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/Haskell 9

GHC.Integer.GMP.Internals

Copyright (c) Herbert Valerio Riedel 2014
License BSD3
Maintainer [email protected]
Stability provisional
Portability non-portable (GHC Extensions)
Safe Haskell None
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 (i.e., fits into an Int), the IS constructor is used. Otherwise IP and IN constructors are used to store a BigNat representing the positive or the negative value magnitude, respectively.

Invariant: IP and IN are used iff the value does not 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
PrintfArg Integer Source

Since: base-2.1
Instance details

Defined in Text.Printf

Methods

formatArg :: Integer -> FieldFormatter Source

parseFormat :: Integer -> ModifierParser Source

Bits Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Bits

Methods

(.&.) :: Integer -> Integer -> Integer Source

(.|.) :: Integer -> Integer -> Integer Source

xor :: Integer -> Integer -> Integer Source

complement :: Integer -> Integer Source

shift :: Integer -> Int -> Integer Source

rotate :: Integer -> Int -> Integer Source

zeroBits :: Integer Source

bit :: Int -> Integer Source

setBit :: Integer -> Int -> Integer Source

clearBit :: Integer -> Int -> Integer Source

complementBit :: Integer -> Int -> Integer Source

testBit :: Integer -> Int -> Bool Source

bitSizeMaybe :: Integer -> Maybe Int Source

bitSize :: Integer -> Int Source

isSigned :: Integer -> Bool Source

shiftL :: Integer -> Int -> Integer Source

unsafeShiftL :: Integer -> Int -> Integer Source

shiftR :: Integer -> Int -> Integer Source

unsafeShiftR :: Integer -> Int -> Integer Source

rotateL :: Integer -> Int -> Integer Source

rotateR :: Integer -> Int -> Integer Source

popCount :: Integer -> Int Source

Data Integer Source

Since: base-4.0.0.0
Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Integer -> c Integer Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Integer Source

toConstr :: Integer -> Constr Source

dataTypeOf :: Integer -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Integer) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Integer) Source

gmapT :: (forall b. Data b => b -> b) -> Integer -> Integer Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Integer -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Integer -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Integer -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Integer -> m Integer Source

Enum Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Enum

Methods

succ :: Integer -> Integer Source

pred :: Integer -> Integer Source

toEnum :: Int -> Integer Source

fromEnum :: Integer -> Int Source

enumFrom :: Integer -> [Integer] Source

enumFromThen :: Integer -> Integer -> [Integer] Source

enumFromTo :: Integer -> Integer -> [Integer] Source

enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] Source

Ix Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Ix

Methods

range :: (Integer, Integer) -> [Integer] Source

index :: (Integer, Integer) -> Integer -> Int Source

unsafeIndex :: (Integer, Integer) -> Integer -> Int Source

inRange :: (Integer, Integer) -> Integer -> Bool Source

rangeSize :: (Integer, Integer) -> Int Source

unsafeRangeSize :: (Integer, Integer) -> Int Source

Num Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Num

Methods

(+) :: Integer -> Integer -> Integer Source

(-) :: Integer -> Integer -> Integer Source

(*) :: Integer -> Integer -> Integer Source

negate :: Integer -> Integer Source

abs :: Integer -> Integer Source

signum :: Integer -> Integer Source

fromInteger :: Integer -> Integer Source

Read Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS Integer Source

readList :: ReadS [Integer] Source

readPrec :: ReadPrec Integer Source

readListPrec :: ReadPrec [Integer] Source

Integral Integer Source

Since: base-2.0.1
Instance details

Defined in GHC.Internal.Real

Methods

quot :: Integer -> Integer -> Integer Source

rem :: Integer -> Integer -> Integer Source

div :: Integer -> Integer -> Integer Source

mod :: Integer -> Integer -> Integer Source

quotRem :: Integer -> Integer -> (Integer, Integer) Source

divMod :: Integer -> Integer -> (Integer, Integer) Source

toInteger :: Integer -> Integer Source

Real Integer Source

Since: base-2.0.1
Instance details

Defined in GHC.Internal.Real

Methods

toRational :: Integer -> Rational Source

Show Integer Source

Since: base-2.1
Instance details

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> Integer -> ShowS Source

show :: Integer -> String Source

showList :: [Integer] -> ShowS Source

Eq Integer Source
Instance details

Defined in GHC.Num.Integer

Methods

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

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

Ord Integer Source
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

Lift Integer Source
Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Integer -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Integer -> Code m Integer Source

isValidInteger# :: Integer -> Int# Source

Deprecated: Use integerCheck# instead

Basic Integer operations

module GHC.Internal.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

Instances
Instances details
Eq BigNat Source
Instance details

Defined in GHC.Num.BigNat

Methods

(==) :: BigNat -> BigNat -> Bool Source

(/=) :: BigNat -> BigNat -> Bool Source

Ord BigNat Source
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

type GmpLimb = Word Source

type GmpLimb# = Word# Source

type GmpSize = Int Source

type GmpSize# = Int# Source

isValidBigNat# :: BigNat -> Int# Source

Deprecated: Use bigNatCheck# instead

sizeofBigNat# :: BigNat -> GmpSize# Source

Deprecated: Use bigNatSize# instead

zeroBigNat :: BigNat Source

Deprecated: Use bigNatZero instead

oneBigNat :: BigNat Source

Deprecated: Use bigNatOne instead

Conversions to/from BigNat

byteArrayToBigNat# :: ByteArray# -> GmpSize# -> BigNat Source

Deprecated: Use bigNatFromWordArray instead

wordToBigNat :: Word# -> BigNat Source

wordToBigNat2 :: Word# -> Word# -> BigNat Source

bigNatToInt :: BigNat -> Int# Source

bigNatToWord :: BigNat -> Word# Source

indexBigNat# :: BigNat -> GmpSize# -> GmpLimb# Source

Deprecated: Use bigNatIndex# instead

BigNat arithmetic operations

plusBigNat :: BigNat -> BigNat -> BigNat Source

Deprecated: Use bigNatAdd instead

plusBigNatWord :: BigNat -> GmpLimb# -> BigNat Source

Deprecated: Use bigNatAddWord# instead

minusBigNat :: BigNat -> BigNat -> BigNat Source

Deprecated: Use bigNatSub instead

minusBigNatWord :: BigNat -> GmpLimb# -> BigNat Source

Deprecated: Use bigNatSubWord# instead

timesBigNat :: BigNat -> BigNat -> BigNat Source

Deprecated: Use bigNatMul instead

timesBigNatWord :: BigNat -> GmpLimb# -> BigNat Source

Deprecated: Use bigNatMulWord# instead

sqrBigNat :: BigNat -> BigNat Source

Deprecated: Use bigNatSqr instead

quotRemBigNat :: BigNat -> BigNat -> (# BigNat, BigNat #) Source

Deprecated: Use bigNatQuotRem# instead

quotRemBigNatWord :: BigNat -> GmpLimb# -> (# BigNat, GmpLimb# #) Source

Deprecated: Use bigNatQuotRemWord# instead

quotBigNatWord :: BigNat -> GmpLimb# -> BigNat Source

Deprecated: Use bigNatQuotWord# instead

quotBigNat :: BigNat -> BigNat -> BigNat Source

Deprecated: Use bigNatQuot instead

remBigNat :: BigNat -> BigNat -> BigNat Source

Deprecated: Use bigNatRem instead

remBigNatWord :: BigNat -> GmpLimb# -> Word# Source

Deprecated: Use bigNatRemWord# instead

gcdBigNat :: BigNat -> BigNat -> BigNat Source

Deprecated: Use bigNatGcd instead

gcdBigNatWord :: BigNat -> Word# -> Word# Source

Deprecated: Use bigNatGcdWord# instead

BigNat logic operations

shiftRBigNat :: BigNat -> Int# -> BigNat Source

Deprecated: Use bigNatShiftR# instead

shiftLBigNat :: BigNat -> Int# -> BigNat Source

Deprecated: Use bigNatShiftL# instead

testBitBigNat :: BigNat -> Int# -> Bool Source

Deprecated: Use bigNatTestBit# instead

clearBitBigNat :: BigNat -> Int# -> BigNat Source

Deprecated: Use bigNatClearBit# instead

complementBitBigNat :: BigNat -> Int# -> BigNat Source

Deprecated: Use bigNatComplementBit# instead

setBitBigNat :: BigNat -> Int# -> BigNat Source

Deprecated: Use bigNatSetBit# instead

andBigNat :: BigNat -> BigNat -> BigNat Source

Deprecated: Use bigNatAnd instead

xorBigNat :: BigNat -> BigNat -> BigNat Source

Deprecated: Use bigNatXor instead

popCountBigNat :: BigNat -> Int# Source

Deprecated: Use bigNatPopCount# instead

orBigNat :: BigNat -> BigNat -> BigNat Source

Deprecated: Use bigNatOr instead

bitBigNat :: Int# -> BigNat Source

Deprecated: Use bigNatBit# instead

BigNat comparison predicates

isZeroBigNat :: BigNat -> Bool Source

Deprecated: Use bigNatIsZero instead

compareBigNatWord :: BigNat -> GmpLimb# -> Ordering Source

Deprecated: Use bigNatCompareWord# instead

compareBigNat :: BigNat -> BigNat -> Ordering Source

Deprecated: Use bigNatCompare instead

eqBigNatWord :: BigNat -> GmpLimb# -> Bool Source

Deprecated: Use bigNatEqWord# instead

eqBigNatWord# :: BigNat -> GmpLimb# -> Int# Source

Deprecated: Use bigNatEqWord# instead

eqBigNat :: BigNat -> BigNat -> Bool Source

Deprecated: Use bigNatEq instead

eqBigNat# :: BigNat -> BigNat -> Int# Source

Deprecated: Use bigNatEq# instead

gtBigNatWord# :: BigNat -> GmpLimb# -> Int# Source

Deprecated: Use bigNatGtWord# instead

Import/export functions

Compute size of serialisation

sizeInBaseBigNat :: BigNat -> Int# -> Word# Source

Deprecated: Use bigNatSizeInBase# instead

sizeInBaseInteger :: Integer -> Int# -> Word# Source

Deprecated: Use integerSizeInBase# instead

sizeInBaseWord# :: Word# -> Int# -> Word# Source

Deprecated: Use wordSizeInBase# instead

Export

exportBigNatToAddr :: BigNat -> Addr# -> Int# -> IO Word Source

Deprecated: Use bigNatToAddr# instead

exportIntegerToAddr :: Integer -> Addr# -> Int# -> IO Word Source

Deprecated: Use integerToAddr# instead

exportBigNatToMutableByteArray :: BigNat -> MutableByteArray# RealWorld -> Word# -> Int# -> IO Word Source

Deprecated: Use bigNatToMutableByteArray# instead

exportIntegerToMutableByteArray :: Integer -> MutableByteArray# RealWorld -> Word# -> Int# -> IO Word Source

Deprecated: Use integerToMutableByteArray# instead

Import

importBigNatFromAddr :: Addr# -> Word# -> Int# -> IO BigNat Source

Deprecated: Use bigNatFromAddr# instead

importIntegerFromAddr :: Addr# -> Word# -> Int# -> IO Integer Source

Deprecated: Use integerFromAddr# instead

importBigNatFromByteArray :: ByteArray# -> Word# -> Word# -> Int# -> BigNat Source

Deprecated: Use bigNatFromByteArray# instead

importIntegerFromByteArray :: ByteArray# -> Word# -> Word# -> Int# -> Integer Source

Deprecated: Use integerFromByteArray# instead

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.12.1/docs/libraries/integer-gmp-1.1-9b79/GHC-Integer-GMP-Internals.html