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GHC.Natural

Safe Haskell Trustworthy
Language Haskell2010

Description

Compatibility module for pre ghc-bignum code.

data Natural where Source

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Bundled Patterns

pattern NatS# :: Word# -> Natural
pattern NatJ# :: BigNat -> Natural
Instances
Instances details
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 :: forall r r'. (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
Bits Natural Source

Since: base-4.8.0
Instance details

Defined in GHC.Bits

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
Enum Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Enum

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
Ix Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Ix

Methods

range :: (Natural, Natural) -> [Natural] Source

index :: (Natural, Natural) -> Natural -> Int Source

unsafeIndex :: (Natural, Natural) -> Natural -> Int Source

inRange :: (Natural, Natural) -> Natural -> Bool Source

rangeSize :: (Natural, Natural) -> Int Source

unsafeRangeSize :: (Natural, Natural) -> Int Source
Num Natural Source

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
Instance details

Defined in GHC.Num

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
Read Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Natural Source

readList :: ReadS [Natural] Source

readPrec :: ReadPrec Natural Source

readListPrec :: ReadPrec [Natural] Source
Integral Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Real

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
Real Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Real

Methods

toRational :: Natural -> Rational Source
Show Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS Source

show :: Natural -> String Source

showList :: [Natural] -> ShowS Source
PrintfArg Natural Source

Since: base-4.8.0.0
Instance details

Defined in Text.Printf

Methods

formatArg :: Natural -> FieldFormatter Source

parseFormat :: Natural -> ModifierParser Source
Eq Natural
Instance details

Defined in GHC.Num.Natural

Methods

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

(/=) :: Natural -> Natural -> Bool Source
Ord Natural
Instance details

Defined in GHC.Num.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
KnownNat n => HasResolution (n :: Nat) Source

For example, Fixed 1000 will give you a Fixed with a resolution of 1000.
Instance details

Defined in Data.Fixed

Methods

resolution :: p n -> Integer Source
type Compare (a :: Natural) (b :: Natural) Source
Instance details

Defined in Data.Type.Ord

type Compare (a :: Natural) (b :: Natural) = CmpNat a b

data BigNat Source

A lifted BigNat

Represented as an array of limbs (Word#) stored in little-endian order (Word# themselves use machine order).

Invariant (canonical representation): higher Word# is non-zero.

As a consequence, zero is represented with a WordArray# whose size is 0.

Constructors

BN#

Fields
Instances
Instances details
Eq BigNat
Instance details

Defined in GHC.Num.BigNat

Methods

(==) :: BigNat -> BigNat -> Bool Source

(/=) :: BigNat -> BigNat -> Bool Source
Ord BigNat
Instance details

Defined in GHC.Num.BigNat

Methods

compare :: BigNat -> BigNat -> Ordering Source

(<) :: BigNat -> BigNat -> Bool Source

(<=) :: BigNat -> BigNat -> Bool Source

(>) :: BigNat -> BigNat -> Bool Source

(>=) :: BigNat -> BigNat -> Bool Source

max :: BigNat -> BigNat -> BigNat Source

min :: BigNat -> BigNat -> BigNat Source

mkNatural :: [Word] -> Natural Source

Construct Natural value from list of Words.

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

Arithmetic

plusNatural :: Natural -> Natural -> Natural Source

Natural Addition

minusNatural :: Natural -> Natural -> Natural Source

Natural subtraction. May throw Underflow.

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

Natural subtraction. Returns Nothings for non-positive results.

Since: base-4.8.0.0

timesNatural :: Natural -> Natural -> Natural Source

Natural multiplication

negateNatural :: Natural -> Natural Source

signumNatural :: Natural -> Natural Source

quotRemNatural :: Natural -> Natural -> (Natural, Natural) Source

quotNatural :: Natural -> Natural -> Natural Source

remNatural :: Natural -> Natural -> Natural Source

gcdNatural :: Natural -> Natural -> Natural Source

Compute greatest common divisor.

lcmNatural :: Natural -> Natural -> Natural Source

Compute least common multiple.

Bits

andNatural :: Natural -> Natural -> Natural Source

orNatural :: Natural -> Natural -> Natural Source

xorNatural :: Natural -> Natural -> Natural Source

bitNatural :: Int# -> Natural Source

testBitNatural :: Natural -> Int -> Bool Source

popCountNatural :: Natural -> Int Source

shiftLNatural :: Natural -> Int -> Natural Source

shiftRNatural :: Natural -> Int -> Natural Source

Conversions

naturalToInteger :: Natural -> Integer Source

Since: base-4.12.0.0

naturalToWord :: Natural -> Word Source

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

wordToNatural :: Word -> Natural Source

Construct Natural from Word value.

Since: base-4.8.0.0

wordToNatural# :: Word -> Natural Source

naturalFromInteger :: Integer -> Natural Source

Since: base-4.10.0.0

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

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/GHC-Natural.html