{-# LANGUAGE NoImplicitPrelude #-}
module Algebra.ToRational where
import qualified Algebra.Real as Real
import Algebra.Field (fromRational, )
import Algebra.Ring (fromInteger, )
import Number.Ratio (Rational, )
import Data.Int (Int, Int8, Int16, Int32, Int64, )
import Data.Word (Word, Word8, Word16, Word32, Word64, )
import qualified Prelude as P
import PreludeBase
import Prelude(Int,Integer,Float,Double)
{- |
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.RealField".
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 'Algebra.Transcendental'
Laws that must be satisfied by instances:
> fromRational' . toRational === id
-}
class (Real.C a) => C a where
-- | Lossless conversion from any representation of a rational to 'Rational'
toRational :: a -> Rational
instance C Integer where
{-#INLINE toRational #-}
toRational = fromInteger
instance C Float where
{-#INLINE toRational #-}
toRational = fromRational . P.toRational
instance C Double where
{-#INLINE toRational #-}
toRational = fromRational . P.toRational
instance C Int where {-#INLINE toRational #-}; toRational = toRational . P.toInteger
instance C Int8 where {-#INLINE toRational #-}; toRational = toRational . P.toInteger
instance C Int16 where {-#INLINE toRational #-}; toRational = toRational . P.toInteger
instance C Int32 where {-#INLINE toRational #-}; toRational = toRational . P.toInteger
instance C Int64 where {-#INLINE toRational #-}; toRational = toRational . P.toInteger
instance C Word where {-#INLINE toRational #-}; toRational = toRational . P.toInteger
instance C Word8 where {-#INLINE toRational #-}; toRational = toRational . P.toInteger
instance C Word16 where {-#INLINE toRational #-}; toRational = toRational . P.toInteger
instance C Word32 where {-#INLINE toRational #-}; toRational = toRational . P.toInteger
instance C Word64 where {-#INLINE toRational #-}; toRational = toRational . P.toInteger