base-4.18.1.0: Basic libraries

GHC.Integer

Description

Compatibility module for pre ghc-bignum code.

Synopsis

# Documentation

data Integer Source #

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

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

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

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

#### Instances

Instances details
 Source # Since: base-4.0.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer Source #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer Source #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) Source #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) Source #gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer Source #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source #gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] Source #gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u Source #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Bits Methods Source # Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Source # Since: base-2.1 Instance detailsDefined in GHC.Ix Methodsrange :: (Integer, Integer) -> [Integer] Source #index :: (Integer, Integer) -> Integer -> Int Source #unsafeIndex :: (Integer, Integer) -> Integer -> Int Source #inRange :: (Integer, Integer) -> Integer -> Bool Source #rangeSize :: (Integer, Integer) -> Int Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Num Methods Source # Since: base-2.1 Instance detailsDefined in GHC.Read Methods Source # Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods Source # Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods Source # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowList :: [Integer] -> ShowS Source # Source # Since: base-2.1 Instance detailsDefined in Text.Printf Methods Instance detailsDefined in GHC.Num.Integer Methods Instance detailsDefined in GHC.Num.Integer Methods

# Arithmetic operations

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

#### Example

Expand
>>> plusInteger 3 2
5

>>> (+) 3 2
5


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

#### Example

Expand
>>> minusInteger 3 2
1

>>> (-) 3 2
1


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

#### Example

Expand
>>> timesInteger 3 2
6

>>> (*) 3 2
6


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

#### Example

Expand
>>> negateInteger (-6)
6

>>> negate (-6)
6


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

#### Example

Expand
>>> absInteger (-6)
6

>>> abs (-6)
6


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

#### Example

Expand
>>> signumInteger 5
1

>>> signum 5
1


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

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

(div x y, mod x y)

#### Example

Expand
>>> divModInteger 10 2
(5,0)

>>> divMod 10 2
(5,0)


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

#### Example

Expand
>>> 10 divInteger 2
5

>>> 10 div 2


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

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

#### Example

Expand
>>> 7 modInteger 3
1

>>> 7 mod 3
1


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

(quot x y, mod x y)

#### Example

Expand
>>> quotRemInteger 10 2
(5,0)

>>> quotRem 10 2
(5,0)


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

#### Example

Expand
>>> quotInteger 10 2
5

>>> quot 10 2
5


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

Expand
>>> remInteger 3 2
1

>>> rem 3 2
1


# Comparison predicates

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

#### Example

Expand
>>> 6 eqInteger 6
True

>>> 6 == 6
True


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

#### Example

Expand
>>> 6 neqInteger 7
True

>>> 6 /= 7
True


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

#### Example

Expand
>>> 3 leInteger 5
True

>>> 3 <= 5
True


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

#### Example

Expand
>>> 5 gtInteger 3
True

>>> 5 > 3
True


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

#### Example

Expand
>>> 3 ltInteger 5
True

>>> 3 < 5
True


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

#### Example

Expand
>>> 5 geInteger 3
True

>>> 5 >= 3
True


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

Expand
>>> 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