Relude.Numeric

Documentation

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

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

A simpler version of this function is:

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

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

Since: base-4.8.0.0

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

Bitwise "xor"

data Int

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

Instances

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]

Eq Int

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

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

Num Int

Since: base-2.1

Defined in GHC.Num

Methods

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

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

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

negate :: Int -> Int

abs :: Int -> Int

signum :: Int -> Int

fromInteger :: Integer -> Int

Ord Int

Defined in GHC.Classes

Methods

compare :: Int -> Int -> Ordering

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

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

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

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

max :: Int -> Int -> Int

min :: Int -> Int -> Int

Read Int

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Int

readList :: ReadS [Int]

readPrec :: ReadPrec Int

readListPrec :: ReadPrec [Int]

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

Ix Int

Since: base-2.1

Defined in GHC.Arr

Methods

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

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

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

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

rangeSize :: (Int, Int) -> Int

unsafeRangeSize :: (Int, Int) -> Int

Bits Int

Since: base-2.1

Defined in Data.Bits

Methods

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

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

xor :: Int -> Int -> Int

complement :: Int -> Int

shift :: Int -> Int -> Int

rotate :: Int -> Int -> Int

zeroBits :: Int

bit :: Int -> Int

setBit :: Int -> Int -> Int

clearBit :: Int -> Int -> Int

complementBit :: Int -> Int -> Int

testBit :: Int -> Int -> Bool

bitSizeMaybe :: Int -> Maybe Int

bitSize :: Int -> Int

isSigned :: Int -> Bool

shiftL :: Int -> Int -> Int

unsafeShiftL :: Int -> Int -> Int

shiftR :: Int -> Int -> Int

unsafeShiftR :: Int -> Int -> Int

rotateL :: Int -> Int -> Int

rotateR :: Int -> Int -> Int

popCount :: Int -> Int

FiniteBits Int

Since: base-4.6.0.0

Defined in Data.Bits

Methods

finiteBitSize :: Int -> Int

countLeadingZeros :: Int -> Int

countTrailingZeros :: Int -> Int

NFData Int

Defined in Control.DeepSeq

Methods

rnf :: Int -> ()

Hashable Int

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int -> Int

hash :: Int -> Int

Generic1 (URec Int :: k -> Type)

Defined in GHC.Generics

Associated Types

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

Methods

from1 :: URec Int a -> Rep1 (URec Int) a

to1 :: Rep1 (URec Int) a -> URec Int 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

Foldable (URec Int :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

toList :: URec Int a -> [a]

null :: URec Int a -> Bool

length :: URec Int a -> Int

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

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

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

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

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

Traversable (URec Int :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

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

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

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

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

Eq (URec Int p)

Since: base-4.9.0.0

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

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

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

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

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]

Eq Int8

Since: base-2.1

Defined in GHC.Int

Methods

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

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

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

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

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

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

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

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

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

Num Int8

Since: base-2.1

Defined in GHC.Int

Methods

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

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

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

negate :: Int8 -> Int8

abs :: Int8 -> Int8

signum :: Int8 -> Int8

fromInteger :: Integer -> Int8

Ord Int8

Since: base-2.1

Defined in GHC.Int

Methods

compare :: Int8 -> Int8 -> Ordering

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

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

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

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

max :: Int8 -> Int8 -> Int8

min :: Int8 -> Int8 -> Int8

Read Int8

Since: base-2.1

Defined in GHC.Int

Methods

readsPrec :: Int -> ReadS Int8

readList :: ReadS [Int8]

readPrec :: ReadPrec Int8

readListPrec :: ReadPrec [Int8]

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

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

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

NFData Int8

Defined in Control.DeepSeq

Methods

rnf :: Int8 -> ()

Hashable Int8

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int8 -> Int

hash :: Int8 -> Int

data Int16

16-bit signed integer type

Instances

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]

Eq Int16

Since: base-2.1

Defined in GHC.Int

Methods

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

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

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

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

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

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

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

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

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

Num Int16

Since: base-2.1

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

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

Read Int16

Since: base-2.1

Defined in GHC.Int

Methods

readsPrec :: Int -> ReadS Int16

readList :: ReadS [Int16]

readPrec :: ReadPrec Int16

readListPrec :: ReadPrec [Int16]

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

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

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

NFData Int16

Defined in Control.DeepSeq

Methods

rnf :: Int16 -> ()

Hashable Int16

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int16 -> Int

hash :: Int16 -> Int

data Int32

32-bit signed integer type

Instances

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]

Eq Int32

Since: base-2.1

Defined in GHC.Int

Methods

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

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

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

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

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

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

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

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

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

Num Int32

Since: base-2.1

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

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

Read Int32

Since: base-2.1

Defined in GHC.Int

Methods

readsPrec :: Int -> ReadS Int32

readList :: ReadS [Int32]

readPrec :: ReadPrec Int32

readListPrec :: ReadPrec [Int32]

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

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

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

NFData Int32

Defined in Control.DeepSeq

Methods

rnf :: Int32 -> ()

Hashable Int32

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int32 -> Int

hash :: Int32 -> Int

data Int64

64-bit signed integer type

Instances

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]

Eq Int64

Since: base-2.1

Defined in GHC.Int

Methods

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

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

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

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

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

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

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

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

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

Num Int64

Since: base-2.1

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

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

Read Int64

Since: base-2.1

Defined in GHC.Int

Methods

readsPrec :: Int -> ReadS Int64

readList :: ReadS [Int64]

readPrec :: ReadPrec Int64

readListPrec :: ReadPrec [Int64]

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

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

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

NFData Int64

Defined in Control.DeepSeq

Methods

rnf :: Int64 -> ()

Hashable Int64

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Int64 -> Int

hash :: Int64 -> Int

data Word

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

Instances

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]

Eq Word

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

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

Num Word

Since: base-2.1

Defined in GHC.Num

Methods

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

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

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

negate :: Word -> Word

abs :: Word -> Word

signum :: Word -> Word

fromInteger :: Integer -> Word

Ord Word

Defined in GHC.Classes

Methods

compare :: Word -> Word -> Ordering

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

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

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

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

max :: Word -> Word -> Word

min :: Word -> Word -> Word

Read Word

Since: base-4.5.0.0

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word

readList :: ReadS [Word]

readPrec :: ReadPrec Word

readListPrec :: ReadPrec [Word]

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

Ix Word

Since: base-4.6.0.0

Defined in GHC.Arr

Methods

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

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

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

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

rangeSize :: (Word, Word) -> Int

unsafeRangeSize :: (Word, Word) -> Int

Bits Word

Since: base-2.1

Defined in Data.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 Data.Bits

Methods

finiteBitSize :: Word -> Int

countLeadingZeros :: Word -> Int

countTrailingZeros :: Word -> Int

NFData Word

Defined in Control.DeepSeq

Methods

rnf :: Word -> ()

Hashable Word

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word -> Int

hash :: Word -> Int

Generic1 (URec Word :: k -> Type)

Defined in GHC.Generics

Associated Types

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

Methods

from1 :: URec Word a -> Rep1 (URec Word) a

to1 :: Rep1 (URec Word) a -> URec Word 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

Foldable (URec Word :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

toList :: URec Word a -> [a]

null :: URec Word a -> Bool

length :: URec Word a -> Int

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

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

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

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

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

Traversable (URec Word :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

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

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

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

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

Eq (URec Word p)

Since: base-4.9.0.0

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

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

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

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 Word8

8-bit unsigned integer type

Instances

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]

Eq Word8

Since: base-2.1

Defined in GHC.Word

Methods

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

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

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

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

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

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

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

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

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

Num Word8

Since: base-2.1

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

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

Read Word8

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word8

readList :: ReadS [Word8]

readPrec :: ReadPrec Word8

readListPrec :: ReadPrec [Word8]

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

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

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

NFData Word8

Defined in Control.DeepSeq

Methods

rnf :: Word8 -> ()

Hashable Word8

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word8 -> Int

hash :: Word8 -> Int

data Word16

16-bit unsigned integer type

Instances

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]

Eq Word16

Since: base-2.1

Defined in GHC.Word

Methods

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

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

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

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

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

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

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

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

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

Num Word16

Since: base-2.1

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

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

Read Word16

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word16

readList :: ReadS [Word16]

readPrec :: ReadPrec Word16

readListPrec :: ReadPrec [Word16]

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

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

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

NFData Word16

Defined in Control.DeepSeq

Methods

rnf :: Word16 -> ()

Hashable Word16

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word16 -> Int

hash :: Word16 -> Int

data Word32

32-bit unsigned integer type

Instances

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]

Eq Word32

Since: base-2.1

Defined in GHC.Word

Methods

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

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

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

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

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

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

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

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

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

Num Word32

Since: base-2.1

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

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

Read Word32

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word32

readList :: ReadS [Word32]

readPrec :: ReadPrec Word32

readListPrec :: ReadPrec [Word32]

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

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

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

NFData Word32

Defined in Control.DeepSeq

Methods

rnf :: Word32 -> ()

Hashable Word32

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word32 -> Int

hash :: Word32 -> Int

data Word64

64-bit unsigned integer type

Instances

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]

Eq Word64

Since: base-2.1

Defined in GHC.Word

Methods

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

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

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

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

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

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

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

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

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

Num Word64

Since: base-2.1

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

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

Read Word64

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word64

readList :: ReadS [Word64]

readPrec :: ReadPrec Word64

readListPrec :: ReadPrec [Word64]

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

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

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

NFData Word64

Defined in Control.DeepSeq

Methods

rnf :: Word64 -> ()

Hashable Word64

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Word64 -> Int

hash :: Word64 -> Int

byteSwap64 :: Word64 -> Word64

Reverse order of bytes in Word64.

Since: base-4.7.0.0

byteSwap32 :: Word32 -> Word32

Reverse order of bytes in Word32.

Since: base-4.7.0.0

byteSwap16 :: Word16 -> Word16

Swap bytes in Word16.

Since: base-4.7.0.0

maxInt :: Int

minInt :: Int

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

Floating CFloat

Defined in Foreign.C.Types

Methods

pi :: CFloat

exp :: CFloat -> CFloat

log :: CFloat -> CFloat

sqrt :: CFloat -> CFloat

(**) :: CFloat -> CFloat -> CFloat

logBase :: CFloat -> CFloat -> CFloat

sin :: CFloat -> CFloat

cos :: CFloat -> CFloat

tan :: CFloat -> CFloat

asin :: CFloat -> CFloat

acos :: CFloat -> CFloat

atan :: CFloat -> CFloat

sinh :: CFloat -> CFloat

cosh :: CFloat -> CFloat

tanh :: CFloat -> CFloat

asinh :: CFloat -> CFloat

acosh :: CFloat -> CFloat

atanh :: CFloat -> CFloat

log1p :: CFloat -> CFloat

expm1 :: CFloat -> CFloat

log1pexp :: CFloat -> CFloat

log1mexp :: CFloat -> CFloat

Floating CDouble

Defined in Foreign.C.Types

Methods

pi :: CDouble

exp :: CDouble -> CDouble

log :: CDouble -> CDouble

sqrt :: CDouble -> CDouble

(**) :: CDouble -> CDouble -> CDouble

logBase :: CDouble -> CDouble -> CDouble

sin :: CDouble -> CDouble

cos :: CDouble -> CDouble

tan :: CDouble -> CDouble

asin :: CDouble -> CDouble

acos :: CDouble -> CDouble

atan :: CDouble -> CDouble

sinh :: CDouble -> CDouble

cosh :: CDouble -> CDouble

tanh :: CDouble -> CDouble

asinh :: CDouble -> CDouble

acosh :: CDouble -> CDouble

atanh :: CDouble -> CDouble

log1p :: CDouble -> CDouble

expm1 :: CDouble -> CDouble

log1pexp :: CDouble -> CDouble

log1mexp :: CDouble -> CDouble

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 (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.

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

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 CFloat

Defined in Foreign.C.Types

Methods

floatRadix :: CFloat -> Integer

floatDigits :: CFloat -> Int

floatRange :: CFloat -> (Int, Int)

decodeFloat :: CFloat -> (Integer, Int)

encodeFloat :: Integer -> Int -> CFloat

exponent :: CFloat -> Int

significand :: CFloat -> CFloat

scaleFloat :: Int -> CFloat -> CFloat

isNaN :: CFloat -> Bool

isInfinite :: CFloat -> Bool

isDenormalized :: CFloat -> Bool

isNegativeZero :: CFloat -> Bool

isIEEE :: CFloat -> Bool

atan2 :: CFloat -> CFloat -> CFloat

RealFloat CDouble

Defined in Foreign.C.Types

Methods

floatRadix :: CDouble -> Integer

floatDigits :: CDouble -> Int

floatRange :: CDouble -> (Int, Int)

decodeFloat :: CDouble -> (Integer, Int)

encodeFloat :: Integer -> Int -> CDouble

exponent :: CDouble -> Int

significand :: CDouble -> CDouble

scaleFloat :: Int -> CDouble -> CDouble

isNaN :: CDouble -> Bool

isInfinite :: CDouble -> Bool

isDenormalized :: CDouble -> Bool

isNegativeZero :: CDouble -> Bool

isIEEE :: CDouble -> Bool

atan2 :: CDouble -> CDouble -> CDouble

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 (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 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

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

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

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

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

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

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

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

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

Ord Double

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

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

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

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

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

Read Double

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Double

readList :: ReadS [Double]

readPrec :: ReadPrec Double

readListPrec :: ReadPrec [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

NFData Double

Defined in Control.DeepSeq

Methods

rnf :: Double -> ()

Hashable Double

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Double -> Int

hash :: Double -> Int

Generic1 (URec Double :: k -> Type)

Defined in GHC.Generics

Associated Types

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

Methods

from1 :: URec Double a -> Rep1 (URec Double) a

to1 :: Rep1 (URec Double) a -> URec Double 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

Foldable (URec Double :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

toList :: URec Double a -> [a]

null :: URec Double a -> Bool

length :: URec Double a -> Int

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

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

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

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

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

Traversable (URec Double :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

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

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

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

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

Eq (URec Double p)

Since: base-4.9.0.0

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

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

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

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)))

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

Eq Float

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

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

Ord Float

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

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

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

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

Defined in GHC.Classes

Methods

compare :: Float -> Float -> Ordering

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

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

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

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

max :: Float -> Float -> Float

min :: Float -> Float -> Float

Read Float

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Float

readList :: ReadS [Float]

readPrec :: ReadPrec Float

readListPrec :: ReadPrec [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

NFData Float

Defined in Control.DeepSeq

Methods

rnf :: Float -> ()

Hashable Float

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Float -> Int

hash :: Float -> Int

Generic1 (URec Float :: k -> Type)

Defined in GHC.Generics

Associated Types

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

Methods

from1 :: URec Float a -> Rep1 (URec Float) a

to1 :: Rep1 (URec Float) a -> URec Float 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

Foldable (URec Float :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

toList :: URec Float a -> [a]

null :: URec Float a -> Bool

length :: URec Float a -> Int

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

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

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

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

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

Traversable (URec Float :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

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

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

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

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

Eq (URec Float p)

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

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

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

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)))

class Num a where

Basic numeric class.

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

Associativity of (+)

(x + y) + z = x + (y + z)

Commutativity of (+)

x + y = y + x

fromInteger 0 is the additive identity

x + fromInteger 0 = x

negate gives the additive inverse

x + negate x = fromInteger 0

Associativity of (*)

(x * y) * z = x * (y * z)

fromInteger 1 is the multiplicative identity

x * fromInteger 1 = x and fromInteger 1 * x = x

Distributivity of (*) with respect to (+)

a * (b + c) = (a * b) + (a * c) and (b + c) * a = (b * a) + (c * a)

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

Minimal complete definition

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

Methods

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

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

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

negate :: a -> a

Unary negation.

abs :: a -> a

Absolute value.

signum :: a -> a

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

abs x * signum x == x

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

fromInteger :: Integer -> a

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

Instances

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 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 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 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 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

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 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 CChar

Defined in Foreign.C.Types

Methods

(+) :: CChar -> CChar -> CChar

(-) :: CChar -> CChar -> CChar

(*) :: CChar -> CChar -> CChar

negate :: CChar -> CChar

abs :: CChar -> CChar

signum :: CChar -> CChar

fromInteger :: Integer -> CChar

Num CSChar

Defined in Foreign.C.Types

Methods

(+) :: CSChar -> CSChar -> CSChar

(-) :: CSChar -> CSChar -> CSChar

(*) :: CSChar -> CSChar -> CSChar

negate :: CSChar -> CSChar

abs :: CSChar -> CSChar

signum :: CSChar -> CSChar

fromInteger :: Integer -> CSChar

Num CUChar

Defined in Foreign.C.Types

Methods

(+) :: CUChar -> CUChar -> CUChar

(-) :: CUChar -> CUChar -> CUChar

(*) :: CUChar -> CUChar -> CUChar

negate :: CUChar -> CUChar

abs :: CUChar -> CUChar

signum :: CUChar -> CUChar

fromInteger :: Integer -> CUChar

Num CShort

Defined in Foreign.C.Types

Methods

(+) :: CShort -> CShort -> CShort

(-) :: CShort -> CShort -> CShort

(*) :: CShort -> CShort -> CShort

negate :: CShort -> CShort

abs :: CShort -> CShort

signum :: CShort -> CShort

fromInteger :: Integer -> CShort

Num CUShort

Defined in Foreign.C.Types

Methods

(+) :: CUShort -> CUShort -> CUShort

(-) :: CUShort -> CUShort -> CUShort

(*) :: CUShort -> CUShort -> CUShort

negate :: CUShort -> CUShort

abs :: CUShort -> CUShort

signum :: CUShort -> CUShort

fromInteger :: Integer -> CUShort

Num CInt

Defined in Foreign.C.Types

Methods

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

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

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

negate :: CInt -> CInt

abs :: CInt -> CInt

signum :: CInt -> CInt

fromInteger :: Integer -> CInt

Num CUInt

Defined in Foreign.C.Types

Methods

(+) :: CUInt -> CUInt -> CUInt

(-) :: CUInt -> CUInt -> CUInt

(*) :: CUInt -> CUInt -> CUInt

negate :: CUInt -> CUInt

abs :: CUInt -> CUInt

signum :: CUInt -> CUInt

fromInteger :: Integer -> CUInt

Num CLong

Defined in Foreign.C.Types

Methods

(+) :: CLong -> CLong -> CLong

(-) :: CLong -> CLong -> CLong

(*) :: CLong -> CLong -> CLong

negate :: CLong -> CLong

abs :: CLong -> CLong

signum :: CLong -> CLong

fromInteger :: Integer -> CLong

Num CULong

Defined in Foreign.C.Types

Methods

(+) :: CULong -> CULong -> CULong

(-) :: CULong -> CULong -> CULong

(*) :: CULong -> CULong -> CULong

negate :: CULong -> CULong

abs :: CULong -> CULong

signum :: CULong -> CULong

fromInteger :: Integer -> CULong

Num CLLong

Defined in Foreign.C.Types

Methods

(+) :: CLLong -> CLLong -> CLLong

(-) :: CLLong -> CLLong -> CLLong

(*) :: CLLong -> CLLong -> CLLong

negate :: CLLong -> CLLong

abs :: CLLong -> CLLong

signum :: CLLong -> CLLong

fromInteger :: Integer -> CLLong

Num CULLong

Defined in Foreign.C.Types

Methods

(+) :: CULLong -> CULLong -> CULLong

(-) :: CULLong -> CULLong -> CULLong

(*) :: CULLong -> CULLong -> CULLong

negate :: CULLong -> CULLong

abs :: CULLong -> CULLong

signum :: CULLong -> CULLong

fromInteger :: Integer -> CULLong

Num CBool

Defined in Foreign.C.Types

Methods

(+) :: CBool -> CBool -> CBool

(-) :: CBool -> CBool -> CBool

(*) :: CBool -> CBool -> CBool

negate :: CBool -> CBool

abs :: CBool -> CBool

signum :: CBool -> CBool

fromInteger :: Integer -> CBool

Num CFloat

Defined in Foreign.C.Types

Methods

(+) :: CFloat -> CFloat -> CFloat

(-) :: CFloat -> CFloat -> CFloat

(*) :: CFloat -> CFloat -> CFloat

negate :: CFloat -> CFloat

abs :: CFloat -> CFloat

signum :: CFloat -> CFloat

fromInteger :: Integer -> CFloat

Num CDouble

Defined in Foreign.C.Types

Methods

(+) :: CDouble -> CDouble -> CDouble

(-) :: CDouble -> CDouble -> CDouble

(*) :: CDouble -> CDouble -> CDouble

negate :: CDouble -> CDouble

abs :: CDouble -> CDouble

signum :: CDouble -> CDouble

fromInteger :: Integer -> CDouble

Num CPtrdiff

Defined in Foreign.C.Types

Methods

(+) :: CPtrdiff -> CPtrdiff -> CPtrdiff

(-) :: CPtrdiff -> CPtrdiff -> CPtrdiff

(*) :: CPtrdiff -> CPtrdiff -> CPtrdiff

negate :: CPtrdiff -> CPtrdiff

abs :: CPtrdiff -> CPtrdiff

signum :: CPtrdiff -> CPtrdiff

fromInteger :: Integer -> CPtrdiff

Num CSize

Defined in Foreign.C.Types

Methods

(+) :: CSize -> CSize -> CSize

(-) :: CSize -> CSize -> CSize

(*) :: CSize -> CSize -> CSize

negate :: CSize -> CSize

abs :: CSize -> CSize

signum :: CSize -> CSize

fromInteger :: Integer -> CSize

Num CWchar

Defined in Foreign.C.Types

Methods

(+) :: CWchar -> CWchar -> CWchar

(-) :: CWchar -> CWchar -> CWchar

(*) :: CWchar -> CWchar -> CWchar

negate :: CWchar -> CWchar

abs :: CWchar -> CWchar

signum :: CWchar -> CWchar

fromInteger :: Integer -> CWchar

Num CSigAtomic

Defined in Foreign.C.Types

Methods

(+) :: CSigAtomic -> CSigAtomic -> CSigAtomic

(-) :: CSigAtomic -> CSigAtomic -> CSigAtomic

(*) :: CSigAtomic -> CSigAtomic -> CSigAtomic

negate :: CSigAtomic -> CSigAtomic

abs :: CSigAtomic -> CSigAtomic

signum :: CSigAtomic -> CSigAtomic

fromInteger :: Integer -> CSigAtomic

Num CClock

Defined in Foreign.C.Types

Methods

(+) :: CClock -> CClock -> CClock

(-) :: CClock -> CClock -> CClock

(*) :: CClock -> CClock -> CClock

negate :: CClock -> CClock

abs :: CClock -> CClock

signum :: CClock -> CClock

fromInteger :: Integer -> CClock

Num CTime

Defined in Foreign.C.Types

Methods

(+) :: CTime -> CTime -> CTime

(-) :: CTime -> CTime -> CTime

(*) :: CTime -> CTime -> CTime

negate :: CTime -> CTime

abs :: CTime -> CTime

signum :: CTime -> CTime

fromInteger :: Integer -> CTime

Num CUSeconds

Defined in Foreign.C.Types

Methods

(+) :: CUSeconds -> CUSeconds -> CUSeconds

(-) :: CUSeconds -> CUSeconds -> CUSeconds

(*) :: CUSeconds -> CUSeconds -> CUSeconds

negate :: CUSeconds -> CUSeconds

abs :: CUSeconds -> CUSeconds

signum :: CUSeconds -> CUSeconds

fromInteger :: Integer -> CUSeconds

Num CSUSeconds

Defined in Foreign.C.Types

Methods

(+) :: CSUSeconds -> CSUSeconds -> CSUSeconds

(-) :: CSUSeconds -> CSUSeconds -> CSUSeconds

(*) :: CSUSeconds -> CSUSeconds -> CSUSeconds

negate :: CSUSeconds -> CSUSeconds

abs :: CSUSeconds -> CSUSeconds

signum :: CSUSeconds -> CSUSeconds

fromInteger :: Integer -> CSUSeconds

Num CIntPtr

Defined in Foreign.C.Types

Methods

(+) :: CIntPtr -> CIntPtr -> CIntPtr

(-) :: CIntPtr -> CIntPtr -> CIntPtr

(*) :: CIntPtr -> CIntPtr -> CIntPtr

negate :: CIntPtr -> CIntPtr

abs :: CIntPtr -> CIntPtr

signum :: CIntPtr -> CIntPtr

fromInteger :: Integer -> CIntPtr

Num CUIntPtr

Defined in Foreign.C.Types

Methods

(+) :: CUIntPtr -> CUIntPtr -> CUIntPtr

(-) :: CUIntPtr -> CUIntPtr -> CUIntPtr

(*) :: CUIntPtr -> CUIntPtr -> CUIntPtr

negate :: CUIntPtr -> CUIntPtr

abs :: CUIntPtr -> CUIntPtr

signum :: CUIntPtr -> CUIntPtr

fromInteger :: Integer -> CUIntPtr

Num CIntMax

Defined in Foreign.C.Types

Methods

(+) :: CIntMax -> CIntMax -> CIntMax

(-) :: CIntMax -> CIntMax -> CIntMax

(*) :: CIntMax -> CIntMax -> CIntMax

negate :: CIntMax -> CIntMax

abs :: CIntMax -> CIntMax

signum :: CIntMax -> CIntMax

fromInteger :: Integer -> CIntMax

Num CUIntMax

Defined in Foreign.C.Types

Methods

(+) :: CUIntMax -> CUIntMax -> CUIntMax

(-) :: CUIntMax -> CUIntMax -> CUIntMax

(*) :: CUIntMax -> CUIntMax -> CUIntMax

negate :: CUIntMax -> CUIntMax

abs :: CUIntMax -> CUIntMax

signum :: CUIntMax -> CUIntMax

fromInteger :: Integer -> CUIntMax

Num WordPtr

Defined in Foreign.Ptr

Methods

(+) :: WordPtr -> WordPtr -> WordPtr

(-) :: WordPtr -> WordPtr -> WordPtr

(*) :: WordPtr -> WordPtr -> WordPtr

negate :: WordPtr -> WordPtr

abs :: WordPtr -> WordPtr

signum :: WordPtr -> WordPtr

fromInteger :: Integer -> WordPtr

Num IntPtr

Defined in Foreign.Ptr

Methods

(+) :: IntPtr -> IntPtr -> IntPtr

(-) :: IntPtr -> IntPtr -> IntPtr

(*) :: IntPtr -> IntPtr -> IntPtr

negate :: IntPtr -> IntPtr

abs :: IntPtr -> IntPtr

signum :: IntPtr -> IntPtr

fromInteger :: Integer -> IntPtr

Num CodePoint

Defined in Data.Text.Encoding

Methods

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

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

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

negate :: CodePoint -> CodePoint

abs :: CodePoint -> CodePoint

signum :: CodePoint -> CodePoint

fromInteger :: Integer -> CodePoint

Num DecoderState

Defined in Data.Text.Encoding

Methods

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

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

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

negate :: DecoderState -> DecoderState

abs :: DecoderState -> DecoderState

signum :: DecoderState -> DecoderState

fromInteger :: Integer -> DecoderState

Integral a => Num (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

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

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

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

negate :: Ratio a -> Ratio a

abs :: Ratio a -> Ratio a

signum :: Ratio a -> Ratio a

fromInteger :: Integer -> Ratio a

RealFloat a => Num (Complex a)

Since: base-2.1

Defined in Data.Complex

Methods

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

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

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

negate :: Complex a -> Complex a

abs :: Complex a -> Complex a

signum :: Complex a -> Complex a

fromInteger :: Integer -> Complex a

HasResolution a => Num (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

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

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

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

negate :: Fixed a -> Fixed a

abs :: Fixed a -> Fixed a

signum :: Fixed a -> Fixed a

fromInteger :: Integer -> Fixed a

Num a => Num (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

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

negate :: Min a -> Min a

abs :: Min a -> Min a

signum :: Min a -> Min a

fromInteger :: Integer -> Min a

Num a => Num (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

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

negate :: Max a -> Max a

abs :: Max a -> Max a

signum :: Max a -> Max a

fromInteger :: Integer -> Max a

Num a => Num (Identity a)

Since: base-4.9.0.0

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 (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

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 (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 (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)

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

data Integer

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

Useful properties resulting from the invariants:

• abs (S# _) <= abs (Jp# _)

• abs (S# _) <  abs (Jn# _)

Instances

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]

Eq Integer

Defined in GHC.Integer.Type

Methods

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

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

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

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

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

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

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

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

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

Num Integer

Since: base-2.1

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

Ord Integer

Defined in GHC.Integer.Type

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

Read Integer

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Integer

readList :: ReadS [Integer]

readPrec :: ReadPrec Integer

readListPrec :: ReadPrec [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

Ix Integer

Since: base-2.1

Defined in GHC.Arr

Methods

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

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

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

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

rangeSize :: (Integer, Integer) -> Int

unsafeRangeSize :: (Integer, Integer) -> Int

Bits Integer

Since: base-2.1

Defined in Data.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

NFData Integer

Defined in Control.DeepSeq

Methods

rnf :: Integer -> ()

Hashable Integer

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Integer -> Int

hash :: Integer -> Int

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

the same as flip (-).

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

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

general coercion from integral types

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

general coercion to fractional types

class Num a => Fractional a where

Fractional numbers, supporting real division.

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

recip gives the multiplicative inverse

x * recip x = recip x * x = fromInteger 1

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

Minimal complete definition

fromRational, (recip | (/))

Methods

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

fractional division

recip :: a -> a

reciprocal fraction

fromRational :: Rational -> a

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

Instances

Fractional CFloat

Defined in Foreign.C.Types

Methods

(/) :: CFloat -> CFloat -> CFloat

recip :: CFloat -> CFloat

fromRational :: Rational -> CFloat

Fractional CDouble

Defined in Foreign.C.Types

Methods

(/) :: CDouble -> CDouble -> CDouble

recip :: CDouble -> CDouble

fromRational :: Rational -> CDouble

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

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

HasResolution a => Fractional (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

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

recip :: Fixed a -> Fixed a

fromRational :: Rational -> Fixed a

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

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

recip :: Identity a -> Identity a

fromRational :: Rational -> Identity 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 (Real a, Enum a) => Integral a where

Integral numbers, supporting integer division.

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

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

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

Minimal complete definition

quotRem, toInteger

Methods

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

integer division truncated toward zero

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

integer remainder, satisfying

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

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

integer division truncated toward negative infinity

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

integer modulus, satisfying

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

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

simultaneous quot and rem

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

simultaneous div and mod

toInteger :: a -> Integer

conversion to Integer

Instances

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 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 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 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 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 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 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 CChar

Defined in Foreign.C.Types

Methods

quot :: CChar -> CChar -> CChar

rem :: CChar -> CChar -> CChar

div :: CChar -> CChar -> CChar

mod :: CChar -> CChar -> CChar

quotRem :: CChar -> CChar -> (CChar, CChar)

divMod :: CChar -> CChar -> (CChar, CChar)

toInteger :: CChar -> Integer

Integral CSChar

Defined in Foreign.C.Types

Methods

quot :: CSChar -> CSChar -> CSChar

rem :: CSChar -> CSChar -> CSChar

div :: CSChar -> CSChar -> CSChar

mod :: CSChar -> CSChar -> CSChar

quotRem :: CSChar -> CSChar -> (CSChar, CSChar)

divMod :: CSChar -> CSChar -> (CSChar, CSChar)

toInteger :: CSChar -> Integer

Integral CUChar

Defined in Foreign.C.Types

Methods

quot :: CUChar -> CUChar -> CUChar

rem :: CUChar -> CUChar -> CUChar

div :: CUChar -> CUChar -> CUChar

mod :: CUChar -> CUChar -> CUChar

quotRem :: CUChar -> CUChar -> (CUChar, CUChar)

divMod :: CUChar -> CUChar -> (CUChar, CUChar)

toInteger :: CUChar -> Integer

Integral CShort

Defined in Foreign.C.Types

Methods

quot :: CShort -> CShort -> CShort

rem :: CShort -> CShort -> CShort

div :: CShort -> CShort -> CShort

mod :: CShort -> CShort -> CShort

quotRem :: CShort -> CShort -> (CShort, CShort)

divMod :: CShort -> CShort -> (CShort, CShort)

toInteger :: CShort -> Integer

Integral CUShort

Defined in Foreign.C.Types

Methods

quot :: CUShort -> CUShort -> CUShort

rem :: CUShort -> CUShort -> CUShort

div :: CUShort -> CUShort -> CUShort

mod :: CUShort -> CUShort -> CUShort

quotRem :: CUShort -> CUShort -> (CUShort, CUShort)

divMod :: CUShort -> CUShort -> (CUShort, CUShort)

toInteger :: CUShort -> Integer

Integral CInt

Defined in Foreign.C.Types

Methods

quot :: CInt -> CInt -> CInt

rem :: CInt -> CInt -> CInt

div :: CInt -> CInt -> CInt

mod :: CInt -> CInt -> CInt

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

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

toInteger :: CInt -> Integer

Integral CUInt

Defined in Foreign.C.Types

Methods

quot :: CUInt -> CUInt -> CUInt

rem :: CUInt -> CUInt -> CUInt

div :: CUInt -> CUInt -> CUInt

mod :: CUInt -> CUInt -> CUInt

quotRem :: CUInt -> CUInt -> (CUInt, CUInt)

divMod :: CUInt -> CUInt -> (CUInt, CUInt)

toInteger :: CUInt -> Integer

Integral CLong

Defined in Foreign.C.Types

Methods

quot :: CLong -> CLong -> CLong

rem :: CLong -> CLong -> CLong

div :: CLong -> CLong -> CLong

mod :: CLong -> CLong -> CLong

quotRem :: CLong -> CLong -> (CLong, CLong)

divMod :: CLong -> CLong -> (CLong, CLong)

toInteger :: CLong -> Integer

Integral CULong

Defined in Foreign.C.Types

Methods

quot :: CULong -> CULong -> CULong

rem :: CULong -> CULong -> CULong

div :: CULong -> CULong -> CULong

mod :: CULong -> CULong -> CULong

quotRem :: CULong -> CULong -> (CULong, CULong)

divMod :: CULong -> CULong -> (CULong, CULong)

toInteger :: CULong -> Integer

Integral CLLong

Defined in Foreign.C.Types

Methods

quot :: CLLong -> CLLong -> CLLong

rem :: CLLong -> CLLong -> CLLong

div :: CLLong -> CLLong -> CLLong

mod :: CLLong -> CLLong -> CLLong

quotRem :: CLLong -> CLLong -> (CLLong, CLLong)

divMod :: CLLong -> CLLong -> (CLLong, CLLong)

toInteger :: CLLong -> Integer

Integral CULLong

Defined in Foreign.C.Types

Methods

quot :: CULLong -> CULLong -> CULLong

rem :: CULLong -> CULLong -> CULLong

div :: CULLong -> CULLong -> CULLong

mod :: CULLong -> CULLong -> CULLong

quotRem :: CULLong -> CULLong -> (CULLong, CULLong)

divMod :: CULLong -> CULLong -> (CULLong, CULLong)

toInteger :: CULLong -> Integer

Integral CBool

Defined in Foreign.C.Types

Methods

quot :: CBool -> CBool -> CBool

rem :: CBool -> CBool -> CBool

div :: CBool -> CBool -> CBool

mod :: CBool -> CBool -> CBool

quotRem :: CBool -> CBool -> (CBool, CBool)

divMod :: CBool -> CBool -> (CBool, CBool)

toInteger :: CBool -> Integer

Integral CPtrdiff

Defined in Foreign.C.Types

Methods

quot :: CPtrdiff -> CPtrdiff -> CPtrdiff

rem :: CPtrdiff -> CPtrdiff -> CPtrdiff

div :: CPtrdiff -> CPtrdiff -> CPtrdiff

mod :: CPtrdiff -> CPtrdiff -> CPtrdiff

quotRem :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff)

divMod :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff)

toInteger :: CPtrdiff -> Integer

Integral CSize

Defined in Foreign.C.Types

Methods

quot :: CSize -> CSize -> CSize

rem :: CSize -> CSize -> CSize

div :: CSize -> CSize -> CSize

mod :: CSize -> CSize -> CSize

quotRem :: CSize -> CSize -> (CSize, CSize)

divMod :: CSize -> CSize -> (CSize, CSize)

toInteger :: CSize -> Integer

Integral CWchar

Defined in Foreign.C.Types

Methods

quot :: CWchar -> CWchar -> CWchar

rem :: CWchar -> CWchar -> CWchar

div :: CWchar -> CWchar -> CWchar

mod :: CWchar -> CWchar -> CWchar

quotRem :: CWchar -> CWchar -> (CWchar, CWchar)

divMod :: CWchar -> CWchar -> (CWchar, CWchar)

toInteger :: CWchar -> Integer

Integral CSigAtomic

Defined in Foreign.C.Types

Methods

quot :: CSigAtomic -> CSigAtomic -> CSigAtomic

rem :: CSigAtomic -> CSigAtomic -> CSigAtomic

div :: CSigAtomic -> CSigAtomic -> CSigAtomic

mod :: CSigAtomic -> CSigAtomic -> CSigAtomic

quotRem :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic)

divMod :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic)

toInteger :: CSigAtomic -> Integer

Integral CIntPtr

Defined in Foreign.C.Types

Methods

quot :: CIntPtr -> CIntPtr -> CIntPtr

rem :: CIntPtr -> CIntPtr -> CIntPtr

div :: CIntPtr -> CIntPtr -> CIntPtr

mod :: CIntPtr -> CIntPtr -> CIntPtr

quotRem :: CIntPtr -> CIntPtr -> (CIntPtr, CIntPtr)

divMod :: CIntPtr -> CIntPtr -> (CIntPtr, CIntPtr)

toInteger :: CIntPtr -> Integer

Integral CUIntPtr

Defined in Foreign.C.Types

Methods

quot :: CUIntPtr -> CUIntPtr -> CUIntPtr

rem :: CUIntPtr -> CUIntPtr -> CUIntPtr

div :: CUIntPtr -> CUIntPtr -> CUIntPtr

mod :: CUIntPtr -> CUIntPtr -> CUIntPtr

quotRem :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr)

divMod :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr)

toInteger :: CUIntPtr -> Integer

Integral CIntMax

Defined in Foreign.C.Types

Methods

quot :: CIntMax -> CIntMax -> CIntMax

rem :: CIntMax -> CIntMax -> CIntMax

div :: CIntMax -> CIntMax -> CIntMax

mod :: CIntMax -> CIntMax -> CIntMax

quotRem :: CIntMax -> CIntMax -> (CIntMax, CIntMax)

divMod :: CIntMax -> CIntMax -> (CIntMax, CIntMax)

toInteger :: CIntMax -> Integer

Integral CUIntMax

Defined in Foreign.C.Types

Methods

quot :: CUIntMax -> CUIntMax -> CUIntMax

rem :: CUIntMax -> CUIntMax -> CUIntMax

div :: CUIntMax -> CUIntMax -> CUIntMax

mod :: CUIntMax -> CUIntMax -> CUIntMax

quotRem :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax)

divMod :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax)

toInteger :: CUIntMax -> Integer

Integral WordPtr

Defined in Foreign.Ptr

Methods

quot :: WordPtr -> WordPtr -> WordPtr

rem :: WordPtr -> WordPtr -> WordPtr

div :: WordPtr -> WordPtr -> WordPtr

mod :: WordPtr -> WordPtr -> WordPtr

quotRem :: WordPtr -> WordPtr -> (WordPtr, WordPtr)

divMod :: WordPtr -> WordPtr -> (WordPtr, WordPtr)

toInteger :: WordPtr -> Integer

Integral IntPtr

Defined in Foreign.Ptr

Methods

quot :: IntPtr -> IntPtr -> IntPtr

rem :: IntPtr -> IntPtr -> IntPtr

div :: IntPtr -> IntPtr -> IntPtr

mod :: IntPtr -> IntPtr -> IntPtr

quotRem :: IntPtr -> IntPtr -> (IntPtr, IntPtr)

divMod :: IntPtr -> IntPtr -> (IntPtr, IntPtr)

toInteger :: IntPtr -> 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

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

Methods

toRational :: a -> Rational

the rational equivalent of its real argument with full precision

Instances

Real Int

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Int -> Rational

Real Int8

Since: base-2.1

Defined in GHC.Int

Methods

toRational :: Int8 -> Rational

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 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 Word

Since: base-2.1

Defined in GHC.Real

Methods

toRational :: Word -> Rational

Real Word8

Since: base-2.1

Defined in GHC.Word

Methods

toRational :: Word8 -> 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 CChar

Defined in Foreign.C.Types

Methods

toRational :: CChar -> Rational

Real CSChar

Defined in Foreign.C.Types

Methods

toRational :: CSChar -> Rational

Real CUChar

Defined in Foreign.C.Types

Methods

toRational :: CUChar -> Rational

Real CShort

Defined in Foreign.C.Types

Methods

toRational :: CShort -> Rational

Real CUShort

Defined in Foreign.C.Types

Methods

toRational :: CUShort -> Rational

Real CInt

Defined in Foreign.C.Types

Methods

toRational :: CInt -> Rational

Real CUInt

Defined in Foreign.C.Types

Methods

toRational :: CUInt -> Rational

Real CLong

Defined in Foreign.C.Types

Methods

toRational :: CLong -> Rational

Real CULong

Defined in Foreign.C.Types

Methods

toRational :: CULong -> Rational

Real CLLong

Defined in Foreign.C.Types

Methods

toRational :: CLLong -> Rational

Real CULLong

Defined in Foreign.C.Types

Methods

toRational :: CULLong -> Rational

Real CBool

Defined in Foreign.C.Types

Methods

toRational :: CBool -> Rational

Real CFloat

Defined in Foreign.C.Types

Methods

toRational :: CFloat -> Rational

Real CDouble

Defined in Foreign.C.Types

Methods

toRational :: CDouble -> Rational

Real CPtrdiff

Defined in Foreign.C.Types

Methods

toRational :: CPtrdiff -> Rational

Real CSize

Defined in Foreign.C.Types

Methods

toRational :: CSize -> Rational

Real CWchar

Defined in Foreign.C.Types

Methods

toRational :: CWchar -> Rational

Real CSigAtomic

Defined in Foreign.C.Types

Methods

toRational :: CSigAtomic -> Rational

Real CClock

Defined in Foreign.C.Types

Methods

toRational :: CClock -> Rational

Real CTime

Defined in Foreign.C.Types

Methods

toRational :: CTime -> Rational

Real CUSeconds

Defined in Foreign.C.Types

Methods

toRational :: CUSeconds -> Rational

Real CSUSeconds

Defined in Foreign.C.Types

Methods

toRational :: CSUSeconds -> Rational

Real CIntPtr

Defined in Foreign.C.Types

Methods

toRational :: CIntPtr -> Rational

Real CUIntPtr

Defined in Foreign.C.Types

Methods

toRational :: CUIntPtr -> Rational

Real CIntMax

Defined in Foreign.C.Types

Methods

toRational :: CIntMax -> Rational

Real CUIntMax

Defined in Foreign.C.Types

Methods

toRational :: CUIntMax -> Rational

Real WordPtr

Defined in Foreign.Ptr

Methods

toRational :: WordPtr -> Rational

Real IntPtr

Defined in Foreign.Ptr

Methods

toRational :: IntPtr -> Rational

Integral a => Real (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Ratio a -> Rational

HasResolution a => Real (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

toRational :: Fixed a -> 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 (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 CFloat

Defined in Foreign.C.Types

Methods

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

truncate :: Integral b => CFloat -> b

round :: Integral b => CFloat -> b

ceiling :: Integral b => CFloat -> b

floor :: Integral b => CFloat -> b

RealFrac CDouble

Defined in Foreign.C.Types

Methods

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

truncate :: Integral b => CDouble -> b

round :: Integral b => CDouble -> b

ceiling :: Integral b => CDouble -> b

floor :: Integral b => CDouble -> 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

HasResolution a => RealFrac (Fixed a)

Since: base-2.1

Defined in Data.Fixed

Methods

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

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

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

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

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

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 (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 => 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]

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 => 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

(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 :: (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 => 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 => 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

(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 => 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 -> ()

Hashable a => Hashable (Ratio a)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Ratio a -> Int

hash :: Ratio a -> Int

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.

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

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

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.

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

raise a number to an integral power

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

raise a number to a non-negative integral power

odd :: Integral a => a -> Bool

even :: Integral a => a -> Bool

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.

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.

data Natural

Type representing arbitrary-precision non-negative integers.

>>> 2^100 :: Natural
1267650600228229401496703205376

Operations whose result would be negative throw (Underflow :: ArithException),

>>> -1 :: Natural
*** Exception: arithmetic underflow

Since: base-4.8.0.0

Instances

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]

Eq Natural

Since: base-4.8.0.0

Defined in GHC.Natural

Methods

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

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

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

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 :: (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

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

Ord Natural

Since: base-4.8.0.0

Defined in GHC.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

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]

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

Ix Natural

Since: base-4.8.0.0

Defined in GHC.Arr

Methods

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

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

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

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

rangeSize :: (Natural, Natural) -> Int

unsafeRangeSize :: (Natural, Natural) -> Int

Bits Natural

Since: base-4.8.0

Defined in Data.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

NFData Natural

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Natural -> ()

Hashable Natural

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Natural -> Int

hash :: Natural -> Int

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

integerToNatural :: Integer -> Maybe Natural

Tranforms 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