Basement.Compat.Natural

Documentation

data Natural

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: base-4.8.0.0

Instances

Enum Natural

Since: base-4.8.0.0

Defined in GHC.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]

Eq Natural

Since: base-4.8.0.0

Defined in GHC.Natural

Methods

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

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

Integral Natural

Since: base-4.8.0.0

Defined in GHC.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

Data Natural

Since: base-4.8.0.0

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

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

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.Num

Methods

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

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

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

negate :: Natural -> Natural

abs :: Natural -> Natural

signum :: Natural -> Natural

fromInteger :: Integer -> Natural

Ord Natural

Since: base-4.8.0.0

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

Since: base-4.8.0.0

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Natural

readList :: ReadS [Natural]

readPrec :: ReadPrec Natural

readListPrec :: ReadPrec [Natural]

Real Natural

Since: base-4.8.0.0

Defined in GHC.Real

Methods

toRational :: Natural -> Rational

Show Natural

Since: base-4.8.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS

show :: Natural -> String

showList :: [Natural] -> ShowS

Ix Natural

Since: base-4.8.0.0

Defined in GHC.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

Bits Natural

Since: base-4.8.0

Defined in Data.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

Integral Natural

Defined in Basement.Compat.NumLiteral

Methods

fromInteger :: Integer -> Natural

IsNatural Natural

Defined in Basement.Numerical.Number

Methods

toNatural :: Natural -> Natural

IsIntegral Natural

Defined in Basement.Numerical.Number

Methods

toInteger :: Natural -> Integer

Subtractive Natural

Defined in Basement.Numerical.Subtractive

Associated Types

type Difference Natural

Methods

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

Additive Natural

Defined in Basement.Numerical.Additive

Methods

azero :: Natural

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

scale :: IsNatural n => n -> Natural -> Natural

IDivisible Natural

Defined in Basement.Numerical.Multiplicative

Methods

div :: Natural -> Natural -> Natural

mod :: Natural -> Natural -> Natural

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

Multiplicative Natural

Defined in Basement.Numerical.Multiplicative

Methods

midentity :: Natural

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

(^) :: (IsNatural n, Enum n, IDivisible n) => Natural -> n -> Natural

NormalForm Natural

Defined in Basement.NormalForm

Methods

toNormalForm :: Natural -> ()

IsNatural a => IntegralUpsize a Natural

Defined in Basement.IntegralConv

Methods

integralUpsize :: a -> Natural

IntegralDownsize Integer Natural

Defined in Basement.IntegralConv

Methods

integralDownsize :: Integer -> Natural

integralDownsizeCheck :: Integer -> Maybe Natural

IntegralDownsize Natural Word8

Defined in Basement.IntegralConv

Methods

integralDownsize :: Natural -> Word8

integralDownsizeCheck :: Natural -> Maybe Word8

IntegralDownsize Natural Word16

Defined in Basement.IntegralConv

Methods

integralDownsize :: Natural -> Word16

integralDownsizeCheck :: Natural -> Maybe Word16

IntegralDownsize Natural Word32

Defined in Basement.IntegralConv

Methods

integralDownsize :: Natural -> Word32

integralDownsizeCheck :: Natural -> Maybe Word32

IntegralDownsize Natural Word64

Defined in Basement.IntegralConv

Methods

integralDownsize :: Natural -> Word64

integralDownsizeCheck :: Natural -> Maybe Word64

IsNatural n => From n Natural

Defined in Basement.From

Methods

from :: n -> Natural

type Difference Natural

Defined in Basement.Numerical.Subtractive

type Difference Natural = Maybe Natural

integerToNatural :: Integer -> Natural

naturalToInteger :: Natural -> Integer