GHC.Integer.GMP.Internals

Copyright	(c) Herbert Valerio Riedel 2014
License	BSD3
Maintainer	ghc-devs@haskell.org
Stability	provisional
Portability	non-portable (GHC Extensions)
Safe Haskell	Safe-Inferred
Language	Haskell2010

Description

The Integer type

data Integer where 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

Bundled Patterns

pattern S# :: Int# -> Integer	Deprecated: Use IS constructor instead
pattern Jn# :: BigNat -> Integer	Deprecated: Use IN constructor instead
pattern Jp# :: BigNat -> Integer	Deprecated: Use IP constructor instead

Instances

Instances details

Show Integer	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS Source show :: Integer -> String Source showList :: [Integer] -> ShowS Source
Eq Integer
Instance details Defined in GHC.Num.Integer Methods (==) :: Integer -> Integer -> Bool Source (/=) :: Integer -> Integer -> Bool Source
Ord Integer
Instance details Defined in GHC.Num.Integer Methods compare :: Integer -> Integer -> Ordering Source (<) :: Integer -> Integer -> Bool Source (<=) :: Integer -> Integer -> Bool Source (>) :: Integer -> Integer -> Bool Source (>=) :: Integer -> Integer -> Bool Source max :: Integer -> Integer -> Integer Source min :: Integer -> Integer -> Integer Source

isValidInteger# :: Integer -> Int# Source

Deprecated: Use integerCheck# instead

Basic `Integer` operations

module GHC.Integer

Additional `Integer` operations

gcdInteger :: Integer -> Integer -> Integer Source

Deprecated: Use integerGcd instead

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

Deprecated: Use integerGcde instead

lcmInteger :: Integer -> Integer -> Integer Source

Deprecated: Use integerLcm instead

sqrInteger :: Integer -> Integer Source

Deprecated: Use integerSqr instead

powModInteger :: Integer -> Integer -> Integer -> Integer Source

Deprecated: Use integerPowMod# instead

recipModInteger :: Integer -> Integer -> Integer Source

Deprecated: Use integerRecipMod# instead

Additional conversion operations to `Integer`

wordToNegInteger :: Word# -> Integer Source

Deprecated: Use integerFromWordNeg# instead

bigNatToInteger :: BigNat -> Integer Source

Deprecated: Use integerFromBigNat# instead

bigNatToNegInteger :: BigNat -> Integer Source

Deprecated: Use integerFromBigNatNeg# instead

The BigNat type

data BigNat Source

A lifted BigNat

Represented as an array of limbs (Word#) stored in little-endian order (Word# themselves use machine order).

Invariant (canonical representation): higher Word# is non-zero.

As a consequence, zero is represented with a WordArray# whose size is 0.

Constructors

BN#
Fields unBigNat :: BigNat#

Instances

Instances details

Eq BigNat
Instance details Defined in GHC.Num.BigNat Methods (==) :: BigNat -> BigNat -> Bool Source (/=) :: BigNat -> BigNat -> Bool Source
Ord BigNat
Instance details Defined in GHC.Num.BigNat Methods compare :: BigNat -> BigNat -> Ordering Source (<) :: BigNat -> BigNat -> Bool Source (<=) :: BigNat -> BigNat -> Bool Source (>) :: BigNat -> BigNat -> Bool Source (>=) :: BigNat -> BigNat -> Bool Source max :: BigNat -> BigNat -> BigNat Source min :: BigNat -> BigNat -> BigNat Source