NumHask.Data.Rational

Integral classes

Documentation

data Ratio a

Constructors

!a :% !a

Instances

(Eq a, Additive a) => Eq (Ratio a)

Defined in NumHask.Data.Rational

Methods

(==) :: Ratio a -> Ratio a -> Bool

(/=) :: Ratio a -> Ratio a -> Bool

(Ord a, Multiplicative a, Additive a) => Ord (Ratio a)

Defined in NumHask.Data.Rational

Methods

compare :: Ratio a -> Ratio a -> Ordering

(<) :: Ratio a -> Ratio a -> Bool

(<=) :: Ratio a -> Ratio a -> Bool

(>) :: Ratio a -> Ratio a -> Bool

(>=) :: Ratio a -> Ratio a -> Bool

max :: Ratio a -> Ratio a -> Ratio a

min :: Ratio a -> Ratio a -> Ratio a

Show a => Show (Ratio a)

Defined in NumHask.Data.Rational

Methods

showsPrec :: Int -> Ratio a -> ShowS

show :: Ratio a -> String

showList :: [Ratio a] -> ShowS

GCDConstraints a => Subtractive (Ratio a)

Defined in NumHask.Data.Rational

Methods

negate :: Ratio a -> Ratio a

(-) :: Ratio a -> Ratio a -> Ratio a

GCDConstraints a => Additive (Ratio a)

Defined in NumHask.Data.Rational

Methods

(+) :: Ratio a -> Ratio a -> Ratio a

zero :: Ratio a

GCDConstraints a => Divisive (Ratio a)

Defined in NumHask.Data.Rational

Methods

recip :: Ratio a -> Ratio a

(/) :: Ratio a -> Ratio a -> Ratio a

GCDConstraints a => Multiplicative (Ratio a)

Defined in NumHask.Data.Rational

Methods

(*) :: Ratio a -> Ratio a -> Ratio a

one :: Ratio a

GCDConstraints a => IntegralDomain (Ratio a)

Defined in NumHask.Data.Rational

GCDConstraints a => Distributive (Ratio a)

Defined in NumHask.Data.Rational

(GCDConstraints a, Field a) => LowerBoundedField (Ratio a)

Defined in NumHask.Data.Rational

Methods

negInfinity :: Ratio a

(GCDConstraints a, Distributive a, IntegralDomain a) => UpperBoundedField (Ratio a)

Defined in NumHask.Data.Rational

Methods

infinity :: Ratio a

nan :: Ratio a

GCDConstraints a => Field (Ratio a)

Defined in NumHask.Data.Rational

GCDConstraints a => MeetSemiLattice (Ratio a)

Defined in NumHask.Data.Rational

Methods

(/\) :: Ratio a -> Ratio a -> Ratio a

GCDConstraints a => JoinSemiLattice (Ratio a)

Defined in NumHask.Data.Rational

Methods

(\/) :: Ratio a -> Ratio a -> Ratio a

(GCDConstraints a, MeetSemiLattice a) => Epsilon (Ratio a)

Defined in NumHask.Data.Rational

Methods

epsilon :: Ratio a

nearZero :: Ratio a -> Bool

aboutEqual :: Ratio a -> Ratio a -> Bool

GCDConstraints a => Signed (Ratio a)

Defined in NumHask.Data.Rational

Methods

sign :: Ratio a -> Ratio a

abs :: Ratio a -> Ratio a

(FromIntegral a b, Multiplicative a) => FromIntegral (Ratio a) b

Defined in NumHask.Data.Rational

Methods

fromIntegral_ :: b -> Ratio a

(GCDConstraints a, GCDConstraints b, ToInteger a, Field a, FromIntegral b a) => QuotientField (Ratio a) b

Defined in NumHask.Data.Rational

Methods

properFraction :: Ratio a -> (b, Ratio a)

round :: Ratio a -> b

ceiling :: Ratio a -> b

floor :: Ratio a -> b

truncate :: Ratio a -> b

FromRatio (Ratio Integer) Integer

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Ratio Integer

ToRatio (Ratio Integer) Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Ratio Integer -> Ratio Integer

GCDConstraints a => Metric (Ratio a) (Ratio a)

Defined in NumHask.Data.Rational

Methods

distanceL1 :: Ratio a -> Ratio a -> Ratio a

distanceL2 :: Ratio a -> Ratio a -> Ratio a

GCDConstraints a => Normed (Ratio a) (Ratio a)

Defined in NumHask.Data.Rational

Methods

normL1 :: Ratio a -> Ratio a

normL2 :: Ratio a -> 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.

class ToRatio a b where

toRatio is equivalent to Real in base, but is polymorphic in the Integral type.

Minimal complete definition

Nothing

Methods

toRatio :: a -> Ratio b

toRatio :: (Ratio c ~ a, ToIntegral c Integer, ToRatio (Ratio b) b, FromInteger b) => a -> Ratio b

Instances

ToRatio Double Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Double -> Ratio Integer

ToRatio Float Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Float -> Ratio Integer

ToRatio Int Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Int -> Ratio Integer

ToRatio Int8 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Int8 -> Ratio Integer

ToRatio Int16 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Int16 -> Ratio Integer

ToRatio Int32 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Int32 -> Ratio Integer

ToRatio Int64 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Int64 -> Ratio Integer

ToRatio Integer Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Integer -> Ratio Integer

ToRatio Natural Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Natural -> Ratio Integer

ToRatio Rational Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Rational -> Ratio Integer

ToRatio Word Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Word -> Ratio Integer

ToRatio Word8 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Word8 -> Ratio Integer

ToRatio Word16 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Word16 -> Ratio Integer

ToRatio Word32 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Word32 -> Ratio Integer

ToRatio Word64 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Word64 -> Ratio Integer

ToRatio (Ratio Integer) Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Ratio Integer -> Ratio Integer

(ToRatio a b, ExpField a) => ToRatio (LogField a) b

Defined in NumHask.Data.LogField

Methods

toRatio :: LogField a -> Ratio b

ToRatio a b => ToRatio (Wrapped a) b

Defined in NumHask.Data.Wrapped

Methods

toRatio :: Wrapped a -> Ratio b

type ToRational a = ToRatio a Integer

toRational :: ToRatio a Integer => a -> Ratio Integer

class FromRatio a b where

Fractional in base splits into fromRatio and Field FIXME: work out why the default type isn't firing so that an explicit instance is needed for `FromRatio (Ratio Integer) Integer`

Minimal complete definition

Nothing

Methods

fromRatio :: Ratio b -> a

fromRatio :: Ratio b ~ a => Ratio b -> a

Instances

FromRatio Double Integer

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Double

FromRatio Float Integer

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Float

FromRatio Rational Integer

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Rational

FromRatio (Ratio Integer) Integer

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Ratio Integer

FromRatio a b => FromRatio (Pair a) b

Defined in NumHask.Data.Pair

Methods

fromRatio :: Ratio b -> Pair a

(FromRatio a b, ExpField a) => FromRatio (LogField a) b

Defined in NumHask.Data.LogField

Methods

fromRatio :: Ratio b -> LogField a

FromRatio a b => FromRatio (Wrapped a) b

Defined in NumHask.Data.Wrapped

Methods

fromRatio :: Ratio b -> Wrapped a

class FromRational a

with RebindableSyntax the literal '1.0' mean exactly `fromRational (1.0::GHC.Real.Rational)`.

Instances

FromRational Double

Defined in NumHask.Data.Rational

Methods

fromRational :: Rational -> Double

FromRational Float

Defined in NumHask.Data.Rational

Methods

fromRational :: Rational -> Float

FromRational Rational

Defined in NumHask.Data.Rational

Methods

fromRational :: Rational -> Rational

fromRational :: FromRational a => Rational -> a

fromRational' :: (FromRatio b Integer, ToRatio a Integer) => a -> b

Given that fromRational is reserved, fromRational' provides general conversion between numhask rationals.

fromBaseRational :: Rational -> Ratio Integer

$integral_functionality

reduce :: (Eq a, Subtractive a, Signed a, Integral a) => a -> a -> Ratio a

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.

gcd :: (Eq a, Signed a, Integral a) => a -> a -> a

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.