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, Integral 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

(FromInteger a, Multiplicative a) => FromInteger (Ratio a)

Defined in NumHask.Data.Rational

Methods

fromInteger :: Integer -> Ratio a

(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

isNaN :: Ratio a -> Bool

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

FromInteger a => FromRatio (Ratio a)

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Ratio a

ToInteger a => ToRatio (Ratio a)

Defined in NumHask.Data.Rational

Methods

toRatio :: Ratio a -> Ratio Integer

(GCDConstraints a, GCDConstraints b, ToInteger a, Field a, FromInteger b) => 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

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

class ToRatio a where

toRatio is equivalent to Real in base.

Methods

toRatio :: a -> Ratio Integer

Instances

ToRatio Double

Defined in NumHask.Data.Rational

Methods

toRatio :: Double -> Ratio Integer

ToRatio Float

Defined in NumHask.Data.Rational

Methods

toRatio :: Float -> Ratio Integer

ToRatio Int

Defined in NumHask.Data.Rational

Methods

toRatio :: Int -> Ratio Integer

ToRatio Int8

Defined in NumHask.Data.Rational

Methods

toRatio :: Int8 -> Ratio Integer

ToRatio Int16

Defined in NumHask.Data.Rational

Methods

toRatio :: Int16 -> Ratio Integer

ToRatio Int32

Defined in NumHask.Data.Rational

Methods

toRatio :: Int32 -> Ratio Integer

ToRatio Int64

Defined in NumHask.Data.Rational

Methods

toRatio :: Int64 -> Ratio Integer

ToRatio Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Integer -> Ratio Integer

ToRatio Natural

Defined in NumHask.Data.Rational

Methods

toRatio :: Natural -> Ratio Integer

ToRatio Rational

Defined in NumHask.Data.Rational

Methods

toRatio :: Rational -> Ratio Integer

ToRatio Word

Defined in NumHask.Data.Rational

Methods

toRatio :: Word -> Ratio Integer

ToRatio Word8

Defined in NumHask.Data.Rational

Methods

toRatio :: Word8 -> Ratio Integer

ToRatio Word16

Defined in NumHask.Data.Rational

Methods

toRatio :: Word16 -> Ratio Integer

ToRatio Word32

Defined in NumHask.Data.Rational

Methods

toRatio :: Word32 -> Ratio Integer

ToRatio Word64

Defined in NumHask.Data.Rational

Methods

toRatio :: Word64 -> Ratio Integer

ToInteger a => ToRatio (Ratio a)

Defined in NumHask.Data.Rational

Methods

toRatio :: Ratio a -> Ratio Integer

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

Defined in NumHask.Data.LogField

Methods

toRatio :: LogField a -> Ratio Integer

ToRatio a => ToRatio (Wrapped a)

Defined in NumHask.Data.Wrapped

Methods

toRatio :: Wrapped a -> Ratio Integer

class FromRatio a where

Fractional in base splits into fromRatio and Field

Methods

fromRatio :: Ratio Integer -> a

Instances

FromRatio Double

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Double

FromRatio Float

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Float

FromInteger a => FromRatio (Ratio a)

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Ratio a

FromRatio a => FromRatio (Pair a)

Defined in NumHask.Data.Pair

Methods

fromRatio :: Ratio Integer -> Pair a

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

Defined in NumHask.Data.LogField

Methods

fromRatio :: Ratio Integer -> LogField a

FromRatio a => FromRatio (Wrapped a)

Defined in NumHask.Data.Wrapped

Methods

fromRatio :: Ratio Integer -> Wrapped a

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

coercion of Rationals

fromRational a == a

$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.