Safe Haskell	None
Language	Haskell98

Algebra.ToRational

Synopsis

class (C a, C a, Ord a) => C a where
realToField :: (C a, C b) => a -> b

Documentation

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

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 #

Lossless conversion from any representation of a rational to Rational

Instances

C Double #
Instance details Defined in Algebra.ToRational Methods toRational :: Double -> Rational #
C Float #
Instance details Defined in Algebra.ToRational Methods toRational :: Float -> Rational #
C Int #
Instance details Defined in Algebra.ToRational Methods toRational :: Int -> Rational #
C Int8 #
Instance details Defined in Algebra.ToRational Methods toRational :: Int8 -> Rational #
C Int16 #
Instance details Defined in Algebra.ToRational Methods toRational :: Int16 -> Rational #
C Int32 #
Instance details Defined in Algebra.ToRational Methods toRational :: Int32 -> Rational #
C Int64 #
Instance details Defined in Algebra.ToRational Methods toRational :: Int64 -> Rational #
C Integer #
Instance details Defined in Algebra.ToRational Methods toRational :: Integer -> Rational #
C Word #
Instance details Defined in Algebra.ToRational Methods toRational :: Word -> Rational #
C Word8 #
Instance details Defined in Algebra.ToRational Methods toRational :: Word8 -> Rational #
C Word16 #
Instance details Defined in Algebra.ToRational Methods toRational :: Word16 -> Rational #
C Word32 #
Instance details Defined in Algebra.ToRational Methods toRational :: Word32 -> Rational #
C Word64 #
Instance details Defined in Algebra.ToRational Methods toRational :: Word64 -> Rational #
C T #
Instance details Defined in Number.Peano Methods toRational :: T -> Rational #
(Ord a, C a) => C (T a) #
Instance details Defined in Number.NonNegative Methods toRational :: T a -> Rational #
(C a, C a) => C (T a) #
Instance details Defined in Algebra.ToInteger Methods toRational :: T a -> Rational #
Real a => C (T a) #
Instance details Defined in MathObj.Wrapper.Haskell98 Methods toRational :: T a -> Rational #
(C a, C a) => C (T a) #
Instance details Defined in Number.NonNegativeChunky Methods toRational :: T a -> Rational #
C a => C (T a) #
Instance details Defined in MathObj.Wrapper.NumericPrelude Methods toRational :: T a -> Rational #

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

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.