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.GMP.Internals

Contents

The Integer type
The BigNat type
Import/export functions

Description

Synopsis

data Integer where
- pattern S# :: Int# -> Integer
- pattern Jn# :: BigNat -> Integer
- pattern Jp# :: BigNat -> Integer
isValidInteger# :: Integer -> Int#
module GHC.Integer
gcdInteger :: Integer -> Integer -> Integer
gcdExtInteger :: Integer -> Integer -> (# Integer, Integer #)
lcmInteger :: Integer -> Integer -> Integer
sqrInteger :: Integer -> Integer
powModInteger :: Integer -> Integer -> Integer -> Integer
recipModInteger :: Integer -> Integer -> Integer
wordToNegInteger :: Word# -> Integer
bigNatToInteger :: BigNat -> Integer
bigNatToNegInteger :: BigNat -> Integer
data BigNat = BN# {
- unBigNat :: BigNat#
}
type GmpLimb = Word
type GmpLimb# = Word#
type GmpSize = Int
type GmpSize# = Int#
isValidBigNat# :: BigNat -> Int#
sizeofBigNat# :: BigNat -> GmpSize#
zeroBigNat :: BigNat
oneBigNat :: BigNat
byteArrayToBigNat# :: ByteArray# -> GmpSize# -> BigNat
wordToBigNat :: Word# -> BigNat
wordToBigNat2 :: Word# -> Word# -> BigNat
bigNatToInt :: BigNat -> Int#
bigNatToWord :: BigNat -> Word#
indexBigNat# :: BigNat -> GmpSize# -> GmpLimb#
plusBigNat :: BigNat -> BigNat -> BigNat
plusBigNatWord :: BigNat -> GmpLimb# -> BigNat
minusBigNat :: BigNat -> BigNat -> BigNat
minusBigNatWord :: BigNat -> GmpLimb# -> BigNat
timesBigNat :: BigNat -> BigNat -> BigNat
timesBigNatWord :: BigNat -> GmpLimb# -> BigNat
sqrBigNat :: BigNat -> BigNat
quotRemBigNat :: BigNat -> BigNat -> (# BigNat, BigNat #)
quotRemBigNatWord :: BigNat -> GmpLimb# -> (# BigNat, GmpLimb# #)
quotBigNatWord :: BigNat -> GmpLimb# -> BigNat
quotBigNat :: BigNat -> BigNat -> BigNat
remBigNat :: BigNat -> BigNat -> BigNat
remBigNatWord :: BigNat -> GmpLimb# -> Word#
gcdBigNat :: BigNat -> BigNat -> BigNat
gcdBigNatWord :: BigNat -> Word# -> Word#
shiftRBigNat :: BigNat -> Int# -> BigNat
shiftLBigNat :: BigNat -> Int# -> BigNat
testBitBigNat :: BigNat -> Int# -> Bool
clearBitBigNat :: BigNat -> Int# -> BigNat
complementBitBigNat :: BigNat -> Int# -> BigNat
setBitBigNat :: BigNat -> Int# -> BigNat
andBigNat :: BigNat -> BigNat -> BigNat
xorBigNat :: BigNat -> BigNat -> BigNat
popCountBigNat :: BigNat -> Int#
orBigNat :: BigNat -> BigNat -> BigNat
bitBigNat :: Int# -> BigNat
isZeroBigNat :: BigNat -> Bool
compareBigNatWord :: BigNat -> GmpLimb# -> Ordering
compareBigNat :: BigNat -> BigNat -> Ordering
eqBigNatWord :: BigNat -> GmpLimb# -> Bool
eqBigNatWord# :: BigNat -> GmpLimb# -> Int#
eqBigNat :: BigNat -> BigNat -> Bool
eqBigNat# :: BigNat -> BigNat -> Int#
gtBigNatWord# :: BigNat -> GmpLimb# -> Int#
sizeInBaseBigNat :: BigNat -> Int# -> Word#
sizeInBaseInteger :: Integer -> Int# -> Word#
sizeInBaseWord# :: Word# -> Int# -> Word#
exportBigNatToAddr :: BigNat -> Addr# -> Int# -> IO Word
exportIntegerToAddr :: Integer -> Addr# -> Int# -> IO Word
exportBigNatToMutableByteArray :: BigNat -> MutableByteArray# RealWorld -> Word# -> Int# -> IO Word
exportIntegerToMutableByteArray :: Integer -> MutableByteArray# RealWorld -> Word# -> Int# -> IO Word
importBigNatFromAddr :: Addr# -> Word# -> Int# -> IO BigNat
importIntegerFromAddr :: Addr# -> Word# -> Int# -> IO Integer
importBigNatFromByteArray :: ByteArray# -> Word# -> Word# -> Int# -> BigNat
importIntegerFromByteArray :: ByteArray# -> Word# -> Word# -> Int# -> Integer

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 IP and IN constructors are used to store a BigNat representing respectively the positive or the negative value magnitude.

Invariant: IP 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

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 #
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 #

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#

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 Integer type

Instances

Basic Integer operations

Additional Integer operations

Additional conversion operations to Integer

The BigNat type

Conversions to/from BigNat

BigNat arithmetic operations

BigNat logic operations

BigNat comparison predicates