base-4.10.1.0: Basic libraries

Copyright | (C) 2014 Herbert Valerio Riedel (C) 2011 Edward Kmett
License | see libraries/base/LICENSE
Maintainer | libraries@haskell.org
Stability | provisional
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Numeric.Natural

Description

The arbitrary-precision `Natural` number type.

Since: 4.8.0.0

Synopsis

- data Natural

# Documentation

data Natural #

Type representing arbitrary-precision non-negative integers.

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

Since: 4.8.0.0

Instances

Enum Natural # | Since: 4.8.0.0
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] #
Eq Natural # |
Methods (==) :: Natural -> Natural -> Bool Source # (/=) :: Natural -> Natural -> Bool Source #
Integral Natural # | Since: 4.8.0.0
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 #
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 #

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 :: (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 #

Num Natural # | Since: 4.8.0.0
Methods (+) :: Natural -> Natural -> Natural # (-) :: Natural -> Natural -> Natural # (*) :: Natural -> Natural -> Natural # negate :: Natural -> Natural # abs :: Natural -> Natural # signum :: Natural -> Natural # fromInteger :: Integer -> Natural #
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 # readList :: ReadS [Natural] # readPrec :: ReadPrec Natural # readListPrec :: ReadPrec [Natural] #
Real Natural # | Since: 4.8.0.0
Methods toRational :: Natural -> Rational #
Show Natural # | Since: 4.8.0.0
Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Ix Natural # | Since: 4.8.0.0
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
Bits Natural # | Since: 4.8.0.0

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 #

PrintfArg Natural # | Since: 4.8.0.0
Methods formatArg :: Natural -> FieldFormatter # parseFormat :: Natural -> ModifierParser #