GHC.Integer

Compatibility module for pre ghc-bignum code.

Documentation

data Integer

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

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

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

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

Instances

Data Integer

Since: base-4.0.0.0

Defined in Data.Data

Methods

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

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

toConstr :: Integer -> Constr

dataTypeOf :: Integer -> DataType

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

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

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

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

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

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

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

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

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

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

Bits Integer

Since: base-2.1

Defined in GHC.Bits

Methods

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

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

xor :: Integer -> Integer -> Integer

complement :: Integer -> Integer

shift :: Integer -> Int -> Integer

rotate :: Integer -> Int -> Integer

zeroBits :: Integer

bit :: Int -> Integer

setBit :: Integer -> Int -> Integer

clearBit :: Integer -> Int -> Integer

complementBit :: Integer -> Int -> Integer

testBit :: Integer -> Int -> Bool

bitSizeMaybe :: Integer -> Maybe Int

bitSize :: Integer -> Int

isSigned :: Integer -> Bool

shiftL :: Integer -> Int -> Integer

unsafeShiftL :: Integer -> Int -> Integer

shiftR :: Integer -> Int -> Integer

unsafeShiftR :: Integer -> Int -> Integer

rotateL :: Integer -> Int -> Integer

rotateR :: Integer -> Int -> Integer

popCount :: Integer -> Int

Enum Integer

Since: base-2.1

Defined in GHC.Enum

Methods

succ :: Integer -> Integer

pred :: Integer -> Integer

toEnum :: Int -> Integer

fromEnum :: Integer -> Int

enumFrom :: Integer -> [Integer]

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

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

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

Ix Integer

Since: base-2.1

Defined in GHC.Ix

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

Num Integer

Since: base-2.1

Defined in GHC.Num

Methods

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

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

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

negate :: Integer -> Integer

abs :: Integer -> Integer

signum :: Integer -> Integer

fromInteger :: Integer -> Integer

Read Integer

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Integer

readList :: ReadS [Integer]

readPrec :: ReadPrec Integer

readListPrec :: ReadPrec [Integer]

Integral Integer

Since: base-2.0.1

Defined in GHC.Real

Methods

quot :: Integer -> Integer -> Integer

rem :: Integer -> Integer -> Integer

div :: Integer -> Integer -> Integer

mod :: Integer -> Integer -> Integer

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

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

toInteger :: Integer -> Integer

Real Integer

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Integer -> Rational

Show Integer

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Integer -> ShowS

show :: Integer -> String

showList :: [Integer] -> ShowS

PrintfArg Integer

Since: base-2.1

Defined in Text.Printf

Methods

formatArg :: Integer -> FieldFormatter

parseFormat :: Integer -> ModifierParser

Eq Integer

Defined in GHC.Num.Integer

Methods

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

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

Ord Integer

Defined in GHC.Num.Integer

Methods

compare :: Integer -> Integer -> Ordering

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

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

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

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

max :: Integer -> Integer -> Integer

min :: Integer -> Integer -> Integer

Construct Integers

smallInteger :: Int# -> Integer

wordToInteger :: Word# -> Integer

Conversion to other integral types

integerToWord :: Integer -> Word#

integerToInt :: Integer -> Int#

Helpers for RealFloat type-class operations

encodeFloatInteger :: Integer -> Int# -> Float#

encodeDoubleInteger :: Integer -> Int# -> Double#

decodeDoubleInteger :: Double# -> (# Integer, Int# #)

Arithmetic operations

plusInteger :: Integer -> Integer -> Integer

Used to implement (+) for the Num typeclass. This gives the sum of two integers.

Example

>>> plusInteger 3 2
5

>>> (+) 3 2
5

minusInteger :: Integer -> Integer -> Integer

Used to implement (-) for the Num typeclass. This gives the difference of two integers.

Example

>>> minusInteger 3 2
1

>>> (-) 3 2
1

timesInteger :: Integer -> Integer -> Integer

Used to implement (*) for the Num typeclass. This gives the product of two integers.

Example

>>> timesInteger 3 2
6

>>> (*) 3 2
6

negateInteger :: Integer -> Integer

Used to implement negate for the Num typeclass. This changes the sign of whatever integer is passed into it.

Example

>>> negateInteger (-6)
6

>>> negate (-6)
6

absInteger :: Integer -> Integer

Used to implement abs for the Num typeclass. This gives the absolute value of whatever integer is passed into it.

Example

>>> absInteger (-6)
6

>>> abs (-6)
6

signumInteger :: Integer -> Integer

Used to implement signum for the Num typeclass. This gives 1 for a positive integer, and -1 for a negative integer.

Example

>>> signumInteger 5
1

>>> signum 5
1

divModInteger :: Integer -> Integer -> (# Integer, Integer #)

Used to implement divMod for the Integral typeclass. This gives a tuple equivalent to

(div x y, mod x y)

Example

>>> divModInteger 10 2
(5,0)

>>> divMod 10 2
(5,0)

divInteger :: Integer -> Integer -> Integer

Used to implement div for the Integral typeclass. This performs integer division on its two parameters, truncated towards negative infinity.

Example

>>> 10 `divInteger` 2
5

>>> 10 `div` 2

modInteger :: Integer -> Integer -> Integer

Used to implement mod for the Integral typeclass. This performs the modulo operation, satisfying

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

Example

>>> 7 `modInteger` 3
1

>>> 7 `mod` 3
1

quotRemInteger :: Integer -> Integer -> (# Integer, Integer #)

Used to implement quotRem for the Integral typeclass. This gives a tuple equivalent to

(quot x y, mod x y)

Example

>>> quotRemInteger 10 2
(5,0)

>>> quotRem 10 2
(5,0)

quotInteger :: Integer -> Integer -> Integer

Used to implement quot for the Integral typeclass. This performs integer division on its two parameters, truncated towards zero.

Example

>>> quotInteger 10 2
5

>>> quot 10 2
5

remInteger :: Integer -> Integer -> Integer

Used to implement rem for the Integral typeclass. This gives the remainder after integer division of its two parameters, satisfying

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

Example

>>> remInteger 3 2
1

>>> rem 3 2
1

Comparison predicates

eqInteger :: Integer -> Integer -> Bool

Used to implement (==) for the Eq typeclass. Outputs True if two integers are equal to each other.

Example

>>> 6 `eqInteger` 6
True

>>> 6 == 6
True

neqInteger :: Integer -> Integer -> Bool

Used to implement (/=) for the Eq typeclass. Outputs True if two integers are not equal to each other.

Example

>>> 6 `neqInteger` 7
True

>>> 6 /= 7
True

leInteger :: Integer -> Integer -> Bool

Used to implement (<=) for the Ord typeclass. Outputs True if the first argument is less than or equal to the second.

Example

>>> 3 `leInteger` 5
True

>>> 3 <= 5
True

gtInteger :: Integer -> Integer -> Bool

Used to implement (>) for the Ord typeclass. Outputs True if the first argument is greater than the second.

Example

>>> 5 `gtInteger` 3
True

>>> 5 > 3
True

ltInteger :: Integer -> Integer -> Bool

Used to implement (<) for the Ord typeclass. Outputs True if the first argument is less than the second.

Example

>>> 3 `ltInteger` 5
True

>>> 3 < 5
True

geInteger :: Integer -> Integer -> Bool

Used to implement (>=) for the Ord typeclass. Outputs True if the first argument is greater than or equal to the second.

Example

>>> 5 `geInteger` 3
True

>>> 5 >= 3
True

compareInteger :: Integer -> Integer -> Ordering

Used to implement compare for the Integral typeclass. This takes two integers, and outputs whether the first is less than, equal to, or greater than the second.

Example

>>> compareInteger 2 10
LT

>>> compare 2 10
LT

Int#-boolean valued versions of comparison predicates

These operations return 0# and 1# instead of False and True respectively. See PrimBool wiki-page for more details

eqInteger# :: Integer -> Integer -> Int#

neqInteger# :: Integer -> Integer -> Int#

leInteger# :: Integer -> Integer -> Int#

gtInteger# :: Integer -> Integer -> Int#

ltInteger# :: Integer -> Integer -> Int#

geInteger# :: Integer -> Integer -> Int#

Bit-operations

andInteger :: Integer -> Integer -> Integer

orInteger :: Integer -> Integer -> Integer

xorInteger :: Integer -> Integer -> Integer

complementInteger :: Integer -> Integer

shiftLInteger :: Integer -> Int# -> Integer

shiftRInteger :: Integer -> Int# -> Integer

testBitInteger :: Integer -> Int# -> Bool

popCountInteger :: Integer -> Int#

bitInteger :: Int# -> Integer

Hashing

hashInteger :: Integer -> Int#