NumHask.Data.Rational

Rational classes

Documentation

data Ratio a

A rational number, represented as the ratio of two Integral numbers.

Constructors

!a :% !a

Instances

FromRatio Rational Integer

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Rational

Show a => Show (Ratio a)

Defined in NumHask.Data.Rational

Methods

showsPrec :: Int -> Ratio a -> ShowS

show :: Ratio a -> String

showList :: [Ratio a] -> ShowS

(Eq a, Subtractive a, EndoBased a, Absolute a, Integral a) => Eq (Ratio a)

Defined in NumHask.Data.Rational

Methods

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

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

(Ord a, Integral a, EndoBased a, Subtractive 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

(Ord a, EndoBased a, Integral a, Ring a) => Additive (Ratio a)

Defined in NumHask.Data.Rational

Methods

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

zero :: Ratio a

(Ord a, EndoBased a, Integral a, Ring a) => Subtractive (Ratio a)

Defined in NumHask.Data.Rational

Methods

negate :: Ratio a -> Ratio a

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

(Ord a, EndoBased a, Absolute a, ToInt a, Integral a, Ring a) => QuotientField (Ratio a)

Defined in NumHask.Data.Rational

Associated Types

type Whole (Ratio a)

Methods

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

round :: Ratio a -> Whole (Ratio a)

ceiling :: Ratio a -> Whole (Ratio a)

floor :: Ratio a -> Whole (Ratio a)

truncate :: Ratio a -> Whole (Ratio a)

(Ord a, Integral a, EndoBased a, Subtractive a) => JoinSemiLattice (Ratio a)

Defined in NumHask.Data.Rational

Methods

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

(Ord a, Integral a, EndoBased a, Subtractive a) => MeetSemiLattice (Ratio a)

Defined in NumHask.Data.Rational

Methods

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

(Ord a, EndoBased a, Integral a, Ring a) => Basis (Ratio a)

Defined in NumHask.Data.Rational

Associated Types

type Mag (Ratio a)

type Base (Ratio a)

Methods

magnitude :: Ratio a -> Mag (Ratio a)

basis :: Ratio a -> Base (Ratio a)

(Ord a, EndoBased a, Integral a, Ring a, MeetSemiLattice a) => Epsilon (Ratio a)

Defined in NumHask.Data.Rational

Methods

epsilon :: Ratio a

(Ord a, EndoBased a, Integral a, Ring a) => Divisive (Ratio a)

Defined in NumHask.Data.Rational

Methods

recip :: Ratio a -> Ratio a

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

(Ord a, EndoBased a, Integral a, Ring a) => Multiplicative (Ratio a)

Defined in NumHask.Data.Rational

Methods

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

one :: Ratio a

FromRational (Ratio Integer)

Defined in NumHask.Data.Rational

Methods

fromRational :: Rational -> Ratio Integer

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

Defined in NumHask.Data.Rational

Methods

fromIntegral :: b -> Ratio a

ToRatio (Ratio Integer) Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Ratio Integer -> Ratio Integer

type Whole (Ratio a)

Defined in NumHask.Data.Rational

type Whole (Ratio a) = Int

type Base (Ratio a)

Defined in NumHask.Data.Rational

type Base (Ratio a) = Ratio a

type Mag (Ratio a)

Defined in NumHask.Data.Rational

type Mag (Ratio a) = Ratio a

type Rational = Ratio Integer

Ratio of two integers

class ToRatio a b where

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

>>> toRatio (3.1415927 :: Float) :: Ratio Integer
13176795 :% 4194304

Methods

toRatio :: a -> Ratio b

Instances

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 Int8 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Int8 -> 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 Word8 Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Word8 -> 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 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 Word Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Word -> Ratio Integer

ToRatio a b => ToRatio (Positive a) b

Defined in NumHask.Data.Positive

Methods

toRatio :: Positive a -> Ratio b

ToRatio (Ratio Integer) Integer

Defined in NumHask.Data.Rational

Methods

toRatio :: Ratio Integer -> Ratio Integer

ToRatio a b => ToRatio (Wrapped a) b

Defined in NumHask.Data.Wrapped

Methods

toRatio :: Wrapped a -> Ratio b

class FromRatio a b where

Fractional in base splits into fromRatio and Field

>>> fromRatio (5 :% 2 :: Ratio Integer) :: Double
2.5

Methods

fromRatio :: Ratio b -> a

Instances

FromRatio Rational Integer

Defined in NumHask.Data.Rational

Methods

fromRatio :: Ratio Integer -> Rational

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 a b => FromRatio (Positive a) b

Defined in NumHask.Data.Positive

Methods

fromRatio :: Ratio b -> Positive a

FromRatio a b => FromRatio (Wrapped a) b

Defined in NumHask.Data.Wrapped

Methods

fromRatio :: Ratio b -> Wrapped a

class FromRational a where

fromRational is special in two ways:

• numeric decimal literals (like "53.66") are interpreted as exactly "fromRational (53.66 :: GHC.Real.Ratio Integer)". The prelude version, GHC.Real.fromRational is used as default (or whatever is in scope if RebindableSyntax is set).
• The default rules in haskell2010 specify that contraints on fromRational need to be in a form C v, where v is a Num or a subclass of Num.

So a type synonym of `type FromRational a = FromRatio a Integer` doesn't work well with type defaulting; hence the need for a separate class.

Methods

fromRational :: Rational -> a

Instances

FromRational Double

Defined in NumHask.Data.Rational

Methods

fromRational :: Rational -> Double

FromRational Float

Defined in NumHask.Data.Rational

Methods

fromRational :: Rational -> Float

FromRational a => FromRational (Positive a)

Defined in NumHask.Data.Positive

Methods

fromRational :: Rational -> Positive a

FromRational (Ratio Integer)

Defined in NumHask.Data.Rational

Methods

fromRational :: Rational -> Ratio Integer

FromRational a => FromRational (Wrapped a)

Defined in NumHask.Data.Wrapped

Methods

fromRational :: Rational -> Wrapped a

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

reduce normalises a ratio by dividing both numerator and denominator by their greatest common divisor.

>>> reduce 72 60
6 :% 5

\a b -> reduce a b == a :% b || b == zero

gcd :: (Eq a, EndoBased 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.

>>> gcd 72 60
12