base-4.17.0.0: Basic libraries
Copyright(c) The University of Glasgow 1994-2002
Licensesee libraries/base/LICENSE
Maintainercvs-ghc@haskell.org
Stabilityinternal
Portabilitynon-portable (GHC Extensions)
Safe HaskellTrustworthy
LanguageHaskell2010

GHC.Real

Description

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

Synopsis

Documentation

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

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 #

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

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 #

Integral a => Enum (Ratio a) Source #

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 #

Integral a => Num (Ratio a) Source #

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, Read a) => Read (Ratio a) Source #

Since: base-2.1

Instance details

Defined in GHC.Read

Integral a => Fractional (Ratio a) Source #

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 #

Integral a => Real (Ratio a) Source #

Since: base-2.0.1

Instance details

Defined in GHC.Real

Integral a => RealFrac (Ratio a) Source #

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) Source #

Since: base-2.0.1

Instance details

Defined in GHC.Real

Eq a => Eq (Ratio a) Source #

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 => Ord (Ratio a) Source #

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 #

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.

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 #

Real numbers.

The Haskell report defines no laws for Real, however Real instances are customarily expected to adhere to the following law:

Coherence with fromRational
if the type also implements Fractional, then fromRational is a left inverse for toRational, i.e. fromRational (toRational i) = i

Methods

toRational :: a -> Rational Source #

the rational equivalent of its real argument with full precision

Instances

Instances details
Real CBool Source # 
Instance details

Defined in Foreign.C.Types

Real CChar Source # 
Instance details

Defined in Foreign.C.Types

Real CClock Source # 
Instance details

Defined in Foreign.C.Types

Real CDouble Source # 
Instance details

Defined in Foreign.C.Types

Real CFloat Source # 
Instance details

Defined in Foreign.C.Types

Real CInt Source # 
Instance details

Defined in Foreign.C.Types

Real CIntMax Source # 
Instance details

Defined in Foreign.C.Types

Real CIntPtr Source # 
Instance details

Defined in Foreign.C.Types

Real CLLong Source # 
Instance details

Defined in Foreign.C.Types

Real CLong Source # 
Instance details

Defined in Foreign.C.Types

Real CPtrdiff Source # 
Instance details

Defined in Foreign.C.Types

Real CSChar Source # 
Instance details

Defined in Foreign.C.Types

Real CSUSeconds Source # 
Instance details

Defined in Foreign.C.Types

Real CShort Source # 
Instance details

Defined in Foreign.C.Types

Real CSigAtomic Source # 
Instance details

Defined in Foreign.C.Types

Real CSize Source # 
Instance details

Defined in Foreign.C.Types

Real CTime Source # 
Instance details

Defined in Foreign.C.Types

Real CUChar Source # 
Instance details

Defined in Foreign.C.Types

Real CUInt Source # 
Instance details

Defined in Foreign.C.Types

Real CUIntMax Source # 
Instance details

Defined in Foreign.C.Types

Real CUIntPtr Source # 
Instance details

Defined in Foreign.C.Types

Real CULLong Source # 
Instance details

Defined in Foreign.C.Types

Real CULong Source # 
Instance details

Defined in Foreign.C.Types

Real CUSeconds Source # 
Instance details

Defined in Foreign.C.Types

Real CUShort Source # 
Instance details

Defined in Foreign.C.Types

Real CWchar Source # 
Instance details

Defined in Foreign.C.Types

Real IntPtr Source # 
Instance details

Defined in Foreign.Ptr

Real WordPtr Source # 
Instance details

Defined in Foreign.Ptr

Real Int16 Source #

Since: base-2.1

Instance details

Defined in GHC.Int

Real Int32 Source #

Since: base-2.1

Instance details

Defined in GHC.Int

Real Int64 Source #

Since: base-2.1

Instance details

Defined in GHC.Int

Real Int8 Source #

Since: base-2.1

Instance details

Defined in GHC.Int

Real Word16 Source #

Since: base-2.1

Instance details

Defined in GHC.Word

Real Word32 Source #

Since: base-2.1

Instance details

Defined in GHC.Word

Real Word64 Source #

Since: base-2.1

Instance details

Defined in GHC.Word

Real Word8 Source #

Since: base-2.1

Instance details

Defined in GHC.Word

Real CBlkCnt Source # 
Instance details

Defined in System.Posix.Types

Real CBlkSize Source # 
Instance details

Defined in System.Posix.Types

Real CCc Source # 
Instance details

Defined in System.Posix.Types

Real CClockId Source # 
Instance details

Defined in System.Posix.Types

Real CDev Source # 
Instance details

Defined in System.Posix.Types

Real CFsBlkCnt Source # 
Instance details

Defined in System.Posix.Types

Real CFsFilCnt Source # 
Instance details

Defined in System.Posix.Types

Real CGid Source # 
Instance details

Defined in System.Posix.Types

Real CId Source # 
Instance details

Defined in System.Posix.Types

Real CIno Source # 
Instance details

Defined in System.Posix.Types

Real CKey Source # 
Instance details

Defined in System.Posix.Types

Real CMode Source # 
Instance details

Defined in System.Posix.Types

Real CNfds Source # 
Instance details

Defined in System.Posix.Types

Real CNlink Source # 
Instance details

Defined in System.Posix.Types

Real COff Source # 
Instance details

Defined in System.Posix.Types

Real CPid Source # 
Instance details

Defined in System.Posix.Types

Real CRLim Source # 
Instance details

Defined in System.Posix.Types

Real CSocklen Source # 
Instance details

Defined in System.Posix.Types

Real CSpeed Source # 
Instance details

Defined in System.Posix.Types

Real CSsize Source # 
Instance details

Defined in System.Posix.Types

Real CTcflag Source # 
Instance details

Defined in System.Posix.Types

Real CUid Source # 
Instance details

Defined in System.Posix.Types

Real Fd Source # 
Instance details

Defined in System.Posix.Types

Real Integer Source #

Since: base-2.0.1

Instance details

Defined in GHC.Real

Real Natural Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Real Double Source #

Since: base-2.1

Instance details

Defined in GHC.Float

Real Float Source #

Since: base-2.1

Instance details

Defined in GHC.Float

Real Int Source #

Since: base-2.0.1

Instance details

Defined in GHC.Real

Real Word Source #

Since: base-2.1

Instance details

Defined in GHC.Real

Real a => Real (Identity a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Real a => Real (Down a) Source #

Since: base-4.14.0.0

Instance details

Defined in Data.Ord

Integral a => Real (Ratio a) Source #

Since: base-2.0.1

Instance details

Defined in GHC.Real

HasResolution a => Real (Fixed a) Source #

Since: base-2.1

Instance details

Defined in Data.Fixed

Real a => Real (Const a b) Source #

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.

In addition, toInteger should be total, and fromInteger should be a left inverse for it, i.e. fromInteger (toInteger i) = i.

Minimal complete definition

quotRem, toInteger

Methods

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

integer division truncated toward zero

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

integer remainder, satisfying

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

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

integer division truncated toward negative infinity

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

integer modulus, satisfying

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

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

simultaneous quot and rem

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

simultaneous div and mod

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

toInteger :: a -> Integer Source #

conversion to Integer

Instances

Instances details
Integral CBool Source # 
Instance details

Defined in Foreign.C.Types

Integral CChar Source # 
Instance details

Defined in Foreign.C.Types

Integral CInt Source # 
Instance details

Defined in Foreign.C.Types

Integral CIntMax Source # 
Instance details

Defined in Foreign.C.Types

Integral CIntPtr Source # 
Instance details

Defined in Foreign.C.Types

Integral CLLong Source # 
Instance details

Defined in Foreign.C.Types

Integral CLong Source # 
Instance details

Defined in Foreign.C.Types

Integral CPtrdiff Source # 
Instance details

Defined in Foreign.C.Types

Integral CSChar Source # 
Instance details

Defined in Foreign.C.Types

Integral CShort Source # 
Instance details

Defined in Foreign.C.Types

Integral CSigAtomic Source # 
Instance details

Defined in Foreign.C.Types

Integral CSize Source # 
Instance details

Defined in Foreign.C.Types

Integral CUChar Source # 
Instance details

Defined in Foreign.C.Types

Integral CUInt Source # 
Instance details

Defined in Foreign.C.Types

Integral CUIntMax Source # 
Instance details

Defined in Foreign.C.Types

Integral CUIntPtr Source # 
Instance details

Defined in Foreign.C.Types

Integral CULLong Source # 
Instance details

Defined in Foreign.C.Types

Integral CULong Source # 
Instance details

Defined in Foreign.C.Types

Integral CUShort Source # 
Instance details

Defined in Foreign.C.Types

Integral CWchar Source # 
Instance details

Defined in Foreign.C.Types

Integral IntPtr Source # 
Instance details

Defined in Foreign.Ptr

Integral WordPtr Source # 
Instance details

Defined in Foreign.Ptr

Integral Int16 Source #

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int32 Source #

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int64 Source #

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Int8 Source #

Since: base-2.1

Instance details

Defined in GHC.Int

Integral Word16 Source #

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word32 Source #

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word64 Source #

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word8 Source #

Since: base-2.1

Instance details

Defined in GHC.Word

Integral CBlkCnt Source # 
Instance details

Defined in System.Posix.Types

Integral CBlkSize Source # 
Instance details

Defined in System.Posix.Types

Integral CClockId Source # 
Instance details

Defined in System.Posix.Types

Integral CDev Source # 
Instance details

Defined in System.Posix.Types

Integral CFsBlkCnt Source # 
Instance details

Defined in System.Posix.Types

Integral CFsFilCnt Source # 
Instance details

Defined in System.Posix.Types

Integral CGid Source # 
Instance details

Defined in System.Posix.Types

Integral CId Source # 
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 CIno Source # 
Instance details

Defined in System.Posix.Types

Integral CKey Source # 
Instance details

Defined in System.Posix.Types

Integral CMode Source # 
Instance details

Defined in System.Posix.Types

Integral CNfds Source # 
Instance details

Defined in System.Posix.Types

Integral CNlink Source # 
Instance details

Defined in System.Posix.Types

Integral COff Source # 
Instance details

Defined in System.Posix.Types

Integral CPid Source # 
Instance details

Defined in System.Posix.Types

Integral CRLim Source # 
Instance details

Defined in System.Posix.Types

Integral CSocklen Source # 
Instance details

Defined in System.Posix.Types

Integral CSsize Source # 
Instance details

Defined in System.Posix.Types

Integral CTcflag Source # 
Instance details

Defined in System.Posix.Types

Integral CUid Source # 
Instance details

Defined in System.Posix.Types

Integral Fd Source # 
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 Integer Source #

Since: base-2.0.1

Instance details

Defined in GHC.Real

Integral Natural Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Integral Int Source #

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 Word Source #

Since: base-2.1

Instance details

Defined in GHC.Real

Integral a => Integral (Identity a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Integral a => Integral (Const a b) Source #

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
Totality of toRational
toRational is total
Coherence with toRational
if the type also implements Real, then fromRational is a left inverse for toRational, i.e. fromRational (toRational i) = i

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 CDouble Source # 
Instance details

Defined in Foreign.C.Types

Fractional CFloat Source # 
Instance details

Defined in Foreign.C.Types

Fractional Double Source #

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

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

Additionally, because of NaN this instance does not obey the left-inverse law for toRational/fromRational.

Since: base-2.1

Instance details

Defined in GHC.Float

Fractional Float Source #

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

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

Additionally, because of NaN this instance does not obey the left-inverse law for toRational/fromRational.

Since: base-2.1

Instance details

Defined in GHC.Float

RealFloat a => Fractional (Complex a) Source #

Since: base-2.1

Instance details

Defined in Data.Complex

Fractional a => Fractional (Identity a) Source #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Fractional a => Fractional (Down a) Source #

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 #

Integral a => Fractional (Ratio a) Source #

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 #

HasResolution a => Fractional (Fixed a) Source #

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 (Op a b) Source # 
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 #

Fractional a => Fractional (Const a b) Source #

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 CDouble Source # 
Instance details

Defined in Foreign.C.Types

RealFrac CFloat Source # 
Instance details

Defined in Foreign.C.Types

RealFrac Double Source #

Since: base-2.1

Instance details

Defined in GHC.Float

RealFrac Float Source #

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 a => RealFrac (Identity a) Source #

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 #

RealFrac a => RealFrac (Down a) Source #

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 #

Integral a => RealFrac (Ratio a) Source #

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 #

HasResolution a => RealFrac (Fixed a) Source #

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) Source #

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 #

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.

WARNING: This function performs silent truncation if the result type is not at least as big as the argument's type.

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

General coercion to Fractional types.

WARNING: This function goes through the Rational type, which does not have values for NaN for example. This means it does not round-trip.

For Double it also behaves differently with or without -O0:

Prelude> realToFrac nan -- With -O0
-Infinity
Prelude> realToFrac nan
NaN

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

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.

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 #