Copyright	(C) 2014 Herbert Valerio Riedel (C) 2011 Edward Kmett
License	see libraries/base/LICENSE
Maintainer	libraries@haskell.org
Stability	internal
Portability	non-portable (GHC Extensions)
Safe Haskell	Unsafe
Language	Haskell2010

GHC.Natural (signature^[?])

Contents

The Natural number type
Conversions
Checked subtraction
Modular arithmetic

Description

The arbitrary-precision Natural number type.

Note: This is an internal GHC module with an API subject to change. It's recommended use the Numeric.Natural module to import the Natural type.

Since: 4.8.0.0

Synopsis

The `Natural` number type

Warning: The internal implementation of Natural (i.e. which constructors are available) depends on the Integer backend used!

data Natural Source #

Type representing arbitrary-precision non-negative integers.

Operations whose result would be negative throw (Underflow :: ArithException).

Since: 4.8.0.0

Constructors

NatS# GmpLimb#

in [0, maxBound::Word]

NatJ# !BigNat

in ]maxBound::Word, +inf[

Invariant: NatJ# is used iff value doesn't fit in NatS# constructor.

Instances

Enum Natural #	Since: 4.8.0.0
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 #
Eq Natural #
Methods (==) :: Natural -> Natural -> Bool Source # (/=) :: Natural -> Natural -> Bool Source #
Integral Natural #	Since: 4.8.0.0
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 #
Data Natural #	Since: 4.8.0.0
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 :: (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 #
Num Natural #	Since: 4.8.0.0
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 #
Ord 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 #
Read Natural #	Since: 4.8.0.0
Methods readsPrec :: Int -> ReadS Natural Source # readList :: ReadS [Natural] Source # readPrec :: ReadPrec Natural Source # readListPrec :: ReadPrec [Natural] Source #
Real Natural #	Since: 4.8.0.0
Methods toRational :: Natural -> Rational Source #
Show Natural #	Since: 4.8.0.0
Methods showsPrec :: Int -> Natural -> ShowS Source # show :: Natural -> String Source # showList :: [Natural] -> ShowS Source #
Ix Natural #	Since: 4.8.0.0
Methods range :: (Natural, Natural) -> [Natural] Source # index :: (Natural, Natural) -> Natural -> Int Source # unsafeIndex :: (Natural, Natural) -> Natural -> Int inRange :: (Natural, Natural) -> Natural -> Bool Source # rangeSize :: (Natural, Natural) -> Int Source # unsafeRangeSize :: (Natural, Natural) -> Int
Bits Natural #	Since: 4.8.0.0
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 #
PrintfArg Natural #	Since: 4.8.0.0
Methods formatArg :: Natural -> FieldFormatter Source # parseFormat :: Natural -> ModifierParser Source #