Config.Number

This module provides a representation of numbers in scientific notation.

Documentation

data Number

Numbers are represented as base, coefficient, and exponent.

The most convenient way to get numbers into and out of this form is to use one of: numberToRational, numberToInteger, rationalToNumber, or integerToNumber.

This representation is explicit about the radix and exponent used to facilitate better pretty-printing. By using explicit exponents extremely large numbers can be represented compactly. Consider that it is easy to write `1e100000000` which would use a significant amount of memory if realized as an Integer. This representation allows concerned programs to check bounds before converting to a representation like Integer.

Constructors

MkNumber

Fields

• numberRadix :: !Radix
• numberCoefficient :: !Rational

Instances

Eq Number

Defined in Config.Number

Methods

(==) :: Number -> Number -> Bool

(/=) :: Number -> Number -> Bool

Data Number

Defined in Config.Number

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Number -> c Number

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Number

toConstr :: Number -> Constr

dataTypeOf :: Number -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Number)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Number)

gmapT :: (forall b. Data b => b -> b) -> Number -> Number

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Number -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Number -> r

gmapQ :: (forall d. Data d => d -> u) -> Number -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Number -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Number -> m Number

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Number -> m Number

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Number -> m Number

Ord Number

Defined in Config.Number

Methods

compare :: Number -> Number -> Ordering

(<) :: Number -> Number -> Bool

(<=) :: Number -> Number -> Bool

(>) :: Number -> Number -> Bool

(>=) :: Number -> Number -> Bool

max :: Number -> Number -> Number

min :: Number -> Number -> Number

Read Number

Defined in Config.Number

Methods

readsPrec :: Int -> ReadS Number

readList :: ReadS [Number]

readPrec :: ReadPrec Number

readListPrec :: ReadPrec [Number]

Show Number

Defined in Config.Number

Methods

showsPrec :: Int -> Number -> ShowS

show :: Number -> String

showList :: [Number] -> ShowS

Generic Number

Defined in Config.Number

Associated Types

type Rep Number :: Type -> Type

Methods

from :: Number -> Rep Number x

to :: Rep Number x -> Number

type Rep Number

Defined in Config.Number

type Rep Number = D1 ('MetaData "Number" "Config.Number" "config-value-0.7.0.0-JboFCtXlIzo1Q4jM4SfnDg" 'False) (C1 ('MetaCons "MkNumber" 'PrefixI 'True) (S1 ('MetaSel ('Just "numberRadix") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Radix) :*: S1 ('MetaSel ('Just "numberCoefficient") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Rational)))

data Radix

Radix used for a number. Some radix modes support an exponent.

Constructors

Radix2

binary, base 2

Radix8

octal, base 8

Radix10 !Integer

decimal, base 10, exponent base 10

Radix16 !Integer

hexdecimal, base 16, exponent base 2

Instances

Eq Radix

Defined in Config.Number

Methods

(==) :: Radix -> Radix -> Bool

(/=) :: Radix -> Radix -> Bool

Data Radix

Defined in Config.Number

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Radix -> c Radix

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Radix

toConstr :: Radix -> Constr

dataTypeOf :: Radix -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Radix)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Radix)

gmapT :: (forall b. Data b => b -> b) -> Radix -> Radix

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Radix -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Radix -> r

gmapQ :: (forall d. Data d => d -> u) -> Radix -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Radix -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Radix -> m Radix

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Radix -> m Radix

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Radix -> m Radix

Ord Radix

Defined in Config.Number

Methods

compare :: Radix -> Radix -> Ordering

(<) :: Radix -> Radix -> Bool

(<=) :: Radix -> Radix -> Bool

(>) :: Radix -> Radix -> Bool

(>=) :: Radix -> Radix -> Bool

max :: Radix -> Radix -> Radix

min :: Radix -> Radix -> Radix

Read Radix

Defined in Config.Number

Methods

readsPrec :: Int -> ReadS Radix

readList :: ReadS [Radix]

readPrec :: ReadPrec Radix

readListPrec :: ReadPrec [Radix]

Show Radix

Defined in Config.Number

Methods

showsPrec :: Int -> Radix -> ShowS

show :: Radix -> String

showList :: [Radix] -> ShowS

Generic Radix

Defined in Config.Number

Associated Types

type Rep Radix :: Type -> Type

Methods

from :: Radix -> Rep Radix x

to :: Rep Radix x -> Radix

type Rep Radix

Defined in Config.Number

type Rep Radix = D1 ('MetaData "Radix" "Config.Number" "config-value-0.7.0.0-JboFCtXlIzo1Q4jM4SfnDg" 'False) ((C1 ('MetaCons "Radix2" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Radix8" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "Radix10" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Integer)) :+: C1 ('MetaCons "Radix16" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Integer))))

radixToInt :: Radix -> Int

Returns the radix as an integer ignoring any exponent.

numberToRational :: Number -> Rational

Convert a number to a Rational. Warning: This can use a lot of member in the case of very large exponent parts.

numberToInteger :: Number -> Maybe Integer

Convert a number to a Integer. Warning: This can use a lot of member in the case of very large exponent parts.

integerToNumber :: Integer -> Number

Integer to a radix 10 Number with no exponent

rationalToNumber :: Rational -> Number

Rational to a radix 10 Number with no exponent