Data.Ratio

Copyright (c) The University of Glasgow 2001
License BSD-style (see the file libraries/base/LICENSE)
Maintainer [email protected]
Stability stable
Portability portable
Safe Haskell Safe
Language Haskell2010

Description

Standard functions on rational numbers

data Ratio a Source

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

Note that Ratio's instances inherit the deficiencies from the type parameter's. For example, Ratio Natural's Num instance has similar problems to Natural's.

Instances
Instances details
Integral a => Enum (Ratio a)

Since: base-2.0.1
Instance details

Defined in GHC.Real

Methods

succ :: Ratio a -> Ratio a Source

pred :: Ratio a -> Ratio a Source

toEnum :: Int -> Ratio a Source

fromEnum :: Ratio a -> Int Source

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

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

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

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

Eq a => Eq (Ratio a)

Since: base-2.1
Instance details

Defined in GHC.Real

Methods

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

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

Integral a => Fractional (Ratio a)

Since: base-2.0.1
Instance details

Defined in GHC.Real

Methods

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

recip :: Ratio a -> Ratio a Source

fromRational :: Rational -> Ratio a Source

(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) Source

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

toConstr :: Ratio a -> Constr Source

dataTypeOf :: Ratio a -> DataType Source

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

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

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

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

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

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

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

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

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

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

Integral a => Num (Ratio a)

Since: base-2.0.1
Instance details

Defined in GHC.Real

Methods

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

(-) :: Ratio a -> Ratio a -> Ratio a Source

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

negate :: Ratio a -> Ratio a Source

abs :: Ratio a -> Ratio a Source

signum :: Ratio a -> Ratio a Source

fromInteger :: Integer -> Ratio a Source

Integral a => Ord (Ratio a)

Since: base-2.0.1
Instance details

Defined in GHC.Real

Methods

compare :: Ratio a -> Ratio a -> Ordering Source

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

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

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

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

max :: Ratio a -> Ratio a -> Ratio a Source

min :: Ratio a -> Ratio a -> Ratio a Source

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

Since: base-2.1
Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (Ratio a) Source

readList :: ReadS [Ratio a] Source

readPrec :: ReadPrec (Ratio a) Source

readListPrec :: ReadPrec [Ratio a] Source

Integral a => Real (Ratio a)

Since: base-2.0.1
Instance details

Defined in GHC.Real

Methods

toRational :: Ratio a -> Rational Source

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) Source

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

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

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

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

Show a => Show (Ratio a)

Since: base-2.0.1
Instance details

Defined in GHC.Real

Methods

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

show :: Ratio a -> String Source

showList :: [Ratio a] -> ShowS Source

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

Since: base-4.8.0.0
Instance details

Defined in Foreign.Storable

Methods

sizeOf :: Ratio a -> Int Source

alignment :: Ratio a -> Int Source

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

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

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

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

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

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

type Rational = Ratio Integer Source

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 Source

Forms the ratio of two integral numbers.

numerator :: Ratio a -> a Source

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 Source

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 Source

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.

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.10.2/docs/html/libraries/base-4.14.1.0/Data-Ratio.html