Safe Haskell	None
Language	Haskell98

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

C Double Source #
Methods toRational :: Double -> Rational Source #
C Float Source #
Methods toRational :: Float -> Rational Source #
C Int Source #
Methods toRational :: Int -> Rational Source #
C Int8 Source #
Methods toRational :: Int8 -> Rational Source #
C Int16 Source #
Methods toRational :: Int16 -> Rational Source #
C Int32 Source #
Methods toRational :: Int32 -> Rational Source #
C Int64 Source #
Methods toRational :: Int64 -> Rational Source #
C Integer Source #
Methods toRational :: Integer -> Rational Source #
C Word Source #
Methods toRational :: Word -> Rational Source #
C Word8 Source #
Methods toRational :: Word8 -> Rational Source #
C Word16 Source #
Methods toRational :: Word16 -> Rational Source #
C Word32 Source #
Methods toRational :: Word32 -> Rational Source #
C Word64 Source #
Methods toRational :: Word64 -> Rational Source #
C T Source #
Methods toRational :: T -> Rational Source #
Real a => C (T a) Source #
Methods toRational :: T a -> Rational Source #
(C a, C a) => C (T a) Source #
Methods toRational :: T a -> Rational Source #
C a => C (T a) Source #
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.