base-4.11.1.0: Basic libraries

Copyright (C) 2014 Herbert Valerio Riedel(C) 2011 Edward Kmett see libraries/base/LICENSE [email protected] internal non-portable (GHC Extensions) Unsafe Haskell2010

GHC.Natural

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
 Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods Source # Instance detailsDefined in GHC.Natural Methods Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (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 #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 # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods Source # Instance detailsDefined in GHC.Natural Methods Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural MethodsshowList :: [Natural] -> ShowS Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methodsrange :: (Natural, Natural) -> [Natural] Source #index :: (Natural, Natural) -> Natural -> Int Source #unsafeIndex :: (Natural, Natural) -> Natural -> IntinRange :: (Natural, Natural) -> Natural -> Bool Source #rangeSize :: (Natural, Natural) -> Int Source #unsafeRangeSize :: (Natural, Natural) -> Int Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods Source # Since: base-4.8.0.0 Instance detailsDefined in Text.Printf Methods

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

Since: base-4.10.0.0

Construct Natural from Word value.

Since: base-4.8.0.0

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

Since: base-4.8.0.0

# Checked subtraction

Natural subtraction. Returns Nothings for non-positive results.

Since: base-4.8.0.0

# Modular arithmetic

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

Since: base-4.8.0.0