -> Double -> Bool

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

(>) :: Double -> Double -> Bool

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

max :: Double -> Double -> Double

min :: Double -> Double -> 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

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Double -> Int

hash :: Double -> Int

Lift Double

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Double -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Double -> Code m Double

Generic1 (URec Double :: k -> Type)

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

Foldable (UDouble :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => UDouble m -> m

foldMap :: Monoid m => (a -> m) -> UDouble a -> m

foldMap' :: Monoid m => (a -> m) -> UDouble a -> m

foldr :: (a -> b -> b) -> b -> UDouble a -> b

foldr' :: (a -> b -> b) -> b -> UDouble a -> b

foldl :: (b -> a -> b) -> b -> UDouble a -> b

foldl' :: (b -> a -> b) -> b -> UDouble a -> b

foldr1 :: (a -> a -> a) -> UDouble a -> a

foldl1 :: (a -> a -> a) -> UDouble a -> a

toList :: UDouble a -> [a]

null :: UDouble a -> Bool

length :: UDouble a -> Int

elem :: Eq a => a -> UDouble a -> Bool

maximum :: Ord a => UDouble a -> a

minimum :: Ord a => UDouble a -> a

sum :: Num a => UDouble a -> a

product :: Num a => UDouble a -> a

Traversable (UDouble :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b)

sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a)

mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b)

sequence :: Monad m => UDouble (m a) -> m (UDouble a)

Functor (URec Double :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

Generic (URec Double p)

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

Show (URec Double p)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

show :: URec Double p -> String

showList :: [URec Double p] -> ShowS

Eq (URec Double p)

Since: base-4.9.0.0

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

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

data URec Double (p :: k)

Used for marking occurrences of Double#

Since: base-4.9.0.0

Defined in GHC.Generics

data URec Double (p :: k) = UDouble {

• uDouble# :: Double#

}

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

Since: base-4.9.0.0

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)

Since: base-4.9.0.0

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)))

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

Floating Double

Since: base-2.1

Defined in GHC.Float

Methods

pi :: Double

exp :: Double -> Double

log :: Double -> Double

sqrt :: Double -> Double

(**) :: Double -> Double -> Double

logBase :: Double -> Double -> Double

sin :: Double -> Double

cos :: Double -> Double

tan :: Double -> Double

asin :: Double -> Double

acos :: Double -> Double

atan :: Double -> Double

sinh :: Double -> Double

cosh :: Double -> Double

tanh :: Double -> Double

asinh :: Double -> Double

acosh :: Double -> Double

atanh :: Double -> Double

log1p :: Double -> Double

expm1 :: Double -> Double

log1pexp :: Double -> Double

log1mexp :: Double -> Double

Floating Float

Since: base-2.1

Defined in GHC.Float

Methods

pi :: Float

exp :: Float -> Float

log :: Float -> Float

sqrt :: Float -> Float

(**) :: Float -> Float -> Float

logBase :: Float -> Float -> Float

sin :: Float -> Float

cos :: Float -> Float

tan :: Float -> Float

asin :: Float -> Float

acos :: Float -> Float

atan :: Float -> Float

sinh :: Float -> Float

cosh :: Float -> Float

tanh :: Float -> Float

asinh :: Float -> Float

acosh :: Float -> Float

atanh :: Float -> Float

log1p :: Float -> Float

expm1 :: Float -> Float

log1pexp :: Float -> Float

log1mexp :: Float -> Float

RealFloat a => Floating (Complex a)

Since: base-2.1

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

Defined in Data.Functor.Identity

Methods

pi :: Identity a

exp :: Identity a -> Identity a

log :: Identity a -> Identity a

sqrt :: Identity a -> Identity a

(**) :: Identity a -> Identity a -> Identity a

logBase :: Identity a -> Identity a -> Identity a

sin :: Identity a -> Identity a

cos :: Identity a -> Identity a

tan :: Identity a -> Identity a

asin :: Identity a -> Identity a

acos :: Identity a -> Identity a

atan :: Identity a -> Identity a

sinh :: Identity a -> Identity a

cosh :: Identity a -> Identity a

tanh :: Identity a -> Identity a

asinh :: Identity a -> Identity a

acosh :: Identity a -> Identity a

atanh :: Identity a -> Identity a

log1p :: Identity a -> Identity a

expm1 :: Identity a -> Identity a

log1pexp :: Identity a -> Identity a

log1mexp :: Identity a -> Identity a

Floating a => Floating (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

pi :: Down a

exp :: Down a -> Down a

log :: Down a -> Down a

sqrt :: Down a -> Down a

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

logBase :: Down a -> Down a -> Down a

sin :: Down a -> Down a

cos :: Down a -> Down a

tan :: Down a -> Down a

asin :: Down a -> Down a

acos :: Down a -> Down a

atan :: Down a -> Down a

sinh :: Down a -> Down a

cosh :: Down a -> Down a

tanh :: Down a -> Down a

asinh :: Down a -> Down a

acosh :: Down a -> Down a

atanh :: Down a -> Down a

log1p :: Down a -> Down a

expm1 :: Down a -> Down a

log1pexp :: Down a -> Down a

log1mexp :: Down a -> Down a

Floating a => Floating (Op a b)

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

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.

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

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

RealFloat Double

Since: base-2.1

Defined in GHC.Float

Methods

floatRadix :: Double -> Integer

floatDigits :: Double -> Int

floatRange :: Double -> (Int, Int)

decodeFloat :: Double -> (Integer, Int)

encodeFloat :: Integer -> Int -> Double

exponent :: Double -> Int

significand :: Double -> Double

scaleFloat :: Int -> Double -> Double

isNaN :: Double -> Bool

isInfinite :: Double -> Bool

isDenormalized :: Double -> Bool

isNegativeZero :: Double -> Bool

isIEEE :: Double -> Bool

atan2 :: Double -> Double -> Double

RealFloat Float

Since: base-2.1

Defined in GHC.Float

Methods

floatRadix :: Float -> Integer

floatDigits :: Float -> Int

floatRange :: Float -> (Int, Int)

decodeFloat :: Float -> (Integer, Int)

encodeFloat :: Integer -> Int -> Float

exponent :: Float -> Int

significand :: Float -> Float

scaleFloat :: Int -> Float -> Float

isNaN :: Float -> Bool

isInfinite :: Float -> Bool

isDenormalized :: Float -> Bool

isNegativeZero :: Float -> Bool

isIEEE :: Float -> Bool

atan2 :: Float -> Float -> Float

RealFloat a => RealFloat (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

floatRadix :: Identity a -> Integer

floatDigits :: Identity a -> Int

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

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

encodeFloat :: Integer -> Int -> Identity a

exponent :: Identity a -> Int

significand :: Identity a -> Identity a

scaleFloat :: Int -> Identity a -> Identity a

isNaN :: Identity a -> Bool

isInfinite :: Identity a -> Bool

isDenormalized :: Identity a -> Bool

isNegativeZero :: Identity a -> Bool

isIEEE :: Identity a -> Bool

atan2 :: Identity a -> Identity a -> Identity a

RealFloat a => RealFloat (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

floatRadix :: Down a -> Integer

floatDigits :: Down a -> Int

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

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

encodeFloat :: Integer -> Int -> Down a

exponent :: Down a -> Int

significand :: Down a -> Down a

scaleFloat :: Int -> Down a -> Down a

isNaN :: Down a -> Bool

isInfinite :: Down a -> Bool

isDenormalized :: Down a -> Bool

isNegativeZero :: Down a -> Bool

isIEEE :: Down a -> Bool

atan2 :: Down a -> Down a -> Down a

RealFloat a => RealFloat (Const a b)

Since: base-4.9.0.0

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 Integer

Arbitrary precision integers. In contrast with fixed-size integral types such as Int, the Integer type represents the entire infinite range of integers.

Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.

If the value is small (fit into an Int), IS constructor is used. Otherwise Integer and IN constructors are used to store a BigNat representing respectively the positive or the negative value magnitude.

Invariant: Integer and IN are used iff value doesn't fit in IS

Instances

Data Integer

Since: base-4.0.0.0

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

Bits Integer

Since: base-2.1

Defined in GHC.Bits

Methods

(.&.) :: Integer -> Integer -> Integer

(.|.) :: Integer -> Integer -> Integer

xor :: Integer -> Integer -> Integer

complement :: Integer -> Integer

shift :: Integer -> Int -> Integer

rotate :: Integer -> Int -> Integer

zeroBits :: Integer

bit :: Int -> Integer

setBit :: Integer -> Int -> Integer

clearBit :: Integer -> Int -> Integer

complementBit :: Integer -> Int -> Integer

testBit :: Integer -> Int -> Bool

bitSizeMaybe :: Integer -> Maybe Int

bitSize :: Integer -> Int

isSigned :: Integer -> Bool

shiftL :: Integer -> Int -> Integer

unsafeShiftL :: Integer -> Int -> Integer

shiftR :: Integer -> Int -> Integer

unsafeShiftR :: Integer -> Int -> Integer

rotateL :: Integer -> Int -> Integer

rotateR :: Integer -> Int -> Integer

popCount :: Integer -> Int

Enum Integer

Since: base-2.1

Defined in GHC.Enum

Methods

succ :: Integer -> Integer

pred :: Integer -> Integer

toEnum :: Int -> Integer

fromEnum :: Integer -> Int

enumFrom :: Integer -> [Integer]

enumFromThen :: Integer -> Integer -> [Integer]

enumFromTo :: Integer -> Integer -> [Integer]

enumFromThenTo :: Integer -> Integer -> Integer -> [Integer]

Num Integer

Since: base-2.1

Defined in GHC.Num

Methods

(+) :: Integer -> Integer -> Integer

(-) :: Integer -> Integer -> Integer

(*) :: Integer -> Integer -> Integer

negate :: Integer -> Integer

abs :: Integer -> Integer

signum :: Integer -> Integer

fromInteger :: Integer -> Integer

Read Integer

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Integer

readList :: ReadS [Integer]

readPrec :: ReadPrec Integer

readListPrec :: ReadPrec [Integer]

Integral Integer

Since: base-2.0.1

Defined in GHC.Real

Methods

quot :: Integer -> Integer -> Integer

rem :: Integer -> Integer -> Integer

div :: Integer -> Integer -> Integer

mod :: Integer -> Integer -> Integer

quotRem :: Integer -> Integer -> (Integer, Integer)

divMod :: Integer -> Integer -> (Integer, Integer)

toInteger :: Integer -> Integer

Real Integer

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Integer -> Rational

Show Integer

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Integer -> ShowS

show :: Integer -> String

showList :: [Integer] -> ShowS

NFData Integer

Defined in Control.DeepSeq

Methods

rnf :: Integer -> ()

Eq Integer

Defined in GHC.Num.Integer

Methods

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

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

Ord Integer

Defined in GHC.Num.Integer

Methods

compare :: Integer -> Integer -> Ordering

(<) :: Integer -> Integer -> Bool

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

(>) :: Integer -> Integer -> Bool

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

max :: Integer -> Integer -> Integer

min :: Integer -> Integer -> Integer

Hashable Integer

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Integer -> Int

hash :: Integer -> Int

Lift Integer

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Integer -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Integer -> Code m Integer

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)

Coherence with toInteger

if the type also implements Integral, then fromInteger is a left inverse for toInteger, i.e. fromInteger (toInteger i) == i

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

Num Int16

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int16 -> Int16 -> Int16

(-) :: Int16 -> Int16 -> Int16

(*) :: Int16 -> Int16 -> Int16

negate :: Int16 -> Int16

abs :: Int16 -> Int16

signum :: Int16 -> Int16

fromInteger :: Integer -> Int16

Num Int32

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int32 -> Int32 -> Int32

(-) :: Int32 -> Int32 -> Int32

(*) :: Int32 -> Int32 -> Int32

negate :: Int32 -> Int32

abs :: Int32 -> Int32

signum :: Int32 -> Int32

fromInteger :: Integer -> Int32

Num Int64

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int64 -> Int64 -> Int64

(-) :: Int64 -> Int64 -> Int64

(*) :: Int64 -> Int64 -> Int64

negate :: Int64 -> Int64

abs :: Int64 -> Int64

signum :: Int64 -> Int64

fromInteger :: Integer -> Int64

Num Int8

Since: base-2.1

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 Word16

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word16 -> Word16 -> Word16

(-) :: Word16 -> Word16 -> Word16

(*) :: Word16 -> Word16 -> Word16

negate :: Word16 -> Word16

abs :: Word16 -> Word16

signum :: Word16 -> Word16

fromInteger :: Integer -> Word16

Num Word32

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word32 -> Word32 -> Word32

(-) :: Word32 -> Word32 -> Word32

(*) :: Word32 -> Word32 -> Word32

negate :: Word32 -> Word32

abs :: Word32 -> Word32

signum :: Word32 -> Word32

fromInteger :: Integer -> Word32

Num Word64

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word64 -> Word64 -> Word64

(-) :: Word64 -> Word64 -> Word64

(*) :: Word64 -> Word64 -> Word64

negate :: Word64 -> Word64

abs :: Word64 -> Word64

signum :: Word64 -> Word64

fromInteger :: Integer -> Word64

Num Word8

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word8 -> Word8 -> Word8

(-) :: Word8 -> Word8 -> Word8

(*) :: Word8 -> Word8 -> Word8

negate :: Word8 -> Word8

abs :: Word8 -> Word8

signum :: Word8 -> Word8

fromInteger :: Integer -> Word8

Num Integer

Since: base-2.1

Defined in GHC.Num

Methods

(+) :: Integer -> Integer -> Integer

(-) :: Integer -> Integer -> Integer

(*) :: Integer -> Integer -> Integer

negate :: Integer -> Integer

abs :: Integer -> Integer

signum :: Integer -> Integer

fromInteger :: Integer -> Integer

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

Defined in GHC.Num

Methods

(+) :: Natural -> Natural -> Natural

(-) :: Natural -> Natural -> Natural

(*) :: Natural -> Natural -> Natural

negate :: Natural -> Natural

abs :: Natural -> Natural

signum :: Natural -> Natural

fromInteger :: Integer -> Natural

Num Int

Since: base-2.1

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 Word

Since: base-2.1

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

RealFloat a => Num (Complex a)

Since: base-2.1

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

Num a => Num (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(+) :: Identity a -> Identity a -> Identity a

(-) :: Identity a -> Identity a -> Identity a

(*) :: Identity a -> Identity a -> Identity a

negate :: Identity a -> Identity a

abs :: Identity a -> Identity a

signum :: Identity a -> Identity a

fromInteger :: Integer -> Identity a

Num a => Num (Down a)

Since: base-4.11.0.0

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 (Max a)

Since: base-4.9.0.0

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 (Min a)

Since: base-4.9.0.0

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 (Product a)

Since: base-4.7.0.0

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 (Sum a)

Since: base-4.7.0.0

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

Integral a => Num (Ratio a)

Since: base-2.0.1

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

Num a => Num (Op a b)

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

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)

Note that even if the underlying Num and Applicative instances are lawful, for most Applicatives, this instance will not be lawful. If you use this instance with the list Applicative, the following customary laws will not hold:

Commutativity:

>>> Ap [10,20] + Ap [1,2]
Ap {getAp = [11,12,21,22]}
>>> Ap [1,2] + Ap [10,20]
Ap {getAp = [11,21,12,22]}

Additive inverse:

>>> Ap [] + negate (Ap [])
Ap {getAp = []}
>>> fromInteger 0 :: Ap [] Int
Ap {getAp = [0]}

Distributivity:

>>> Ap [1,2] * (3 + 4)
Ap {getAp = [7,14]}
>>> (Ap [1,2] * 3) + (Ap [1,2] * 4)
Ap {getAp = [7,11,10,14]}

Since: base-4.12.0.0

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

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

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.

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.

In addition, toInteger should be total, and fromInteger should be a left inverse for it, i.e. fromInteger (toInteger i) = i.

Minimal complete definition

quotRem, toInteger

Methods

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

integer division truncated toward zero

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

integer remainder, satisfying

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

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

integer division truncated toward negative infinity

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

integer modulus, satisfying

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

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

simultaneous quot and rem

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

simultaneous div and mod

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

toInteger :: a -> Integer

conversion to Integer

Instances

Integral Int16

Since: base-2.1

Defined in GHC.Int

Methods

quot :: Int16 -> Int16 -> Int16

rem :: Int16 -> Int16 -> Int16

div :: Int16 -> Int16 -> Int16

mod :: Int16 -> Int16 -> Int16

quotRem :: Int16 -> Int16 -> (Int16, Int16)

divMod :: Int16 -> Int16 -> (Int16, Int16)

toInteger :: Int16 -> Integer

Integral Int32

Since: base-2.1

Defined in GHC.Int

Methods

quot :: Int32 -> Int32 -> Int32

rem :: Int32 -> Int32 -> Int32

div :: Int32 -> Int32 -> Int32

mod :: Int32 -> Int32 -> Int32

quotRem :: Int32 -> Int32 -> (Int32, Int32)

divMod :: Int32 -> Int32 -> (Int32, Int32)

toInteger :: Int32 -> Integer

Integral Int64

Since: base-2.1

Defined in GHC.Int

Methods

quot :: Int64 -> Int64 -> Int64

rem :: Int64 -> Int64 -> Int64

div :: Int64 -> Int64 -> Int64

mod :: Int64 -> Int64 -> Int64

quotRem :: Int64 -> Int64 -> (Int64, Int64)

divMod :: Int64 -> Int64 -> (Int64, Int64)

toInteger :: Int64 -> Integer

Integral Int8

Since: base-2.1

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 Word16

Since: base-2.1

Defined in GHC.Word

Methods

quot :: Word16 -> Word16 -> Word16

rem :: Word16 -> Word16 -> Word16

div :: Word16 -> Word16 -> Word16

mod :: Word16 -> Word16 -> Word16

quotRem :: Word16 -> Word16 -> (Word16, Word16)

divMod :: Word16 -> Word16 -> (Word16, Word16)

toInteger :: Word16 -> Integer

Integral Word32

Since: base-2.1

Defined in GHC.Word

Methods

quot :: Word32 -> Word32 -> Word32

rem :: Word32 -> Word32 -> Word32

div :: Word32 -> Word32 -> Word32

mod :: Word32 -> Word32 -> Word32

quotRem :: Word32 -> Word32 -> (Word32, Word32)

divMod :: Word32 -> Word32 -> (Word32, Word32)

toInteger :: Word32 -> Integer

Integral Word64

Since: base-2.1

Defined in GHC.Word

Methods

quot :: Word64 -> Word64 -> Word64

rem :: Word64 -> Word64 -> Word64

div :: Word64 -> Word64 -> Word64

mod :: Word64 -> Word64 -> Word64

quotRem :: Word64 -> Word64 -> (Word64, Word64)

divMod :: Word64 -> Word64 -> (Word64, Word64)

toInteger :: Word64 -> Integer

Integral Word8

Since: base-2.1

Defined in GHC.Word

Methods

quot :: Word8 -> Word8 -> Word8

rem :: Word8 -> Word8 -> Word8

div :: Word8 -> Word8 -> Word8

mod :: Word8 -> Word8 -> Word8

quotRem :: Word8 -> Word8 -> (Word8, Word8)

divMod :: Word8 -> Word8 -> (Word8, Word8)

toInteger :: Word8 -> Integer

Integral Integer

Since: base-2.0.1

Defined in GHC.Real

Methods

quot :: Integer -> Integer -> Integer

rem :: Integer -> Integer -> Integer

div :: Integer -> Integer -> Integer

mod :: Integer -> Integer -> Integer

quotRem :: Integer -> Integer -> (Integer, Integer)

divMod :: Integer -> Integer -> (Integer, Integer)

toInteger :: Integer -> Integer

Integral Natural

Since: base-4.8.0.0

Defined in GHC.Real

Methods

quot :: Natural -> Natural -> Natural

rem :: Natural -> Natural -> Natural

div :: Natural -> Natural -> Natural

mod :: Natural -> Natural -> Natural

quotRem :: Natural -> Natural -> (Natural, Natural)

divMod :: Natural -> Natural -> (Natural, Natural)

toInteger :: Natural -> Integer

Integral Int

Since: base-2.0.1

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 Word

Since: base-2.1

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 a => Integral (Identity a)

Since: base-4.9.0.0

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 -> Identity a -> (Identity a, Identity a)

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

toInteger :: Identity a -> Integer

Integral a => Integral (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

quot :: Const a b -> Const a b -> Const a b

rem :: Const a b -> Const a b -> Const a b

div :: Const a b -> Const a b -> Const a b

mod :: Const a b -> Const a b -> Const a b

quotRem :: Const a b -> Const a b -> (Const a b, Const a b)

divMod :: Const a b -> Const a b -> (Const a b, Const a b)

toInteger :: Const a b -> Integer

type Rational = Ratio Integer

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

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

Totality of toRational

toRational is total

Coherence with toRational

if the type also implements Real, then fromRational is a left inverse for toRational, i.e. fromRational (toRational i) = i

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

RealFloat a => Fractional (Complex a)

Since: base-2.1

Defined in Data.Complex

Methods

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

recip :: Complex a -> Complex a

fromRational :: Rational -> Complex a

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(/) :: Identity a -> Identity a -> Identity a

recip :: Identity a -> Identity a

fromRational :: Rational -> Identity a

Fractional a => Fractional (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

(/) :: Down a -> Down a -> Down a

recip :: Down a -> Down a

fromRational :: Rational -> Down a

Integral a => Fractional (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

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

recip :: Ratio a -> Ratio a

fromRational :: Rational -> Ratio a

Fractional a => Fractional (Op a b)

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

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 (Num a, Ord a) => Real a where

Real numbers.

The Haskell report defines no laws for Real, however Real instances are customarily expected to adhere to the following law:

Coherence with fromRational

if the type also implements Fractional, then fromRational is a left inverse for toRational, i.e. fromRational (toRational i) = i

Methods

toRational :: a -> Rational

the rational equivalent of its real argument with full precision

Instances

Real Int16

Since: base-2.1

Defined in GHC.Int

Methods

toRational :: Int16 -> Rational

Real Int32

Since: base-2.1

Defined in GHC.Int

Methods

toRational :: Int32 -> Rational

Real Int64

Since: base-2.1

Defined in GHC.Int

Methods

toRational :: Int64 -> Rational

Real Int8

Since: base-2.1

Defined in GHC.Int

Methods

toRational :: Int8 -> Rational

Real Word16

Since: base-2.1

Defined in GHC.Word

Methods

toRational :: Word16 -> Rational

Real Word32

Since: base-2.1

Defined in GHC.Word

Methods

toRational :: Word32 -> Rational

Real Word64

Since: base-2.1

Defined in GHC.Word

Methods

toRational :: Word64 -> Rational

Real Word8

Since: base-2.1

Defined in GHC.Word

Methods

toRational :: Word8 -> Rational

Real Integer

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Integer -> Rational

Real Natural

Since: base-4.8.0.0

Defined in GHC.Real

Methods

toRational :: Natural -> Rational

Real Int

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Int -> Rational

Real Word

Since: base-2.1

Defined in GHC.Real

Methods

toRational :: Word -> Rational

Real a => Real (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

toRational :: Identity a -> Rational

Real a => Real (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

toRational :: Down a -> Rational

Integral a => Real (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Ratio a -> Rational

Real a => Real (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

toRational :: Const a b -> Rational

class (Real a, Fractional a) => RealFrac a where

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, a)

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

• n is an integral number with the same sign as x; and
• f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: Integral b => a -> b

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> b

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: Integral b => a -> b

ceiling x returns the least integer not less than x

floor :: Integral b => a -> b

floor x returns the greatest integer not greater than x

Instances

RealFrac a => RealFrac (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

properFraction :: Integral b => Identity a -> (b, Identity a)

truncate :: Integral b => Identity a -> b

round :: Integral b => Identity a -> b

ceiling :: Integral b => Identity a -> b

floor :: Integral b => Identity a -> b

RealFrac a => RealFrac (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

properFraction :: Integral b => Down a -> (b, Down a)

truncate :: Integral b => Down a -> b

round :: Integral b => Down a -> b

ceiling :: Integral b => Down a -> b

floor :: Integral b => Down a -> b

Integral a => RealFrac (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

properFraction :: Integral b => Ratio a -> (b, Ratio a)

truncate :: Integral b => Ratio a -> b

round :: Integral b => Ratio a -> b

ceiling :: Integral b => Ratio a -> b

floor :: Integral b => Ratio a -> b

RealFrac a => RealFrac (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

properFraction :: Integral b0 => Const a b -> (b0, Const a b)

truncate :: Integral b0 => Const a b -> b0

round :: Integral b0 => Const a b -> b0

ceiling :: Integral b0 => Const a b -> b0

floor :: Integral b0 => Const a b -> b0

data Ratio a

Rational numbers, with numerator and denominator of some Integral type.

Note that Ratio's instances inherit the deficiencies from the type parameter's. For example, Ratio Natural's Num instance has similar problems to Natural's.

Instances

NFData1 Ratio

Available on base >=4.9

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Ratio a -> ()

Integral a => Lift (Ratio a :: Type)

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Ratio a -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Ratio a -> Code m (Ratio a)

(Data a, Integral a) => Data (Ratio a)

Since: base-4.0.0.0

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ratio a -> c (Ratio a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ratio a)

toConstr :: Ratio a -> Constr

dataTypeOf :: Ratio a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ratio a))

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

gmapT :: (forall b. Data b => b -> b) -> Ratio a -> Ratio a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r

gmapQ :: (forall d. Data d => d -> u) -> Ratio a -> [u]

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

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a)

Integral a => Enum (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

succ :: Ratio a -> Ratio a

pred :: Ratio a -> Ratio a

toEnum :: Int -> Ratio a

fromEnum :: Ratio a -> Int

enumFrom :: Ratio a -> [Ratio a]

enumFromThen :: Ratio a -> Ratio a -> [Ratio a]

enumFromTo :: Ratio a -> Ratio a -> [Ratio a]

enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a]

Integral a => Num (Ratio a)

Since: base-2.0.1

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

(Integral a, Read a) => Read (Ratio a)

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (Ratio a)

readList :: ReadS [Ratio a]

readPrec :: ReadPrec (Ratio a)

readListPrec :: ReadPrec [Ratio a]

Integral a => Fractional (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

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

recip :: Ratio a -> Ratio a

fromRational :: Rational -> Ratio a

Integral a => Real (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Ratio a -> Rational

Integral a => RealFrac (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

properFraction :: Integral b => Ratio a -> (b, Ratio a)

truncate :: Integral b => Ratio a -> b

round :: Integral b => Ratio a -> b

ceiling :: Integral b => Ratio a -> b

floor :: Integral b => Ratio a -> b

Show a => Show (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

showsPrec :: Int -> Ratio a -> ShowS

show :: Ratio a -> String

showList :: [Ratio a] -> ShowS

NFData a => NFData (Ratio a)

Defined in Control.DeepSeq

Methods

rnf :: Ratio a -> ()

Eq a => Eq (Ratio a)

Since: base-2.1

Defined in GHC.Real

Methods

(==) :: Ratio a -> Ratio a -> Bool

(/=) :: Ratio a -> Ratio a -> Bool

Integral a => Ord (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

compare :: Ratio a -> Ratio a -> Ordering

(<) :: Ratio a -> Ratio a -> Bool

(<=) :: Ratio a -> Ratio a -> Bool

(>) :: Ratio a -> Ratio a -> Bool

(>=) :: Ratio a -> Ratio a -> Bool

max :: Ratio a -> Ratio a -> Ratio a

min :: Ratio a -> Ratio a -> Ratio a

Hashable a => Hashable (Ratio a)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Ratio a -> Int

hash :: Ratio a -> Int

even :: Integral a => a -> Bool

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

General coercion from Integral types.

WARNING: This function performs silent truncation if the result type is not at least as big as the argument's type.

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

General coercion to Fractional types.

WARNING: This function goes through the Rational type, which does not have values for NaN for example. This means it does not round-trip.

For Double it also behaves differently with or without -O0:

Prelude> realToFrac nan -- With -O0
-Infinity
Prelude> realToFrac nan
NaN

(^) :: (Num a, Integral b) => a -> b -> a infixr 8

raise a number to a non-negative integral power

numerator :: Ratio a -> a

Extract the numerator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

denominator :: Ratio a -> a

Extract the denominator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

odd :: Integral a => a -> Bool

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8

raise a number to an integral power

gcd :: Integral a => a -> a -> a

gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.

lcm :: Integral a => a -> a -> a

lcm x y is the smallest positive integer that both x and y divide.

data Natural

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Instances

Data Natural

Since: base-4.8.0.0

Defined in Data.Data

Methods

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

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

toConstr :: Natural -> Constr

dataTypeOf :: Natural -> DataType

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

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

gmapT :: (forall b. Data b => b -> b) -> Natural -> Natural

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

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

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

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

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

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

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

Bits Natural

Since: base-4.8.0

Defined in GHC.Bits

Methods

(.&.) :: Natural -> Natural -> Natural

(.|.) :: Natural -> Natural -> Natural

xor :: Natural -> Natural -> Natural

complement :: Natural -> Natural

shift :: Natural -> Int -> Natural

rotate :: Natural -> Int -> Natural

zeroBits :: Natural

bit :: Int -> Natural

setBit :: Natural -> Int -> Natural

clearBit :: Natural -> Int -> Natural

complementBit :: Natural -> Int -> Natural

testBit :: Natural -> Int -> Bool

bitSizeMaybe :: Natural -> Maybe Int

bitSize :: Natural -> Int

isSigned :: Natural -> Bool

shiftL :: Natural -> Int -> Natural

unsafeShiftL :: Natural -> Int -> Natural

shiftR :: Natural -> Int -> Natural

unsafeShiftR :: Natural -> Int -> Natural

rotateL :: Natural -> Int -> Natural

rotateR :: Natural -> Int -> Natural

popCount :: Natural -> Int

Enum Natural

Since: base-4.8.0.0

Defined in GHC.Enum

Methods

succ :: Natural -> Natural

pred :: Natural -> Natural

toEnum :: Int -> Natural

fromEnum :: Natural -> Int

enumFrom :: Natural -> [Natural]

enumFromThen :: Natural -> Natural -> [Natural]

enumFromTo :: Natural -> Natural -> [Natural]

enumFromThenTo :: Natural -> Natural -> Natural -> [Natural]

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

Defined in GHC.Num

Methods

(+) :: Natural -> Natural -> Natural

(-) :: Natural -> Natural -> Natural

(*) :: Natural -> Natural -> Natural

negate :: Natural -> Natural

abs :: Natural -> Natural

signum :: Natural -> Natural

fromInteger :: Integer -> Natural

Read Natural

Since: base-4.8.0.0

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Natural

readList :: ReadS [Natural]

readPrec :: ReadPrec Natural

readListPrec :: ReadPrec [Natural]

Integral Natural

Since: base-4.8.0.0

Defined in GHC.Real

Methods

quot :: Natural -> Natural -> Natural

rem :: Natural -> Natural -> Natural

div :: Natural -> Natural -> Natural

mod :: Natural -> Natural -> Natural

quotRem :: Natural -> Natural -> (Natural, Natural)

divMod :: Natural -> Natural -> (Natural, Natural)

toInteger :: Natural -> Integer

Real Natural

Since: base-4.8.0.0

Defined in GHC.Real

Methods

toRational :: Natural -> Rational

Show Natural

Since: base-4.8.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS

show :: Natural -> String

showList :: [Natural] -> ShowS

NFData Natural

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Natural -> ()

Eq Natural

Defined in GHC.Num.Natural

Methods

(==) :: Natural -> Natural -> Bool

(/=) :: Natural -> Natural -> Bool

Ord Natural

Defined in GHC.Num.Natural

Methods

compare :: Natural -> Natural -> Ordering

(<) :: Natural -> Natural -> Bool

(<=) :: Natural -> Natural -> Bool

(>) :: Natural -> Natural -> Bool

(>=) :: Natural -> Natural -> Bool

max :: Natural -> Natural -> Natural

min :: Natural -> Natural -> Natural

Hashable Natural

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Natural -> Int

hash :: Natural -> Int

TestCoercion SNat

Since: base-4.18.0.0

Defined in GHC.TypeNats

Methods

testCoercion :: forall (a :: k) (b :: k). SNat a -> SNat b -> Maybe (Coercion a b)

TestEquality SNat

Since: base-4.18.0.0

Defined in GHC.TypeNats

Methods

testEquality :: forall (a :: k) (b :: k). SNat a -> SNat b -> Maybe (a :~: b)

Lift Natural

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Quote m => Natural -> m Exp

liftTyped :: forall (m :: Type -> Type). Quote m => Natural -> Code m Natural

type Compare (a :: Natural) (b :: Natural)

Defined in Data.Type.Ord

type Compare (a :: Natural) (b :: Natural) = CmpNat a b

Combinators

integerToBounded :: forall a. (Integral a, Bounded a) => Integer -> Maybe a

Transforms an integer number to a bounded integral. It returns Nothing for integers outside the bound of the return type.

>>> integerToBounded @Int 42
Just 42

>>> integerToBounded @Int8 1024
Nothing

>>> integerToBounded @Int (toInteger (minBound :: Int))
Just (-9223372036854775808)
>>> integerToBounded @Int $ (toInteger (minBound :: Int)) - 1
Nothing

>>> integerToBounded @Int (toInteger (maxBound :: Int))
Just 9223372036854775807
>>> integerToBounded @Int $ (toInteger (maxBound :: Int)) + 1
Nothing

If you want to convert Int or Word to a bounded type, take a look at toIntegralSized function instead.

Since: 0.5.0

integerToNatural :: Integer -> Maybe Natural

Transforms an integer number to a natural. Only non-negative integers are considered natural, everything else will return Nothing.

>>> integerToNatural (-1)
Nothing

>>> integerToNatural 0
Just 0

>>> integerToNatural 10
Just 10

Since: 0.5.0