base-4.13.0.0: Basic libraries
Copyright(C) 2014 Herbert Valerio Riedel
(C) 2011 Edward Kmett
Licensesee libraries/base/LICENSE
Maintainerlibraries@haskell.org
Stabilityprovisional
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Numeric.Natural

Description

The arbitrary-precision Natural number type.

Since: 4.8.0.0

Synopsis

Documentation

data Natural Source #

Type representing arbitrary-precision non-negative integers.

>>> 2^100 :: Natural
1267650600228229401496703205376

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

>>> -1 :: Natural
*** Exception: arithmetic underflow

Since: 4.8.0.0

Instances

Instances details
Enum Natural Source #

Since: 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 #

Eq Natural Source #

Since: 4.8.0.0

Instance details

Defined in GHC.Natural

Methods

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

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

Integral Natural Source #

Since: 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 #

Data Natural Source #

Since: 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 #

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: 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 #

Ord Natural Source #

Since: 4.8.0.0

Instance details

Defined in GHC.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 #

Read Natural Source #

Since: 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 #

Real Natural Source #

Since: 4.8.0.0

Instance details

Defined in GHC.Real

Methods

toRational :: Natural -> Rational Source #

Show Natural Source #

Since: 4.8.0.0

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS Source #

show :: Natural -> String Source #

showList :: [Natural] -> ShowS Source #

Ix Natural Source #

Since: 4.8.0.0

Instance details

Defined in GHC.Arr

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 #

Bits Natural Source #

Since: 4.8.0

Instance details

Defined in Data.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 #

PrintfArg Natural Source #

Since: 4.8.0.0

Instance details

Defined in Text.Printf

Methods

formatArg :: Natural -> FieldFormatter Source #

parseFormat :: Natural -> ModifierParser Source #