numeric-prelude-0.4.3: An experimental alternative hierarchy of numeric type classes

Algebra.ToRational

Synopsis

# Documentation

class (C a, C a, Ord a) => C a where Source #

This class allows lossless conversion from any representation of a rational to the fixed Rational type. "Lossless" means - don't do any rounding. For rounding see Algebra.RealRing. With the instances for Float and Double we acknowledge that these types actually represent rationals rather than (approximated) real numbers. However, this contradicts to the Transcendental class.

Laws that must be satisfied by instances:

 fromRational' . toRational === id

Minimal complete definition

toRational

Methods

toRational :: a -> Rational Source #

Lossless conversion from any representation of a rational to Rational

Instances

 Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Source # Methods Real a => C (T a) Source # Methods (C a, C a) => C (T a) Source # Methods C a => C (T a) Source # Methods

realToField :: (C a, C b) => a -> b Source #

It should hold

realToField = fromRational' . toRational

but it should be much more efficient for particular pairs of types, such as converting Float to Double. This achieved by optimizer rules.