Safe Haskell	None
Language	Haskell2010

Numeric.Natural

Synopsis

data Natural
naturalLogBase :: Natural -> Natural -> Int
naturalLog2 :: Natural -> Int
naturalLog10 :: Natural -> Int

Documentation

data Natural #

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

Instances

Enum Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural 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
Instance details Defined in GHC.Natural Methods (==) :: Natural -> Natural -> Bool # (/=) :: Natural -> Natural -> Bool #
Integral Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural 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
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 # 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 :: (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	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods (+) :: Natural -> Natural -> Natural # (-) :: Natural -> Natural -> Natural # (*) :: Natural -> Natural -> Natural # negate :: Natural -> Natural # abs :: Natural -> Natural # signum :: Natural -> Natural # fromInteger :: Integer -> Natural #
Ord Natural
Instance details 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
Instance details Defined in GHC.Natural Methods readsPrec :: Int -> ReadS Natural # readList :: ReadS [Natural] # readPrec :: ReadPrec Natural # readListPrec :: ReadPrec [Natural] #
Real Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods toRational :: Natural -> Rational #
Show Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods showsPrec :: Int -> Natural -> ShowS # show :: Natural -> String # showList :: [Natural] -> ShowS #
Ix Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural 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
Lift Natural
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Natural -> Q Exp #
Hashable Natural
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Natural -> Int # hash :: Natural -> Int #
ToJSON Natural
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Natural -> Value # toEncoding :: Natural -> Encoding # toJSONList :: [Natural] -> Value # toEncodingList :: [Natural] -> Encoding #
ToJSONKey Natural
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSONKey :: ToJSONKeyFunction Natural # toJSONKeyList :: ToJSONKeyFunction [Natural] #
FromJSON Natural
Instance details Defined in Data.Aeson.Types.FromJSON Methods parseJSON :: Value -> Parser Natural # parseJSONList :: Value -> Parser [Natural] #
FromJSONKey Natural
Instance details Defined in Data.Aeson.Types.FromJSON Methods fromJSONKey :: FromJSONKeyFunction Natural # fromJSONKeyList :: FromJSONKeyFunction [Natural] #
PrintfArg Natural	Since: base-4.8.0.0
Instance details Defined in Text.Printf Methods formatArg :: Natural -> FieldFormatter # parseFormat :: Natural -> ModifierParser #
Bits Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural 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 #
NFData Natural	Since: deepseq-1.4.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Natural -> () #
Pretty Natural
Instance details Defined in Data.Text.Prettyprint.Doc.Internal Methods pretty :: Natural -> Doc ann # prettyList :: [Natural] -> Doc ann #
Serialise Natural	Since: serialise-0.2.0.0
Instance details Defined in Codec.Serialise.Class Methods encode :: Natural -> Encoding # decode :: Decoder s Natural # encodeList :: [Natural] -> Encoding # decodeList :: Decoder s [Natural] #
() :=> (Enum Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Enum Natural #
() :=> (Eq Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Eq Natural #
() :=> (Integral Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Integral Natural #
() :=> (Num Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Num Natural #
() :=> (Ord Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Ord Natural #
() :=> (Read Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Read Natural #
() :=> (Real Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Real Natural #
() :=> (Show Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Show Natural #
() :=> (Bits Natural)
Instance details Defined in Data.Constraint Methods ins :: () :- Bits Natural #

naturalLogBase :: Natural -> Natural -> Int #

Cacluate the integer logarithm for an arbitrary base. The base must be greater than 1, the second argument, the number whose logarithm is sought, must be positive, otherwise an error is thrown. If base == 2, the specialised version is called, which is more efficient than the general algorithm.

Satisfies:

base ^ integerLogBase base m <= m < base ^ (integerLogBase base m + 1)

for base > 1 and m > 0.

naturalLog2 :: Natural -> Int #

Calculate the natural logarithm of an Natural to base 2. The argument must be non-zero, otherwise an error is thrown.

naturalLog10 :: Natural -> Int #

Calculate the integer logarithm of an Integer to base 10. The argument must be not zero, otherwise an error is thrown.