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GHC.Natural

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

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

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
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
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
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
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
Methods readsPrec :: Int -> ReadS Natural Source readList :: ReadS [Natural] Source readPrec :: ReadPrec Natural Source readListPrec :: ReadPrec [Natural] Source
Real Natural
Methods toRational :: Natural -> Rational Source
Show Natural
Methods showsPrec :: Int -> Natural -> ShowS Source show :: Natural -> String Source showList :: [Natural] -> ShowS Source
Ix Natural
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
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
Methods formatArg :: Natural -> FieldFormatter Source parseFormat :: Natural -> ModifierParser Source

isValidNatural :: Natural -> Bool Source

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: 4.8.0.0

Conversions

wordToNatural :: Word -> Natural Source

Construct Natural from Word value.

Since: 4.8.0.0

naturalToWordMaybe :: Natural -> Maybe Word Source

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

Since: 4.8.0.0

Checked subtraction

minusNaturalMaybe :: Natural -> Natural -> Maybe Natural Source

Natural subtraction. Returns Nothings for non-positive results.

Since: 4.8.0.0

Modular arithmetic

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

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

Since: 4.8.0.0

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.0.1/docs/html/libraries/base-4.9.0.0/GHC-Natural.html

GHC.Natural

GHC.Natural

Contents

Description

The Natural number type

Constructors

Instances

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Methods

Conversions

Checked subtraction

Modular arithmetic