Safe Haskell | Safe-Inferred |
---|---|
Language | Haskell2010 |
- type Rational = Ratio Integer
- 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
- even :: Integral a => a -> Bool
- odd :: Integral a => a -> Bool
- gcd :: Integral a => a -> a -> a
- lcm :: Integral a => a -> a -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
Documentation
class (Num a, Ord a) => Real a where
toRational :: a -> Rational
the rational equivalent of its real argument with full precision
class (Real a, Enum a) => Integral a where
quot :: a -> a -> a infixl 7
integer division truncated toward zero
rem :: a -> a -> a infixl 7
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> a infixl 7
integer division truncated toward negative infinity
mod :: a -> a -> a infixl 7
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a)
divMod :: a -> a -> (a, a)
conversion to Integer
class Num a => Fractional a where
Fractional numbers, supporting real division.
Minimal complete definition: fromRational
and (recip
or (
)/
)
fromRational, (recip | (/))
(/) :: a -> a -> a infixl 7
fractional division
recip :: a -> a
reciprocal fraction
fromRational :: Rational -> a
Conversion from a Rational
(that is
).
A floating literal stands for an application of Ratio
Integer
fromRational
to a value of type Rational
, so such literals have type
(
.Fractional
a) => a
Fractional Double | |
Fractional Float | |
Integral a => Fractional (Ratio a) |
class (Real a, Fractional a) => RealFrac a where
Extracting components of fractions.
Minimal complete definition: properFraction
properFraction :: Integral b => a -> (b, a)
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 asx
; andf
is 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
returns the integer nearest truncate
xx
between zero and x
returns the nearest integer to round
xx
;
the even integer if x
is equidistant between two integers
ceiling :: Integral b => a -> b
returns the least integer not less than ceiling
xx
returns the greatest integer not greater than floor
xx
gcd :: Integral a => a -> a -> a
is the non-negative factor of both gcd
x yx
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 44
.
= gcd
0 00
.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types,
,
the result may be negative if one of the arguments is abs
minBound
< 0
(and
necessarily is if the other is minBound
0
or
) for such types.minBound
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> b
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b
general coercion to fractional types