Safe Haskell	Safe
Language	Haskell2010

Num.Ratio

Synopsis

data Ratio a
type Rational = Ratio Integer
(%) :: Integral a => a -> a -> Ratio a
numerator :: Ratio a -> a
denominator :: Ratio a -> a
approxRational :: RealFrac a => a -> a -> Rational
fromRat :: RealFloat a => Rational -> a

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 Methods readsPrec :: Int -> ReadS (Ratio a) # readList :: ReadS [Ratio a] # readPrec :: ReadPrec (Ratio a) # readListPrec :: ReadPrec [Ratio a] #
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 Methods toJSON :: Ratio a -> Value # toEncoding :: Ratio a -> Encoding # toJSONList :: [Ratio a] -> Value # toEncodingList :: [Ratio a] -> Encoding #
(FromJSON a, Integral a) => FromJSON (Ratio a)
Instance details Defined in Data.Aeson.Types.FromJSON Methods parseJSON :: Value -> Parser (Ratio a) # parseJSONList :: Value -> Parser [Ratio a] #
(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 Methods encode :: Ratio a -> Encoding # decode :: Decoder s (Ratio a) # encodeList :: [Ratio a] -> Encoding # decodeList :: Decoder s [Ratio a] #
(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

abs (numerator y) <= abs (numerator y'), and
denominator y <= denominator y'.

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.