integer-gmp-1.0.0.1: Integer library based on GMP

Copyright	(c) Herbert Valerio Riedel 2014
License	BSD3
Maintainer	ghc-devs@haskell.org
Stability	provisional
Portability	non-portable (GHC Extensions)
Safe Haskell	None
Language	Haskell2010

GHC.Integer

Contents

Construct Integers
Conversion to other integral types
Helpers for RealFloat type-class operations
Arithmetic operations
Comparison predicates
- Int#-boolean valued versions of comparision predicates
Bit-operations
Hashing

Description

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.

Synopsis

Documentation

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 `Integer`s

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 `Word`s rather than 31-bit truncated `Int`s)
-> 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# #