integer-gmp-1.1: Integer library based on GMP
Copyright(c) Herbert Valerio Riedel 2014
LicenseBSD3
Maintainerghc-devs@haskell.org
Stabilityprovisional
Portabilitynon-portable (GHC Extensions)
Safe HaskellNone
LanguageHaskell2010

GHC.Integer.GMP.Internals

Description

 
Synopsis

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 #

Eq Integer Source # 
Instance details

Defined in GHC.Internal.Bignum.Integer

Methods

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

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

Ord Integer Source # 
Instance details

Defined in GHC.Internal.Bignum.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 #

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 #

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# #

Deprecated: Use integerCheck# instead

Basic Integer operations

module GHC.Internal.Integer

Additional Integer operations

gcdInteger :: Integer -> Integer -> Integer #

Deprecated: Use integerGcd instead

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

Deprecated: Use integerGcde instead

lcmInteger :: Integer -> Integer -> Integer #

Deprecated: Use integerLcm instead

sqrInteger :: Integer -> Integer #

Deprecated: Use integerSqr instead

powModInteger :: Integer -> Integer -> Integer -> Integer #

Deprecated: Use integerPowMod# instead

recipModInteger :: Integer -> Integer -> Integer #

Deprecated: Use integerRecipMod# instead

Additional conversion operations to Integer

wordToNegInteger :: Word# -> Integer #

Deprecated: Use integerFromWordNeg# instead

bigNatToInteger :: BigNat -> Integer #

Deprecated: Use integerFromBigNat# instead

bigNatToNegInteger :: BigNat -> Integer #

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.Internal.Bignum.BigNat

Methods

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

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

Ord BigNat Source # 
Instance details

Defined in GHC.Internal.Bignum.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 #

type GmpLimb# = Word# #

type GmpSize = Int #

type GmpSize# = Int# #

isValidBigNat# :: BigNat -> Int# #

Deprecated: Use bigNatCheck# instead

sizeofBigNat# :: BigNat -> GmpSize# #

Deprecated: Use bigNatSize# instead

zeroBigNat :: BigNat #

Deprecated: Use bigNatZero instead

oneBigNat :: BigNat #

Deprecated: Use bigNatOne instead

Conversions to/from BigNat

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

Deprecated: Use bigNatFromWordArray instead

wordToBigNat :: Word# -> BigNat #

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

bigNatToInt :: BigNat -> Int# #

bigNatToWord :: BigNat -> Word# #

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

Deprecated: Use bigNatIndex# instead

BigNat arithmetic operations

plusBigNat :: BigNat -> BigNat -> BigNat #

Deprecated: Use bigNatAdd instead

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

Deprecated: Use bigNatAddWord# instead

minusBigNat :: BigNat -> BigNat -> BigNat #

Deprecated: Use bigNatSub instead

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

Deprecated: Use bigNatSubWord# instead

timesBigNat :: BigNat -> BigNat -> BigNat #

Deprecated: Use bigNatMul instead

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

Deprecated: Use bigNatMulWord# instead

sqrBigNat :: BigNat -> BigNat #

Deprecated: Use bigNatSqr instead

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

Deprecated: Use bigNatQuotRem# instead

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

Deprecated: Use bigNatQuotRemWord# instead

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

Deprecated: Use bigNatQuotWord# instead

quotBigNat :: BigNat -> BigNat -> BigNat #

Deprecated: Use bigNatQuot instead

remBigNat :: BigNat -> BigNat -> BigNat #

Deprecated: Use bigNatRem instead

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

Deprecated: Use bigNatRemWord# instead

gcdBigNat :: BigNat -> BigNat -> BigNat #

Deprecated: Use bigNatGcd instead

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

Deprecated: Use bigNatGcdWord# instead

BigNat logic operations

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

Deprecated: Use bigNatShiftR# instead

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

Deprecated: Use bigNatShiftL# instead

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

Deprecated: Use bigNatTestBit# instead

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

Deprecated: Use bigNatClearBit# instead

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

Deprecated: Use bigNatComplementBit# instead

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

Deprecated: Use bigNatSetBit# instead

andBigNat :: BigNat -> BigNat -> BigNat #

Deprecated: Use bigNatAnd instead

xorBigNat :: BigNat -> BigNat -> BigNat #

Deprecated: Use bigNatXor instead

popCountBigNat :: BigNat -> Int# #

Deprecated: Use bigNatPopCount# instead

orBigNat :: BigNat -> BigNat -> BigNat #

Deprecated: Use bigNatOr instead

bitBigNat :: Int# -> BigNat #

Deprecated: Use bigNatBit# instead

BigNat comparison predicates

isZeroBigNat :: BigNat -> Bool #

Deprecated: Use bigNatIsZero instead

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

Deprecated: Use bigNatCompareWord# instead

compareBigNat :: BigNat -> BigNat -> Ordering #

Deprecated: Use bigNatCompare instead

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

Deprecated: Use bigNatEqWord# instead

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

Deprecated: Use bigNatEqWord# instead

eqBigNat :: BigNat -> BigNat -> Bool #

Deprecated: Use bigNatEq instead

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

Deprecated: Use bigNatEq# instead

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

Deprecated: Use bigNatGtWord# instead

Import/export functions

Compute size of serialisation

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

Deprecated: Use bigNatSizeInBase# instead

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

Deprecated: Use integerSizeInBase# instead

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

Deprecated: Use wordSizeInBase# instead

Export

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

Deprecated: Use bigNatToAddr# instead

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

Deprecated: Use integerToAddr# instead

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

Deprecated: Use bigNatToMutableByteArray# instead

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

Deprecated: Use integerToMutableByteArray# instead

Import

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

Deprecated: Use bigNatFromAddr# instead

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

Deprecated: Use integerFromAddr# instead

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

Deprecated: Use bigNatFromByteArray# instead

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

Deprecated: Use integerFromByteArray# instead