Safe Haskell	None
Language	Haskell98

Algebra.ToRational

Synopsis

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

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

Methods

toRational :: a -> Rational Source #

Lossless conversion from any representation of a rational to Rational

Instances

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

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.