Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.RealNumber.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
data Nat

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

Eq (RealNumber p) Source #
Instance details Defined in Data.RealNumber.Rational Methods (==) :: RealNumber p -> RealNumber p -> Bool # (/=) :: RealNumber p -> RealNumber p -> Bool #
Fractional (RealNumber p) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.RealNumber.Rational Methods toRational :: RealNumber p -> Rational #
RealFrac (RealNumber p) Source #
Instance details 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) Source #
Instance details Defined in Data.RealNumber.Rational Methods showsPrec :: Int -> RealNumber p -> ShowS # show :: RealNumber p -> String # showList :: [RealNumber p] -> ShowS #
Generic (RealNumber p) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.RealNumber.Rational Methods arbitrary :: Gen (RealNumber p) # shrink :: RealNumber p -> [RealNumber p] #
Hashable (RealNumber p) Source #
Instance details Defined in Data.RealNumber.Rational Methods hashWithSalt :: Int -> RealNumber p -> Int # hash :: RealNumber p -> Int #
ToJSON (RealNumber p) Source #
Instance details 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) Source #
Instance details Defined in Data.RealNumber.Rational Methods parseJSON :: Value -> Parser (RealNumber p) # parseJSONList :: Value -> Parser [RealNumber p] #
NFData (RealNumber p) Source #
Instance details Defined in Data.RealNumber.Rational Methods rnf :: RealNumber p -> () #
type Rep (RealNumber p) Source #
Instance details Defined in Data.RealNumber.Rational type Rep (RealNumber p) = D1 ('MetaData "RealNumber" "Data.RealNumber.Rational" "hgeometry-combinatorial-0.12.0.2-BPOszceZMWb3Na6sqXbM08" '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

Eq (AsFixed p) Source #
Instance details Defined in Data.RealNumber.Rational Methods (==) :: AsFixed p -> AsFixed p -> Bool # (/=) :: AsFixed p -> AsFixed p -> Bool #
HasResolution p => Show (AsFixed p) Source #
Instance details 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) 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.

data Nat #

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

Instances

Instances details

KnownNat n => HasResolution (n :: Nat)	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 #
KnownNat n => Dim (n :: Nat)
Instance details Defined in Linear.V Methods reflectDim :: p n -> Int #
KnownNat n => Reifies (n :: Nat) Integer
Instance details Defined in Data.Reflection Methods reflect :: proxy n -> Integer #
Finite (V n)
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details Defined in Linear.V Methods _19 :: Lens (V n a) (V n a) a a #
type Size (V n)
Instance details Defined in Linear.V type Size (V n) = n