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

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

Eq Integer

Methods

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

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

Ord 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

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 two Integers from each other.

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 comparision 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.

Hashing

hashInteger :: Integer -> Int#