base-4.11.0.0: Basic libraries

Copyright(C) 2014 Herbert Valerio Riedel
(C) 2011 Edward Kmett
Licensesee libraries/base/LICENSE
Maintainerlibraries@haskell.org
Stabilityinternal
Portabilitynon-portable (GHC Extensions)
Safe HaskellUnsafe
LanguageHaskell2010

GHC.Natural

Contents

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: base-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.

>>> 2^20 :: Natural
1267650600228229401496703205376

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

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

Since: base-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 Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Eq Natural Source # 
Instance details

Defined in GHC.Natural

Integral Natural Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Data Natural Source #

Since: base-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 :: (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 #

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Ord Natural Source # 
Instance details

Defined in GHC.Natural

Read Natural Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Real Natural Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Show Natural Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Ix Natural Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Bits Natural Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

PrintfArg Natural Source #

Since: base-4.8.0.0

Instance details

Defined in Text.Printf

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: base-4.8.0.0

Conversions

naturalFromInteger :: Integer -> Natural Source #

Since: base-4.10.0.0

wordToNatural :: Word -> Natural Source #

Construct Natural from Word value.

Since: base-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: base-4.8.0.0

Checked subtraction

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

Natural subtraction. Returns Nothings for non-positive results.

Since: base-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: base-4.8.0.0