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

smallInteger :: Int# -> Integer Source

wordToInteger :: Word# -> Integer Source

integerToWord :: Integer -> Word# Source

integerToInt :: Integer -> Int# Source

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

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

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

plusInteger :: Integer -> Integer -> Integer Source

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 Source

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 Source

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 Source

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 Source

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 Source

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 #) Source

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 Source

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 Source

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 #) Source

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 Source

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 Source

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

eqInteger :: Integer -> Integer -> Bool Source

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 Source

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 Source

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 Source

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 Source

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 Source

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 Source

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

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

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

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

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

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

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

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

andInteger :: Integer -> Integer -> Integer Source

orInteger :: Integer -> Integer -> Integer Source

xorInteger :: Integer -> Integer -> Integer Source

complementInteger :: Integer -> Integer Source

shiftLInteger :: Integer -> Int# -> Integer Source

shiftRInteger :: Integer -> Int# -> Integer Source

testBitInteger :: Integer -> Int# -> Bool Source

popCountInteger :: Integer -> Int# Source

bitInteger :: Int# -> Integer Source

hashInteger :: Integer -> Int# Source