Documentation

A rational number

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

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

toRatio (3.1415927 :: Float) :: Ratio Integer

13176795 :% 4194304

Fractional in base splits into fromRatio and Field

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

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.

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

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.