| Copyright | (c) The University of Glasgow 1994-2002 |
|---|---|
| License | see libraries/base/LICENSE |
| Maintainer | cvs-ghc@haskell.org |
| Stability | internal |
| Portability | non-portable (GHC Extensions) |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
GHC.Real
Synopsis
- divZeroError :: a
- ratioZeroDenominatorError :: a
- overflowError :: a
- underflowError :: a
- data Ratio a = !a :% !a
- type Rational = Ratio Integer
- ratioPrec :: Int
- ratioPrec1 :: Int
- infinity :: Rational
- notANumber :: Rational
- (%) :: Integral a => a -> a -> Ratio a
- numerator :: Ratio a -> a
- denominator :: 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
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class (Real a, Fractional a) => RealFrac a where
- 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
- naturalFromInt :: Int -> Natural
- 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
- (^%^) :: Integral a => Rational -> a -> Rational
- (^^%^^) :: Integral a => Rational -> a -> Rational
- 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]
- data FractionalExponentBase
- mkRationalBase2 :: Rational -> Integer -> Rational
- mkRationalBase10 :: Rational -> Integer -> Rational
- mkRationalWithExponentBase :: Rational -> Integer -> FractionalExponentBase -> Rational
Documentation
divZeroError :: a Source #
overflowError :: a Source #
underflowError :: 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
| (Data a, Integral a) => Data (Ratio a) # | Since: base-4.0.0.0 |
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) # | Since: base-4.8.0.0 |
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 # | |
| Integral a => Enum (Ratio a) # | Since: base-2.0.1 |
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) # | Since: base-2.0.1 |
Defined in GHC.Real | |
| (Integral a, Read a) => Read (Ratio a) # | Since: base-2.1 |
| Integral a => Fractional (Ratio a) # | Since: base-2.0.1 |
| Integral a => Real (Ratio a) # | Since: base-2.0.1 |
| Integral a => RealFrac (Ratio a) # | Since: base-2.0.1 |
| Show a => Show (Ratio a) # | Since: base-2.0.1 |
| Eq a => Eq (Ratio a) # | Since: base-2.1 |
| Integral a => Ord (Ratio a) # | Since: base-2.0.1 |
ratioPrec1 :: Int Source #
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
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 ywithrem x y=fromInteger 0org (rem x y)<g yx=y * div x y + mod x ywithmod x y=fromInteger 0orf (mod x y)<f y
An example of a suitable Euclidean function, for Integer's instance, is
abs.
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 #
divMod :: a -> a -> (a, a) Source #
toInteger :: a -> Integer Source #
conversion to Integer
Instances
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:*)
recipgives the multiplicative inversex * 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.
Reciprocal fraction.
fromRational :: Rational -> a Source #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional CDouble # | |
| Fractional CFloat # | |
| Fractional Double # | Note that due to the presence of
Since: base-2.1 |
| Fractional Float # | Note that due to the presence of
Since: base-2.1 |
| RealFloat a => Fractional (Complex a) # | Since: base-2.1 |
| Fractional a => Fractional (Identity a) # | Since: base-4.9.0.0 |
| Fractional a => Fractional (Down a) # | Since: base-4.14.0.0 |
| Integral a => Fractional (Ratio a) # | Since: base-2.0.1 |
| HasResolution a => Fractional (Fixed a) # | Since: base-2.1 |
| Fractional a => Fractional (Op a b) # | |
| Fractional a => Fractional (Const a b) # | Since: base-4.9.0.0 |
class (Real a, Fractional a) => RealFrac a where Source #
Extracting components of fractions.
Minimal complete definition
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:
nis an integral number with the same sign asx; andfis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the ceiling, floor, truncate
and round functions are in terms of properFraction.
truncate :: Integral b => a -> b Source #
truncate xx between zero and x
round :: Integral b => a -> b Source #
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b Source #
ceiling xx
floor :: Integral b => a -> b Source #
floor xx
Instances
| RealFrac CDouble # | |
| RealFrac CFloat # | |
| RealFrac Double # | Since: base-2.1 |
| RealFrac Float # | Since: base-2.1 |
| RealFrac a => RealFrac (Identity a) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity | |
| RealFrac a => RealFrac (Down a) # | Since: base-4.14.0.0 |
| Integral a => RealFrac (Ratio a) # | Since: base-2.0.1 |
| HasResolution a => RealFrac (Fixed a) # | Since: base-2.1 |
| RealFrac a => RealFrac (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
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
naturalFromInt :: Int -> Natural Source #
Convert an Int into a Natural, throwing an underflow exception for negative values.
realToFrac :: (Real a, Fractional b) => a -> b Source #
general coercion to fractional types
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.
(^) :: (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 yx and y of which
every common factor of x and y is also a factor; for example
gcd 4 2 = 2gcd (-4) 6 = 2gcd 0 44. gcd 0 00.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types, abs minBound < 0minBound0 or minBound
lcm :: Integral a => a -> a -> a Source #
lcm x yx 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 #
data FractionalExponentBase Source #