Safe Haskell	Trustworthy
Language	Haskell2010

GHC.Natural

Contents

Arithmetic
Bits
Conversions
Modular arithmetic

Description

Compatibility module for pre ghc-bignum code.

Synopsis

data Natural where
- pattern NatS# :: Word# -> Natural
- pattern NatJ# :: BigNat -> Natural
data BigNat = BN# {
- unBigNat :: BigNat#
}
mkNatural :: [Word] -> Natural
isValidNatural :: Natural -> Bool
plusNatural :: Natural -> Natural -> Natural
minusNatural :: Natural -> Natural -> Natural
minusNaturalMaybe :: Natural -> Natural -> Maybe Natural
timesNatural :: Natural -> Natural -> Natural
negateNatural :: Natural -> Natural
signumNatural :: Natural -> Natural
quotRemNatural :: Natural -> Natural -> (Natural, Natural)
quotNatural :: Natural -> Natural -> Natural
remNatural :: Natural -> Natural -> Natural
gcdNatural :: Natural -> Natural -> Natural
lcmNatural :: Natural -> Natural -> Natural
andNatural :: Natural -> Natural -> Natural
orNatural :: Natural -> Natural -> Natural
xorNatural :: Natural -> Natural -> Natural
bitNatural :: Int# -> Natural
testBitNatural :: Natural -> Int -> Bool
popCountNatural :: Natural -> Int
shiftLNatural :: Natural -> Int -> Natural
shiftRNatural :: Natural -> Int -> Natural
naturalToInteger :: Natural -> Integer
naturalToWord :: Natural -> Word
naturalToWordMaybe :: Natural -> Maybe Word
wordToNatural :: Word -> Natural
wordToNatural# :: Word -> Natural
naturalFromInteger :: Integer -> Natural
powModNatural :: Natural -> Natural -> Natural -> Natural

Documentation

data Natural where Source #

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Bundled Patterns

pattern NatS# :: Word# -> Natural
pattern NatJ# :: BigNat -> Natural

Instances

Instances details

Data Natural Source #	Since: base-4.8.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Natural -> c Natural Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Natural Source # toConstr :: Natural -> Constr Source # dataTypeOf :: Natural -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Natural) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Natural) Source # gmapT :: (forall b. Data b => b -> b) -> Natural -> Natural Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Natural -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Natural -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source #
Bits Natural Source #	Since: base-4.8.0
Instance details Defined in GHC.Bits Methods (.&.) :: Natural -> Natural -> Natural Source # (.\|.) :: Natural -> Natural -> Natural Source # xor :: Natural -> Natural -> Natural Source # complement :: Natural -> Natural Source # shift :: Natural -> Int -> Natural Source # rotate :: Natural -> Int -> Natural Source # zeroBits :: Natural Source # bit :: Int -> Natural Source # setBit :: Natural -> Int -> Natural Source # clearBit :: Natural -> Int -> Natural Source # complementBit :: Natural -> Int -> Natural Source # testBit :: Natural -> Int -> Bool Source # bitSizeMaybe :: Natural -> Maybe Int Source # bitSize :: Natural -> Int Source # isSigned :: Natural -> Bool Source # shiftL :: Natural -> Int -> Natural Source # unsafeShiftL :: Natural -> Int -> Natural Source # shiftR :: Natural -> Int -> Natural Source # unsafeShiftR :: Natural -> Int -> Natural Source # rotateL :: Natural -> Int -> Natural Source # rotateR :: Natural -> Int -> Natural Source # popCount :: Natural -> Int Source #
Enum Natural Source #	Since: base-4.8.0.0
Instance details Defined in GHC.Enum Methods succ :: Natural -> Natural Source # pred :: Natural -> Natural Source # toEnum :: Int -> Natural Source # fromEnum :: Natural -> Int Source # enumFrom :: Natural -> [Natural] Source # enumFromThen :: Natural -> Natural -> [Natural] Source # enumFromTo :: Natural -> Natural -> [Natural] Source # enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source #
Ix Natural Source #	Since: base-4.8.0.0
Instance details Defined in GHC.Ix Methods range :: (Natural, Natural) -> [Natural] Source # index :: (Natural, Natural) -> Natural -> Int Source # unsafeIndex :: (Natural, Natural) -> Natural -> Int Source # inRange :: (Natural, Natural) -> Natural -> Bool Source # rangeSize :: (Natural, Natural) -> Int Source # unsafeRangeSize :: (Natural, Natural) -> Int Source #
Num Natural Source #	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. Since: base-4.8.0.0
Instance details Defined in GHC.Num Methods (+) :: Natural -> Natural -> Natural Source # (-) :: Natural -> Natural -> Natural Source # (*) :: Natural -> Natural -> Natural Source # negate :: Natural -> Natural Source # abs :: Natural -> Natural Source # signum :: Natural -> Natural Source # fromInteger :: Integer -> Natural Source #
Read Natural Source #	Since: base-4.8.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Natural Source # readList :: ReadS [Natural] Source # readPrec :: ReadPrec Natural Source # readListPrec :: ReadPrec [Natural] Source #
Integral Natural Source #	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods quot :: Natural -> Natural -> Natural Source # rem :: Natural -> Natural -> Natural Source # div :: Natural -> Natural -> Natural Source # mod :: Natural -> Natural -> Natural Source # quotRem :: Natural -> Natural -> (Natural, Natural) Source # divMod :: Natural -> Natural -> (Natural, Natural) Source # toInteger :: Natural -> Integer Source #
Real Natural Source #	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods toRational :: Natural -> Rational Source #
Show Natural Source #	Since: base-4.8.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Natural -> ShowS Source # show :: Natural -> String Source # showList :: [Natural] -> ShowS Source #
PrintfArg Natural Source #	Since: base-4.8.0.0
Instance details Defined in Text.Printf Methods formatArg :: Natural -> FieldFormatter Source # parseFormat :: Natural -> ModifierParser Source #
Eq Natural
Instance details Defined in GHC.Num.Natural Methods (==) :: Natural -> Natural -> Bool Source # (/=) :: Natural -> Natural -> Bool Source #
Ord Natural
Instance details Defined in GHC.Num.Natural Methods compare :: Natural -> Natural -> Ordering Source # (<) :: Natural -> Natural -> Bool Source # (<=) :: Natural -> Natural -> Bool Source # (>) :: Natural -> Natural -> Bool Source # (>=) :: Natural -> Natural -> Bool Source # max :: Natural -> Natural -> Natural Source # min :: Natural -> Natural -> Natural Source #
KnownNat n => HasResolution (n :: Nat) Source #	For example, `Fixed 1000` will give you a `Fixed` with a resolution of 1000.
Instance details Defined in Data.Fixed Methods resolution :: p n -> Integer Source #
TestCoercion SNat Source #	Since: base-4.18.0.0
Instance details Defined in GHC.TypeNats Methods testCoercion :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (Coercion a b) Source #
TestEquality SNat Source #	Since: base-4.18.0.0
Instance details Defined in GHC.TypeNats Methods testEquality :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (a :~: b) Source #
type Compare (a :: Natural) (b :: Natural) Source #
Instance details Defined in Data.Type.Ord type Compare (a :: Natural) (b :: Natural) = CmpNat a b

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 #