GHC.Natural

Compatibility module for pre ghc-bignum code.

Documentation

data Natural where

Bundled Patterns

pattern NatS# :: Word# -> Natural

pattern NatJ# :: BigNat -> Natural

Instances

PrintfArg Natural

Since: base-4.8.0.0

Defined in Text.Printf

Methods

formatArg :: Natural -> FieldFormatter

parseFormat :: Natural -> ModifierParser

Bits Natural

Since: base-4.8.0

Defined in GHC.Internal.Bits

Methods

(.&.) :: Natural -> Natural -> Natural

(.|.) :: Natural -> Natural -> Natural

xor :: Natural -> Natural -> Natural

complement :: Natural -> Natural

shift :: Natural -> Int -> Natural

rotate :: Natural -> Int -> Natural

zeroBits :: Natural

bit :: Int -> Natural

setBit :: Natural -> Int -> Natural

clearBit :: Natural -> Int -> Natural

complementBit :: Natural -> Int -> Natural

testBit :: Natural -> Int -> Bool

bitSizeMaybe :: Natural -> Maybe Int

bitSize :: Natural -> Int

isSigned :: Natural -> Bool

shiftL :: Natural -> Int -> Natural

unsafeShiftL :: Natural -> Int -> Natural

shiftR :: Natural -> Int -> Natural

unsafeShiftR :: Natural -> Int -> Natural

rotateL :: Natural -> Int -> Natural

rotateR :: Natural -> Int -> Natural

popCount :: Natural -> Int

Data Natural

Since: base-4.8.0.0

Defined in GHC.Internal.Data.Data

Methods

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

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

toConstr :: Natural -> Constr

dataTypeOf :: Natural -> DataType

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

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

gmapT :: (forall b. Data b => b -> b) -> Natural -> Natural

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

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

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

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

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

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

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

Enum Natural

Since: base-4.8.0.0

Defined in GHC.Internal.Enum

Methods

succ :: Natural -> Natural

pred :: Natural -> Natural

toEnum :: Int -> Natural

fromEnum :: Natural -> Int

enumFrom :: Natural -> [Natural]

enumFromThen :: Natural -> Natural -> [Natural]

enumFromTo :: Natural -> Natural -> [Natural]

enumFromThenTo :: Natural -> Natural -> Natural -> [Natural]

Ix Natural

Since: base-4.8.0.0

Defined in GHC.Internal.Ix

Methods

range :: (Natural, Natural) -> [Natural]

index :: (Natural, Natural) -> Natural -> Int

unsafeIndex :: (Natural, Natural) -> Natural -> Int

inRange :: (Natural, Natural) -> Natural -> Bool

rangeSize :: (Natural, Natural) -> Int

unsafeRangeSize :: (Natural, Natural) -> Int

Num Natural

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

Defined in GHC.Internal.Num

Methods

(+) :: Natural -> Natural -> Natural

(-) :: Natural -> Natural -> Natural

(*) :: Natural -> Natural -> Natural

negate :: Natural -> Natural

abs :: Natural -> Natural

signum :: Natural -> Natural

fromInteger :: Integer -> Natural

Read Natural

Since: base-4.8.0.0

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS Natural

readList :: ReadS [Natural]

readPrec :: ReadPrec Natural

readListPrec :: ReadPrec [Natural]

Integral Natural

Since: base-4.8.0.0

Defined in GHC.Internal.Real

Methods

quot :: Natural -> Natural -> Natural

rem :: Natural -> Natural -> Natural

div :: Natural -> Natural -> Natural

mod :: Natural -> Natural -> Natural

quotRem :: Natural -> Natural -> (Natural, Natural)

divMod :: Natural -> Natural -> (Natural, Natural)

toInteger :: Natural -> Integer

Real Natural

Since: base-4.8.0.0

Defined in GHC.Internal.Real

Methods

toRational :: Natural -> Rational

Show Natural

Since: base-4.8.0.0

Defined in GHC.Internal.Show

Methods

showsPrec :: Int -> Natural -> ShowS

show :: Natural -> String

showList :: [Natural] -> ShowS

Eq Natural

Defined in GHC.Num.Natural

Methods

(==) :: Natural -> Natural -> Bool

(/=) :: Natural -> Natural -> Bool

Ord Natural

Defined in GHC.Num.Natural

Methods

compare :: Natural -> Natural -> Ordering

(<) :: Natural -> Natural -> Bool

(<=) :: Natural -> Natural -> Bool

(>) :: Natural -> Natural -> Bool

(>=) :: Natural -> Natural -> Bool

max :: Natural -> Natural -> Natural

min :: Natural -> Natural -> Natural

KnownNat n => HasResolution (n :: Nat)

For example, Fixed 1000 will give you a Fixed with a resolution of 1000.

Defined in Data.Fixed

Methods

resolution :: p n -> Integer

TestCoercion SNat

Since: base-4.18.0.0

Defined in GHC.Internal.TypeNats

Methods

testCoercion :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (Coercion a b)

TestEquality SNat

Since: base-4.18.0.0

Defined in GHC.Internal.TypeNats

Methods

testEquality :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (a :~: b)

type Compare (a :: Natural) (b :: Natural)

Defined in GHC.Internal.Data.Type.Ord

type Compare (a :: Natural) (b :: Natural) = CmpNat a b

data BigNat

Constructors

BN#

Fields

• unBigNat :: BigNat#

Instances

Eq BigNat

Defined in GHC.Num.BigNat

Methods

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

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

Ord BigNat

Defined in GHC.Num.BigNat

Methods

compare :: BigNat -> BigNat -> Ordering

(<) :: BigNat -> BigNat -> Bool

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

(>) :: BigNat -> BigNat -> Bool

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

max :: BigNat -> BigNat -> BigNat

min :: BigNat -> BigNat -> BigNat

mkNatural :: [Word] -> Natural

Construct Natural value from list of Words.

isValidNatural :: Natural -> Bool

Test whether all internal invariants are satisfied by Natural value

This operation is mostly useful for test-suites and/or code which constructs Integer values directly.

Since: base-4.8.0.0

Arithmetic

plusNatural :: Natural -> Natural -> Natural

Natural Addition

minusNatural :: Natural -> Natural -> Natural

Natural subtraction. May throw Underflow.

minusNaturalMaybe :: Natural -> Natural -> Maybe Natural

Natural subtraction. Returns Nothings for non-positive results.

Since: base-4.8.0.0

timesNatural :: Natural -> Natural -> Natural

Natural multiplication

negateNatural :: Natural -> Natural

signumNatural :: Natural -> Natural

quotRemNatural :: Natural -> Natural -> (Natural, Natural)

quotNatural :: Natural -> Natural -> Natural

remNatural :: Natural -> Natural -> Natural

gcdNatural :: Natural -> Natural -> Natural

Compute greatest common divisor.

lcmNatural :: Natural -> Natural -> Natural

Compute least common multiple.

Bits

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

Conversions

naturalToInteger :: Natural -> Integer

Since: base-4.12.0.0

naturalToWord :: Natural -> Word

naturalToWordMaybe :: Natural -> Maybe Word

Try downcasting Natural to Word value. Returns Nothing if value doesn't fit in Word.

Since: base-4.8.0.0

wordToNatural :: Word -> Natural

Construct Natural from Word value.

Since: base-4.8.0.0

wordToNatural# :: Word -> Natural

naturalFromInteger :: Integer -> Natural

Since: base-4.10.0.0

Modular arithmetic

powModNatural :: Natural -> Natural -> Natural -> Natural

"powModNatural b e m" computes base b raised to exponent e modulo m.

Since: base-4.8.0.0