planet-mitchell-0.0.0: Planet Mitchell

Safe HaskellSafe
LanguageHaskell2010

Numeric.Ratio

Synopsis

Documentation

data Ratio a #

Rational numbers, with numerator and denominator of some Integral type.

Instances
NFData1 Ratio

Available on base >=4.9

Since: deepseq-1.4.3.0

Instance details

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Ratio a -> () #

Integral a => Enum (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

succ :: Ratio a -> Ratio a #

pred :: Ratio a -> Ratio a #

toEnum :: Int -> Ratio a #

fromEnum :: Ratio a -> Int #

enumFrom :: Ratio a -> [Ratio a] #

enumFromThen :: Ratio a -> Ratio a -> [Ratio a] #

enumFromTo :: Ratio a -> Ratio a -> [Ratio a] #

enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] #

Eq a => Eq (Ratio a) 
Instance details

Defined in GHC.Real

Methods

(==) :: Ratio a -> Ratio a -> Bool #

(/=) :: Ratio a -> Ratio a -> Bool #

Integral a => Fractional (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

(/) :: Ratio a -> Ratio a -> Ratio a #

recip :: Ratio a -> Ratio a #

fromRational :: Rational -> Ratio a #

(Data a, Integral a) => Data (Ratio a)

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ratio a -> c (Ratio a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ratio a) #

toConstr :: Ratio a -> Constr #

dataTypeOf :: Ratio a -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ratio a)) #

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

gmapT :: (forall b. Data b => b -> b) -> Ratio a -> Ratio a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ratio a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Ratio a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Ratio a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ratio a -> m (Ratio a) #

Integral a => Num (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

(+) :: Ratio a -> Ratio a -> Ratio a #

(-) :: Ratio a -> Ratio a -> Ratio a #

(*) :: Ratio a -> Ratio a -> Ratio a #

negate :: Ratio a -> Ratio a #

abs :: Ratio a -> Ratio a #

signum :: Ratio a -> Ratio a #

fromInteger :: Integer -> Ratio a #

Integral a => Ord (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

compare :: Ratio a -> Ratio a -> Ordering #

(<) :: Ratio a -> Ratio a -> Bool #

(<=) :: Ratio a -> Ratio a -> Bool #

(>) :: Ratio a -> Ratio a -> Bool #

(>=) :: Ratio a -> Ratio a -> Bool #

max :: Ratio a -> Ratio a -> Ratio a #

min :: Ratio a -> Ratio a -> Ratio a #

(Integral a, Read a) => Read (Ratio a)

Since: base-2.1

Instance details

Defined in GHC.Read

Integral a => Real (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

toRational :: Ratio a -> Rational #

Integral a => RealFrac (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

properFraction :: Integral b => Ratio a -> (b, Ratio a) #

truncate :: Integral b => Ratio a -> b #

round :: Integral b => Ratio a -> b #

ceiling :: Integral b => Ratio a -> b #

floor :: Integral b => Ratio a -> b #

Show a => Show (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

showsPrec :: Int -> Ratio a -> ShowS #

show :: Ratio a -> String #

showList :: [Ratio a] -> ShowS #

Integral a => Lift (Ratio a) 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Ratio a -> Q Exp #

Hashable a => Hashable (Ratio a) 
Instance details

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Ratio a -> Int #

hash :: Ratio a -> Int #

(ToJSON a, Integral a) => ToJSON (Ratio a) 
Instance details

Defined in Data.Aeson.Types.ToJSON

(FromJSON a, Integral a) => FromJSON (Ratio a) 
Instance details

Defined in Data.Aeson.Types.FromJSON

(Storable a, Integral a) => Storable (Ratio a)

Since: base-4.8.0.0

Instance details

Defined in Foreign.Storable

Methods

sizeOf :: Ratio a -> Int #

alignment :: Ratio a -> Int #

peekElemOff :: Ptr (Ratio a) -> Int -> IO (Ratio a) #

pokeElemOff :: Ptr (Ratio a) -> Int -> Ratio a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (Ratio a) #

pokeByteOff :: Ptr b -> Int -> Ratio a -> IO () #

peek :: Ptr (Ratio a) -> IO (Ratio a) #

poke :: Ptr (Ratio a) -> Ratio a -> IO () #

NFData a => NFData (Ratio a) 
Instance details

Defined in Control.DeepSeq

Methods

rnf :: Ratio a -> () #

(Serialise a, Integral a) => Serialise (Ratio a)

Since: serialise-0.2.0.0

Instance details

Defined in Codec.Serialise.Class

(Eq a) :=> (Eq (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Eq a :- Eq (Ratio a) #

(Integral a) :=> (RealFrac (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- RealFrac (Ratio a) #

(Integral a) :=> (Real (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Real (Ratio a) #

(Integral a) :=> (Ord (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Ord (Ratio a) #

(Integral a) :=> (Num (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Num (Ratio a) #

(Integral a) :=> (Fractional (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Fractional (Ratio a) #

(Integral a) :=> (Enum (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: Integral a :- Enum (Ratio a) #

(Integral a, Show a) :=> (Show (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: (Integral a, Show a) :- Show (Ratio a) #

(Integral a, Read a) :=> (Read (Ratio a)) 
Instance details

Defined in Data.Constraint

Methods

ins :: (Integral a, Read a) :- Read (Ratio a) #

type Rational = Ratio Integer #

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

(%) :: Integral a => a -> a -> Ratio a infixl 7 #

Forms the ratio of two integral numbers.

numerator :: Ratio a -> a #

Extract the numerator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

denominator :: Ratio a -> a #

Extract the denominator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

approxRational :: RealFrac a => a -> a -> Rational #

approxRational, applied to two real fractional numbers x and epsilon, returns the simplest rational number within epsilon of x. A rational number y is said to be simpler than another y' if

Any real interval contains a unique simplest rational; in particular, note that 0/1 is the simplest rational of all.

fromRat :: RealFloat a => Rational -> a #

Converts a Rational value into any type in class RealFloat.