Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	Safe-Inferred
Language	GHC2021

HGeometry.Number.Real.Rational

Contents

Converting to and from RealNumber's

Description

Synopsis

newtype RealNumber (p :: Nat) = RealNumber Rational
data AsFixed p
- = Exact !(Fixed p)
- | Lossy !(Fixed p)
asFixed :: KnownNat p => RealNumber p -> AsFixed (NatPrec p)
toFixed :: KnownNat p => RealNumber p -> Fixed (NatPrec p)
fromFixed :: KnownNat p => Fixed (NatPrec p) -> RealNumber p
type Nat = Natural

Documentation

newtype RealNumber (p :: Nat) Source #

Real Numbers represented using Rational numbers. The number type itself is exact in the sense that we can represent any rational number.

The parameter, a natural number, represents the precision (in number of decimals behind the period) with which we display the numbers when printing them (using Show).

If the number cannot be displayed exactly a ~ is printed after the number.

Constructors

RealNumber Rational

Instances

Instances details

FromJSON (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods parseJSON :: Value -> Parser (RealNumber p) Source # parseJSONList :: Value -> Parser [RealNumber p] Source # omittedField :: Maybe (RealNumber p) Source #
ToJSON (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods toJSON :: RealNumber p -> Value Source # toEncoding :: RealNumber p -> Encoding Source # toJSONList :: [RealNumber p] -> Value Source # toEncodingList :: [RealNumber p] -> Encoding Source # omitField :: RealNumber p -> Bool Source #
KnownNat p => Data (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> RealNumber p -> c (RealNumber p) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (RealNumber p) # toConstr :: RealNumber p -> Constr # dataTypeOf :: RealNumber p -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (RealNumber p)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (RealNumber p)) # gmapT :: (forall b. Data b => b -> b) -> RealNumber p -> RealNumber p # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> RealNumber p -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> RealNumber p -> r # gmapQ :: (forall d. Data d => d -> u) -> RealNumber p -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> RealNumber p -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> RealNumber p -> m (RealNumber p) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> RealNumber p -> m (RealNumber p) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> RealNumber p -> m (RealNumber p) #
Generic (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Associated Types type Rep (RealNumber p) :: Type -> Type # Methods from :: RealNumber p -> Rep (RealNumber p) x # to :: Rep (RealNumber p) x -> RealNumber p #
Num (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods (+) :: RealNumber p -> RealNumber p -> RealNumber p # (-) :: RealNumber p -> RealNumber p -> RealNumber p # (*) :: RealNumber p -> RealNumber p -> RealNumber p # negate :: RealNumber p -> RealNumber p # abs :: RealNumber p -> RealNumber p # signum :: RealNumber p -> RealNumber p # fromInteger :: Integer -> RealNumber p #
KnownNat p => Read (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods readsPrec :: Int -> ReadS (RealNumber p) # readList :: ReadS [RealNumber p] # readPrec :: ReadPrec (RealNumber p) # readListPrec :: ReadPrec [RealNumber p] #
Fractional (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods (/) :: RealNumber p -> RealNumber p -> RealNumber p # recip :: RealNumber p -> RealNumber p # fromRational :: Rational -> RealNumber p #
Real (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods toRational :: RealNumber p -> Rational #
RealFrac (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods properFraction :: Integral b => RealNumber p -> (b, RealNumber p) # truncate :: Integral b => RealNumber p -> b # round :: Integral b => RealNumber p -> b # ceiling :: Integral b => RealNumber p -> b # floor :: Integral b => RealNumber p -> b #
KnownNat p => Show (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods showsPrec :: Int -> RealNumber p -> ShowS # show :: RealNumber p -> String # showList :: [RealNumber p] -> ShowS #
NFData (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods rnf :: RealNumber p -> () #
Eq (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods (==) :: RealNumber p -> RealNumber p -> Bool # (/=) :: RealNumber p -> RealNumber p -> Bool #
Ord (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods compare :: RealNumber p -> RealNumber p -> Ordering # (<) :: RealNumber p -> RealNumber p -> Bool # (<=) :: RealNumber p -> RealNumber p -> Bool # (>) :: RealNumber p -> RealNumber p -> Bool # (>=) :: RealNumber p -> RealNumber p -> Bool # max :: RealNumber p -> RealNumber p -> RealNumber p # min :: RealNumber p -> RealNumber p -> RealNumber p #
Random (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods randomR :: RandomGen g => (RealNumber p, RealNumber p) -> g -> (RealNumber p, g) Source # random :: RandomGen g => g -> (RealNumber p, g) Source # randomRs :: RandomGen g => (RealNumber p, RealNumber p) -> g -> [RealNumber p] Source # randoms :: RandomGen g => g -> [RealNumber p] Source #
type Rep (RealNumber p) Source #
Instance details Defined in HGeometry.Number.Real.Rational type Rep (RealNumber p) = D1 ('MetaData "RealNumber" "HGeometry.Number.Real.Rational" "hgeometry-combinatorial-1.0.0.0-inplace" 'True) (C1 ('MetaCons "RealNumber" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Rational)))

Converting to and from RealNumber's

data AsFixed p Source #

Fixed-precision representation of a RealNumber. If there's insufficient precision to accurately represent the RealNumber then the Lossy constructor will be used.

Constructors

Exact !(Fixed p)
Lossy !(Fixed p)

Instances

Instances details

HasResolution p => Show (AsFixed p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods showsPrec :: Int -> AsFixed p -> ShowS # show :: AsFixed p -> String # showList :: [AsFixed p] -> ShowS #
Eq (AsFixed p) Source #
Instance details Defined in HGeometry.Number.Real.Rational Methods (==) :: AsFixed p -> AsFixed p -> Bool # (/=) :: AsFixed p -> AsFixed p -> Bool #

asFixed :: KnownNat p => RealNumber p -> AsFixed (NatPrec p) Source #

Cast RealNumber to a fixed-precision number. Data-loss caused by insufficient precision will be marked by the Lossy constructor.

toFixed :: KnownNat p => RealNumber p -> Fixed (NatPrec p) Source #

Cast RealNumber to a fixed-precision number. Data is silently lost if there's insufficient precision.

fromFixed :: KnownNat p => Fixed (NatPrec p) -> RealNumber p Source #

Cast a fixed-precision number to a RealNumber.

type Nat = Natural #

A type synonym for Natural.

Prevously, this was an opaque data type, but it was changed to a type synonym.

Since: base-4.16.0.0