GHC.Integer

The Integer type.

This module exposes the portable Integer API. See GHC.Integer.GMP.Internals for the integer-gmp-specific internal representation of Integer as well as optimized GMP-specific operations.

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.

For more information about this type's representation, see the comments in its implementation.

Instances

Eq Integer

Defined in GHC.Integer.Type

Methods

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

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

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

Construct Integers

mkInteger

Arguments

:: Bool

sign of integer (True if non-negative)

-> [Int]

absolute value expressed in 31 bit chunks, least significant first (ideally these would be machine-word Words rather than 31-bit truncated Ints)

-> Integer

Construct Integer value from list of Ints.

This function is used by GHC for constructing Integer literals.

smallInteger :: Int# -> Integer

Should rather be called intToInteger

wordToInteger :: Word# -> Integer

Conversion to other integral types

integerToWord :: Integer -> Word#

integerToInt :: Integer -> Int#

Truncates Integer to least-significant Int#

Helpers for RealFloat type-class operations

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

floatFromInteger :: Integer -> Float#

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

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

doubleFromInteger :: Integer -> Double#

Arithmetic operations

plusInteger :: Integer -> Integer -> Integer

Add two Integers

minusInteger :: Integer -> Integer -> Integer

Subtract one Integer from another.

timesInteger :: Integer -> Integer -> Integer

Multiply two Integers

negateInteger :: Integer -> Integer

Negate Integer

absInteger :: Integer -> Integer

Compute absolute value of an Integer

signumInteger :: Integer -> Integer

Return -1, 0, and 1 depending on whether argument is negative, zero, or positive, respectively

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

Simultaneous divInteger and modInteger.

Divisor must be non-zero otherwise the GHC runtime will terminate with a division-by-zero fault.

divInteger :: Integer -> Integer -> Integer

modInteger :: Integer -> Integer -> Integer

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

Simultaneous quotInteger and remInteger.

Divisor must be non-zero otherwise the GHC runtime will terminate with a division-by-zero fault.

quotInteger :: Integer -> Integer -> Integer

remInteger :: Integer -> Integer -> Integer

Comparison predicates

eqInteger :: Integer -> Integer -> Bool

neqInteger :: Integer -> Integer -> Bool

Not-equal predicate.

leInteger :: Integer -> Integer -> Bool

gtInteger :: Integer -> Integer -> Bool

ltInteger :: Integer -> Integer -> Bool

geInteger :: Integer -> Integer -> Bool

compareInteger :: Integer -> Integer -> Ordering

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

Bitwise AND operation

orInteger :: Integer -> Integer -> Integer

Bitwise OR operation

xorInteger :: Integer -> Integer -> Integer

Bitwise XOR operation

complementInteger :: Integer -> Integer

Bitwise NOT operation

shiftLInteger :: Integer -> Int# -> Integer

Shift-left operation

Even though the shift-amount is expressed as Int#, the result is undefined for negative shift-amounts.

shiftRInteger :: Integer -> Int# -> Integer

Arithmetic shift-right operation

Even though the shift-amount is expressed as Int#, the result is undefined for negative shift-amounts.

testBitInteger :: Integer -> Int# -> Bool

Test if n-th bit is set.

popCountInteger :: Integer -> Int#

Count number of set bits. For negative arguments returns negative population count of negated argument.

bitInteger :: Int# -> Integer

Integer for which only n-th bit is set. Undefined behaviour for negative n values.

Hashing

hashInteger :: Integer -> Int#