Data.RealNumber.Rational

Documentation

newtype RealNumber (p :: Nat)

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

Eq (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

(==) :: RealNumber p -> RealNumber p -> Bool

(/=) :: RealNumber p -> RealNumber p -> Bool

Fractional (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

(/) :: RealNumber p -> RealNumber p -> RealNumber p

recip :: RealNumber p -> RealNumber p

fromRational :: Rational -> RealNumber p

KnownNat p => Data (RealNumber p)

Defined in Data.RealNumber.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)

Num (RealNumber p)

Defined in Data.RealNumber.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

Ord (RealNumber p)

Defined in Data.RealNumber.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

KnownNat p => Read (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

readsPrec :: Int -> ReadS (RealNumber p)

readList :: ReadS [RealNumber p]

readPrec :: ReadPrec (RealNumber p)

readListPrec :: ReadPrec [RealNumber p]

Real (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

toRational :: RealNumber p -> Rational

RealFrac (RealNumber p)

Defined in Data.RealNumber.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)

Defined in Data.RealNumber.Rational

Methods

showsPrec :: Int -> RealNumber p -> ShowS

show :: RealNumber p -> String

showList :: [RealNumber p] -> ShowS

Generic (RealNumber p)

Defined in Data.RealNumber.Rational

Associated Types

type Rep (RealNumber p) :: Type -> Type

Methods

from :: RealNumber p -> Rep (RealNumber p) x

to :: Rep (RealNumber p) x -> RealNumber p

Random (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

randomR :: RandomGen g => (RealNumber p, RealNumber p) -> g -> (RealNumber p, g)

random :: RandomGen g => g -> (RealNumber p, g)

randomRs :: RandomGen g => (RealNumber p, RealNumber p) -> g -> [RealNumber p]

randoms :: RandomGen g => g -> [RealNumber p]

KnownNat p => Arbitrary (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

arbitrary :: Gen (RealNumber p)

shrink :: RealNumber p -> [RealNumber p]

Hashable (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

hashWithSalt :: Int -> RealNumber p -> Int

hash :: RealNumber p -> Int

ToJSON (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

toJSON :: RealNumber p -> Value

toEncoding :: RealNumber p -> Encoding

toJSONList :: [RealNumber p] -> Value

toEncodingList :: [RealNumber p] -> Encoding

FromJSON (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

parseJSON :: Value -> Parser (RealNumber p)

parseJSONList :: Value -> Parser [RealNumber p]

NFData (RealNumber p)

Defined in Data.RealNumber.Rational

Methods

rnf :: RealNumber p -> ()

type Rep (RealNumber p)

Defined in Data.RealNumber.Rational

type Rep (RealNumber p) = D1 ('MetaData "RealNumber" "Data.RealNumber.Rational" "hgeometry-combinatorial-0.12.0.0-VIzkyOvE5y1mf3MPLhQ6V" '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

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

Eq (AsFixed p)

Defined in Data.RealNumber.Rational

Methods

(==) :: AsFixed p -> AsFixed p -> Bool

(/=) :: AsFixed p -> AsFixed p -> Bool

HasResolution p => Show (AsFixed p)

Defined in Data.RealNumber.Rational

Methods

showsPrec :: Int -> AsFixed p -> ShowS

show :: AsFixed p -> String

showList :: [AsFixed p] -> ShowS

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

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)

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

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

Cast a fixed-precision number to a RealNumber.

data Nat

(Kind) This is the kind of type-level natural numbers.

Instances

KnownNat n => HasResolution (n :: Nat)

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

Defined in Data.Fixed

Methods

resolution :: p n -> Integer

KnownNat n => Dim (n :: Nat)

Defined in Linear.V

Methods

reflectDim :: p n -> Int

KnownNat n => Reifies (n :: Nat) Integer

Defined in Data.Reflection

Methods

reflect :: proxy n -> Integer

Finite (V n)

Defined in Linear.V

Associated Types

type Size (V n) :: Nat

Methods

toV :: V n a -> V (Size (V n)) a

fromV :: V (Size (V n)) a -> V n a

1 <= n => Field1 (V n a) (V n a) a a

Defined in Linear.V

Methods

_1 :: Lens (V n a) (V n a) a a

2 <= n => Field2 (V n a) (V n a) a a

Defined in Linear.V

Methods

_2 :: Lens (V n a) (V n a) a a

3 <= n => Field3 (V n a) (V n a) a a

Defined in Linear.V

Methods

_3 :: Lens (V n a) (V n a) a a

4 <= n => Field4 (V n a) (V n a) a a

Defined in Linear.V

Methods

_4 :: Lens (V n a) (V n a) a a

5 <= n => Field5 (V n a) (V n a) a a

Defined in Linear.V

Methods

_5 :: Lens (V n a) (V n a) a a

6 <= n => Field6 (V n a) (V n a) a a

Defined in Linear.V

Methods

_6 :: Lens (V n a) (V n a) a a

7 <= n => Field7 (V n a) (V n a) a a

Defined in Linear.V

Methods

_7 :: Lens (V n a) (V n a) a a

8 <= n => Field8 (V n a) (V n a) a a

Defined in Linear.V

Methods

_8 :: Lens (V n a) (V n a) a a

9 <= n => Field9 (V n a) (V n a) a a

Defined in Linear.V

Methods

_9 :: Lens (V n a) (V n a) a a

10 <= n => Field10 (V n a) (V n a) a a

Defined in Linear.V

Methods

_10 :: Lens (V n a) (V n a) a a

11 <= n => Field11 (V n a) (V n a) a a

Defined in Linear.V

Methods

_11 :: Lens (V n a) (V n a) a a

12 <= n => Field12 (V n a) (V n a) a a

Defined in Linear.V

Methods

_12 :: Lens (V n a) (V n a) a a

13 <= n => Field13 (V n a) (V n a) a a

Defined in Linear.V

Methods

_13 :: Lens (V n a) (V n a) a a

14 <= n => Field14 (V n a) (V n a) a a

Defined in Linear.V

Methods

_14 :: Lens (V n a) (V n a) a a

15 <= n => Field15 (V n a) (V n a) a a

Defined in Linear.V

Methods

_15 :: Lens (V n a) (V n a) a a

16 <= n => Field16 (V n a) (V n a) a a

Defined in Linear.V

Methods

_16 :: Lens (V n a) (V n a) a a

17 <= n => Field17 (V n a) (V n a) a a

Defined in Linear.V

Methods

_17 :: Lens (V n a) (V n a) a a

18 <= n => Field18 (V n a) (V n a) a a

Defined in Linear.V

Methods

_18 :: Lens (V n a) (V n a) a a

19 <= n => Field19 (V n a) (V n a) a a

Defined in Linear.V

Methods

_19 :: Lens (V n a) (V n a) a a

type Size (V n)

Defined in Linear.V

type Size (V n) = n