Haskell Core Libraries (base package) Parent Contents Index

GHC.Real Portability non-portable (GHC Extensions) Stability internal Maintainer cvs-ghc@haskell.org

Description

The types Ratio and Rational, and the classes Real, Fractional, Integral, and RealFrac.

Synopsis

data Ratio a = (:%) !a !a type Rational = Ratio Integer ratioPrec :: Int ratioPrec1 :: Int infinity :: Rational notANumber :: Rational (%) :: (Integral a) => a -> a -> Ratio a numerator :: (Integral a) => Ratio a -> a denominator :: (Integral a) => Ratio a -> a reduce :: (Integral a) => a -> a -> Ratio a class (Num a, Ord a) => Real a where toRational :: a -> Rational class (Real a, Enum a) => Integral a where quot :: a -> a -> a rem :: a -> a -> a div :: a -> a -> a mod :: a -> a -> a quotRem :: a -> a -> (a, a) divMod :: a -> a -> (a, a) toInteger :: a -> Integer class (Num a) => Fractional a where (/) :: a -> a -> a recip :: a -> a fromRational :: Rational -> a class (Real a, Fractional a) => RealFrac a where properFraction :: (Integral b) => a -> (b, a) truncate :: (Integral b) => a -> b round :: (Integral b) => a -> b ceiling :: (Integral b) => a -> b floor :: (Integral b) => a -> b numericEnumFrom :: (Fractional a) => a -> [a] numericEnumFromThen :: (Fractional a) => a -> a -> [a] numericEnumFromTo :: (Ord a, Fractional a) => a -> a -> [a] numericEnumFromThenTo :: (Ord a, Fractional a) => a -> a -> a -> [a] fromIntegral :: (Integral a, Num b) => a -> b realToFrac :: (Real a, Fractional b) => a -> b showSigned :: (Real a) => (a -> ShowS) -> Int -> a -> ShowS even :: (Integral a) => a -> Bool odd :: (Integral a) => a -> Bool (^) :: (Num a, Integral b) => a -> b -> a (^^) :: (Fractional a, Integral b) => a -> b -> a gcd :: (Integral a) => a -> a -> a lcm :: (Integral a) => a -> a -> a integralEnumFrom :: (Integral a, Bounded a) => a -> [a] integralEnumFromThen :: (Integral a, Bounded a) => a -> a -> [a] integralEnumFromTo :: (Integral a) => a -> a -> [a] integralEnumFromThenTo :: (Integral a) => a -> a -> a -> [a]

Documentation

data Ratio a

Constructors (:%) !a !a Instances (Integral a, Read a) => Read (Ratio a) (Integral a) => Ord (Ratio a) (Integral a) => Num (Ratio a) (Integral a) => Fractional (Ratio a) (Integral a) => Real (Ratio a) (Integral a) => RealFrac (Ratio a) (Integral a) => Show (Ratio a) (Integral a) => Enum (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.

ratioPrec :: Int

ratioPrec1 :: Int

infinity :: Rational

notANumber :: Rational

(%) :: (Integral a) => a -> a -> Ratio a

numerator :: (Integral a) => Ratio a -> a

denominator :: (Integral a) => Ratio a -> a

reduce :: (Integral a) => a -> a -> Ratio a

class (Num a, Ord a) => Real a where

Methods toRational :: a -> Rational Instances Real Float Real Double Real Int8 Real Int16 Real Int32 Real Int64 Real Int Real Integer (Integral a) => Real (Ratio a) Real Word Real Word8 Real Word16 Real Word32 Real Word64

class (Real a, Enum a) => Integral a where

Methods quot :: a -> a -> a rem :: a -> a -> a div :: a -> a -> a mod :: a -> a -> a quotRem :: a -> a -> (a, a) divMod :: a -> a -> (a, a) toInteger :: a -> Integer Instances Integral Int8 Integral Int16 Integral Int32 Integral Int64 Integral Int Integral Integer Integral Word Integral Word8 Integral Word16 Integral Word32 Integral Word64

class (Num a) => Fractional a where

Methods (/) :: a -> a -> a recip :: a -> a fromRational :: Rational -> a Instances (RealFloat a) => Fractional (Complex a) Fractional Float Fractional Double (Integral a) => Fractional (Ratio a)

class (Real a, Fractional a) => RealFrac a where

Methods properFraction :: (Integral b) => a -> (b, a) truncate :: (Integral b) => a -> b round :: (Integral b) => a -> b ceiling :: (Integral b) => a -> b floor :: (Integral b) => a -> b Instances RealFrac Float RealFrac Double (Integral a) => RealFrac (Ratio a)

numericEnumFrom :: (Fractional a) => a -> [a]

numericEnumFromThen :: (Fractional a) => a -> a -> [a]

numericEnumFromTo :: (Ord a, Fractional a) => a -> a -> [a]

numericEnumFromThenTo :: (Ord a, Fractional a) => a -> a -> a -> [a]

fromIntegral :: (Integral a, Num b) => a -> b

realToFrac :: (Real a, Fractional b) => a -> b

showSigned :: (Real a) => (a -> ShowS) -> Int -> a -> ShowS

even :: (Integral a) => a -> Bool

odd :: (Integral a) => a -> Bool

(^) :: (Num a, Integral b) => a -> b -> a

(^^) :: (Fractional a, Integral b) => a -> b -> a

gcd :: (Integral a) => a -> a -> a

lcm :: (Integral a) => a -> a -> a

integralEnumFrom :: (Integral a, Bounded a) => a -> [a]

integralEnumFromThen :: (Integral a, Bounded a) => a -> a -> [a]

integralEnumFromTo :: (Integral a) => a -> a -> [a]

integralEnumFromThenTo :: (Integral a) => a -> a -> a -> [a]

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