GHC.Real

Copyright (c) The University of Glasgow 1994-2002
License see libraries/base/LICENSE
Maintainer [email protected]
Stability internal
Portability non-portable (GHC Extensions)
Safe Haskell Trustworthy
Language Haskell2010

Description

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

divZeroError :: a Source

ratioZeroDenominatorError :: a Source

overflowError :: a Source

underflowError :: a Source

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.

Constructors

!a :% !a
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

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.

ratioPrec :: Int Source

ratioPrec1 :: Int Source

infinity :: Rational Source

notANumber :: Rational Source

(%) :: 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.

reduce :: Integral a => a -> a -> Ratio a Source

reduce is a subsidiary function used only in this module. It normalises a ratio by dividing both numerator and denominator by their greatest common divisor.

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

Methods

toRational :: a -> Rational Source

the rational equivalent of its real argument with full precision

Instances
Instances details
Real Double

Since: base-2.1

Instance details

Defined in GHC.Float

Real Float

Since: base-2.1

Instance details

Defined in GHC.Float

Real Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

toRational :: Int -> Rational Source

Real Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

toRational :: Int8 -> Rational Source

Real Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Real Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Real Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Real Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Real Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Real Word

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

toRational :: Word -> Rational Source

Real Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Real Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Real Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Real Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Real IntPtr
Instance details

Defined in Foreign.Ptr

Real WordPtr
Instance details

Defined in Foreign.Ptr

Real CUIntMax
Instance details

Defined in Foreign.C.Types

Real CIntMax
Instance details

Defined in Foreign.C.Types

Real CUIntPtr
Instance details

Defined in Foreign.C.Types

Real CIntPtr
Instance details

Defined in Foreign.C.Types

Real CSUSeconds
Instance details

Defined in Foreign.C.Types

Real CUSeconds
Instance details

Defined in Foreign.C.Types

Real CTime
Instance details

Defined in Foreign.C.Types

Real CClock
Instance details

Defined in Foreign.C.Types

Real CSigAtomic
Instance details

Defined in Foreign.C.Types

Real CWchar
Instance details

Defined in Foreign.C.Types

Real CSize
Instance details

Defined in Foreign.C.Types

Real CPtrdiff
Instance details

Defined in Foreign.C.Types

Real CDouble
Instance details

Defined in Foreign.C.Types

Real CFloat
Instance details

Defined in Foreign.C.Types

Real CBool
Instance details

Defined in Foreign.C.Types

Real CULLong
Instance details

Defined in Foreign.C.Types

Real CLLong
Instance details

Defined in Foreign.C.Types

Real CULong
Instance details

Defined in Foreign.C.Types

Real CLong
Instance details

Defined in Foreign.C.Types

Real CUInt
Instance details

Defined in Foreign.C.Types

Real CInt
Instance details

Defined in Foreign.C.Types

Methods

toRational :: CInt -> Rational Source

Real CUShort
Instance details

Defined in Foreign.C.Types

Real CShort
Instance details

Defined in Foreign.C.Types

Real CUChar
Instance details

Defined in Foreign.C.Types

Real CSChar
Instance details

Defined in Foreign.C.Types

Real CChar
Instance details

Defined in Foreign.C.Types

Real Fd
Instance details

Defined in System.Posix.Types

Methods

toRational :: Fd -> Rational Source

Real CNfds
Instance details

Defined in System.Posix.Types

Real CSocklen
Instance details

Defined in System.Posix.Types

Real CKey
Instance details

Defined in System.Posix.Types

Methods

toRational :: CKey -> Rational Source

Real CId
Instance details

Defined in System.Posix.Types

Methods

toRational :: CId -> Rational Source

Real CFsFilCnt
Instance details

Defined in System.Posix.Types

Real CFsBlkCnt
Instance details

Defined in System.Posix.Types

Real CClockId
Instance details

Defined in System.Posix.Types

Real CBlkCnt
Instance details

Defined in System.Posix.Types

Real CBlkSize
Instance details

Defined in System.Posix.Types

Real CRLim
Instance details

Defined in System.Posix.Types

Real CTcflag
Instance details

Defined in System.Posix.Types

Real CSpeed
Instance details

Defined in System.Posix.Types

Real CCc
Instance details

Defined in System.Posix.Types

Methods

toRational :: CCc -> Rational Source

Real CUid
Instance details

Defined in System.Posix.Types

Methods

toRational :: CUid -> Rational Source

Real CNlink
Instance details

Defined in System.Posix.Types

Real CGid
Instance details

Defined in System.Posix.Types

Methods

toRational :: CGid -> Rational Source

Real CSsize
Instance details

Defined in System.Posix.Types

Real CPid
Instance details

Defined in System.Posix.Types

Methods

toRational :: CPid -> Rational Source

Real COff
Instance details

Defined in System.Posix.Types

Methods

toRational :: COff -> Rational Source

Real CMode
Instance details

Defined in System.Posix.Types

Real CIno
Instance details

Defined in System.Posix.Types

Methods

toRational :: CIno -> Rational Source

Real CDev
Instance details

Defined in System.Posix.Types

Methods

toRational :: CDev -> Rational Source

Integral a => Real (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

toRational :: Ratio a -> Rational Source

Real a => Real (Down a)

Since: base-4.14.0.0

Instance details

Defined in Data.Ord

Methods

toRational :: Down a -> Rational Source

Real a => Real (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

HasResolution a => Real (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

toRational :: Fixed a -> Rational Source

Real a => Real (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

toRational :: Const a b -> Rational Source

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

Integral numbers, supporting integer division.

The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the div/mod and quot/rem pairs, given suitable Euclidean functions f and g:

  • x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
  • x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs.

Minimal complete definition

quotRem, toInteger

Methods

quot :: a -> a -> a infixl 7 Source

integer division truncated toward zero

rem :: a -> a -> a infixl 7 Source

integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

div :: a -> a -> a infixl 7 Source

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7 Source

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

quotRem :: a -> a -> (a, a) Source

simultaneous quot and rem

divMod :: a -> a -> (a, a) Source

simultaneous div and mod

toInteger :: a -> Integer Source

conversion to Integer

Instances
Instances details
Integral Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

quot :: Int -> Int -> Int Source

rem :: Int -> Int -> Int Source

div :: Int -> Int -> Int Source

mod :: Int -> Int -> Int Source

quotRem :: Int -> Int -> (Int, Int) Source

divMod :: Int -> Int -> (Int, Int) Source

toInteger :: Int -> Integer Source

Integral Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Integral Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Integral Word

Since: base-2.1

Instance details

Defined in GHC.Real

Integral Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Integral IntPtr
Instance details

Defined in Foreign.Ptr

Integral WordPtr
Instance details

Defined in Foreign.Ptr

Integral CUIntMax
Instance details

Defined in Foreign.C.Types

Integral CIntMax
Instance details

Defined in Foreign.C.Types

Integral CUIntPtr
Instance details

Defined in Foreign.C.Types

Integral CIntPtr
Instance details

Defined in Foreign.C.Types

Integral CSigAtomic
Instance details

Defined in Foreign.C.Types

Integral CWchar
Instance details

Defined in Foreign.C.Types

Integral CSize
Instance details

Defined in Foreign.C.Types

Integral CPtrdiff
Instance details

Defined in Foreign.C.Types

Integral CBool
Instance details

Defined in Foreign.C.Types

Integral CULLong
Instance details

Defined in Foreign.C.Types

Integral CLLong
Instance details

Defined in Foreign.C.Types

Integral CULong
Instance details

Defined in Foreign.C.Types

Integral CLong
Instance details

Defined in Foreign.C.Types

Integral CUInt
Instance details

Defined in Foreign.C.Types

Integral CInt
Instance details

Defined in Foreign.C.Types

Integral CUShort
Instance details

Defined in Foreign.C.Types

Integral CShort
Instance details

Defined in Foreign.C.Types

Integral CUChar
Instance details

Defined in Foreign.C.Types

Integral CSChar
Instance details

Defined in Foreign.C.Types

Integral CChar
Instance details

Defined in Foreign.C.Types

Integral Fd
Instance details

Defined in System.Posix.Types

Methods

quot :: Fd -> Fd -> Fd Source

rem :: Fd -> Fd -> Fd Source

div :: Fd -> Fd -> Fd Source

mod :: Fd -> Fd -> Fd Source

quotRem :: Fd -> Fd -> (Fd, Fd) Source

divMod :: Fd -> Fd -> (Fd, Fd) Source

toInteger :: Fd -> Integer Source

Integral CNfds
Instance details

Defined in System.Posix.Types

Integral CSocklen
Instance details

Defined in System.Posix.Types

Integral CKey
Instance details

Defined in System.Posix.Types

Integral CId
Instance details

Defined in System.Posix.Types

Methods

quot :: CId -> CId -> CId Source

rem :: CId -> CId -> CId Source

div :: CId -> CId -> CId Source

mod :: CId -> CId -> CId Source

quotRem :: CId -> CId -> (CId, CId) Source

divMod :: CId -> CId -> (CId, CId) Source

toInteger :: CId -> Integer Source

Integral CFsFilCnt
Instance details

Defined in System.Posix.Types

Integral CFsBlkCnt
Instance details

Defined in System.Posix.Types

Integral CClockId
Instance details

Defined in System.Posix.Types

Integral CBlkCnt
Instance details

Defined in System.Posix.Types

Integral CBlkSize
Instance details

Defined in System.Posix.Types

Integral CRLim
Instance details

Defined in System.Posix.Types

Integral CTcflag
Instance details

Defined in System.Posix.Types

Integral CUid
Instance details

Defined in System.Posix.Types

Integral CNlink
Instance details

Defined in System.Posix.Types

Integral CGid
Instance details

Defined in System.Posix.Types

Integral CSsize
Instance details

Defined in System.Posix.Types

Integral CPid
Instance details

Defined in System.Posix.Types

Integral COff
Instance details

Defined in System.Posix.Types

Integral CMode
Instance details

Defined in System.Posix.Types

Integral CIno
Instance details

Defined in System.Posix.Types

Integral CDev
Instance details

Defined in System.Posix.Types

Integral a => Integral (Down a)

Since: base-4.14.0.0

Instance details

Defined in Data.Ord

Methods

quot :: Down a -> Down a -> Down a Source

rem :: Down a -> Down a -> Down a Source

div :: Down a -> Down a -> Down a Source

mod :: Down a -> Down a -> Down a Source

quotRem :: Down a -> Down a -> (Down a, Down a) Source

divMod :: Down a -> Down a -> (Down a, Down a) Source

toInteger :: Down a -> Integer Source

Integral a => Integral (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Integral a => Integral (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

quot :: Const a b -> Const a b -> Const a b Source

rem :: Const a b -> Const a b -> Const a b Source

div :: Const a b -> Const a b -> Const a b Source

mod :: Const a b -> Const a b -> Const a b Source

quotRem :: Const a b -> Const a b -> (Const a b, Const a b) Source

divMod :: Const a b -> Const a b -> (Const a b, Const a b) Source

toInteger :: Const a b -> Integer Source

class Num a => Fractional a where Source

Fractional numbers, supporting real division.

The Haskell Report defines no laws for Fractional. However, (+) and (*) are customarily expected to define a division ring and have the following properties:

recip gives the multiplicative inverse
x * recip x = recip x * x = fromInteger 1

Note that it isn't customarily expected that a type instance of Fractional implement a field. However, all instances in base do.

Minimal complete definition

fromRational, (recip | (/))

Methods

(/) :: a -> a -> a infixl 7 Source

Fractional division.

recip :: a -> a Source

Reciprocal fraction.

fromRational :: Rational -> a Source

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

Instances
Instances details
Fractional Double

Note that due to the presence of NaN, not all elements of Double have an multiplicative inverse.

>>> 0/0 * (recip 0/0 :: Double)
NaN

Since: base-2.1

Instance details

Defined in GHC.Float

Fractional Float

Note that due to the presence of NaN, not all elements of Float have an multiplicative inverse.

>>> 0/0 * (recip 0/0 :: Float)
NaN

Since: base-2.1

Instance details

Defined in GHC.Float

Fractional CDouble
Instance details

Defined in Foreign.C.Types

Fractional CFloat
Instance details

Defined in Foreign.C.Types

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

Fractional a => Fractional (Down a)

Since: base-4.14.0.0

Instance details

Defined in Data.Ord

Methods

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

recip :: Down a -> Down a Source

fromRational :: Rational -> Down a Source

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

RealFloat a => Fractional (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Fractional a => Fractional (Op a b)
Instance details

Defined in Data.Functor.Contravariant

Methods

(/) :: Op a b -> Op a b -> Op a b Source

recip :: Op a b -> Op a b Source

fromRational :: Rational -> Op a b Source

HasResolution a => Fractional (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

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

recip :: Fixed a -> Fixed a Source

fromRational :: Rational -> Fixed a Source

Fractional a => Fractional (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

(/) :: Const a b -> Const a b -> Const a b Source

recip :: Const a b -> Const a b Source

fromRational :: Rational -> Const a b Source

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

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, a) Source

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

  • n is an integral number with the same sign as x; and
  • f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

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

truncate x returns the integer nearest x between zero and x

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

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

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

ceiling x returns the least integer not less than x

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

floor x returns the greatest integer not greater than x

Instances
Instances details
RealFrac Double

Since: base-2.1

Instance details

Defined in GHC.Float

Methods

properFraction :: Integral b => Double -> (b, Double) Source

truncate :: Integral b => Double -> b Source

round :: Integral b => Double -> b Source

ceiling :: Integral b => Double -> b Source

floor :: Integral b => Double -> b Source

RealFrac Float

Since: base-2.1

Instance details

Defined in GHC.Float

Methods

properFraction :: Integral b => Float -> (b, Float) Source

truncate :: Integral b => Float -> b Source

round :: Integral b => Float -> b Source

ceiling :: Integral b => Float -> b Source

floor :: Integral b => Float -> b Source

RealFrac CDouble
Instance details

Defined in Foreign.C.Types

RealFrac CFloat
Instance details

Defined in Foreign.C.Types

Methods

properFraction :: Integral b => CFloat -> (b, CFloat) Source

truncate :: Integral b => CFloat -> b Source

round :: Integral b => CFloat -> b Source

ceiling :: Integral b => CFloat -> b Source

floor :: Integral b => CFloat -> b 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

RealFrac a => RealFrac (Down a)

Since: base-4.14.0.0

Instance details

Defined in Data.Ord

Methods

properFraction :: Integral b => Down a -> (b, Down a) Source

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

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

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

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

RealFrac a => RealFrac (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

properFraction :: Integral b => Identity a -> (b, Identity a) Source

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

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

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

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

HasResolution a => RealFrac (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

properFraction :: Integral b => Fixed a -> (b, Fixed a) Source

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

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

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

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

RealFrac a => RealFrac (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

properFraction :: Integral b0 => Const a b -> (b0, Const a b) Source

truncate :: Integral b0 => Const a b -> b0 Source

round :: Integral b0 => Const a b -> b0 Source

ceiling :: Integral b0 => Const a b -> b0 Source

floor :: Integral b0 => Const a b -> b0 Source

numericEnumFrom :: Fractional a => a -> [a] Source

numericEnumFromThen :: Fractional a => a -> a -> [a] Source

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

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

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

general coercion from integral types

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

general coercion to fractional types

showSigned Source

Arguments

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

a function that can show unsigned values

-> Int

the precedence of the enclosing context

-> a

the value to show

-> ShowS

Converts a possibly-negative Real value to a string.

even :: Integral a => a -> Bool Source

odd :: Integral a => a -> Bool Source

(^) :: (Num a, Integral b) => a -> b -> a infixr 8 Source

raise a number to a non-negative integral power

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 Source

raise a number to an integral power

(^%^) :: Integral a => Rational -> a -> Rational Source

(^^%^^) :: Integral a => Rational -> a -> Rational Source

gcd :: Integral a => a -> a -> a Source

gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.

lcm :: Integral a => a -> a -> a Source

lcm x y is the smallest positive integer that both x and y divide.

gcdInt' :: Int -> Int -> Int Source

gcdWord' :: Word -> Word -> Word Source

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

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

integralEnumFromTo :: Integral a => a -> a -> [a] Source

integralEnumFromThenTo :: Integral a => a -> a -> a -> [a] Source

© 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/GHC-Real.html