fromRational x = fromRat x
recip x = 1.0 / x
+{-# RULES "truncate/Float->Int" truncate = float2Int #-}
instance RealFrac Float where
{-# SPECIALIZE properFraction :: Float -> (Int, Float) #-}
- {-# SPECIALIZE truncate :: Float -> Int #-}
{-# SPECIALIZE round :: Float -> Int #-}
{-# SPECIALIZE ceiling :: Float -> Int #-}
{-# SPECIALIZE floor :: Float -> Int #-}
acosh x = log (x + (x+1.0) * sqrt ((x-1.0)/(x+1.0)))
atanh x = log ((x+1.0) / sqrt (1.0-x*x))
+{-# RULES "truncate/Double->Int" truncate = double2Int #-}
instance RealFrac Double where
{-# SPECIALIZE properFraction :: Double -> (Int, Double) #-}
- {-# SPECIALIZE truncate :: Double -> Int #-}
{-# SPECIALIZE round :: Double -> Int #-}
{-# SPECIALIZE ceiling :: Double -> Int #-}
{-# SPECIALIZE floor :: Double -> Int #-}
double2Float :: Double -> Float
double2Float (D# x) = F# (double2Float# x)
+
float2Double :: Float -> Double
float2Double (F# x) = D# (float2Double# x)
%*********************************************************
\begin{code}
-{-# SPECIALIZE fromIntegral ::
- Int -> Rational,
- Integer -> Rational,
- Int -> Int,
- Int -> Integer,
- Int -> Float,
- Int -> Double,
- Integer -> Int,
- Integer -> Integer,
- Integer -> Float,
- Integer -> Double #-}
+{-# RULES
+"fromIntegral/Int->Int" fromIntegral = id :: Int -> Int
+"fromIntegral/Integer->Integer" fromIntegral = id :: Integer -> Integer
+"fromIntegral/Int->Integer" fromIntegral = int2Integer
+"fromIntegral/Integer->Int" fromIntegral = integer2Int
+"fromIntegral/Int->Rational" forall n . fromIntegral n = int2Integer n :% 1
+"fromIntegral/Integer->Rational" forall n . fromIntegral n = n :% (1 :: Integer)
+"fromIntegral/Int->Float" fromIntegral = int2Float
+"fromIntegral/Int->Double" fromIntegral = int2Double
+"fromIntegral/Integer->Float" forall n . fromIntegral n = encodeFloat n 0 :: Float
+"fromIntegral/Integer->Double" forall n . fromIntegral n = encodeFloat n 0 :: Double
+ #-}
fromIntegral :: (Integral a, Num b) => a -> b
fromIntegral = fromInteger . toInteger
-{-# SPECIALIZE realToFrac ::
- Double -> Rational,
- Rational -> Double,
- Float -> Rational,
- Rational -> Float
- #-}
-realToFrac :: (Real a, Fractional b) => a -> b
-realToFrac = fromRational . toRational
-
{-# RULES
-"realToFrac/Double->Float" realToFrac = doubleToFloat
"realToFrac/Float->Double" realToFrac = floatToDouble
-"realToFrac/Double->Double" realToFrac = id :: Double -> Double
-"realToFrac/Float->Float" realToFrac = id :: Float -> Float
-"realToFrac/Rational->Rational" realToFrac = id :: Rational -> Rational
+"realToFrac/Double->Float" realToFrac = doubleToFloat
+"realToFrac/Float->Float" realToFrac = id :: Float -> Float
+"realToFrac/Double->Double" realToFrac = id :: Double -> Double
+"realToFrac/Rational->Rational" realToFrac = id :: Rational -> Rational
+"realToFrac/Float->Rational" realToFrac = rf2rat :: Float -> Rational
+"realToFrac/Double->Rational" realToFrac = rf2rat :: Double -> Rational
+"realToFrac/Rational->Float" realToFrac = fromRat :: Rational -> Float
+"realToFrac/Rational->Double" realToFrac = fromRat :: Rational -> Double
#-}
+realToFrac :: (Real a, Fractional b) => a -> b
+realToFrac = fromRational . toRational
doubleToFloat :: Double -> Float
doubleToFloat (D# d) = F# (double2Float# d)
floatToDouble :: Float -> Double
floatToDouble (F# f) = D# (float2Double# f)
+{-# SPECIALIZE rf2rat ::
+ Float -> Rational,
+ Double -> Rational
+ #-}
+rf2rat :: RealFloat a => a -> Rational
+rf2rat x = if n >= 0 then (m * (b ^ n)) :% 1 else m :% (b ^ (-n))
+ where (m,n) = decodeFloat x
+ b = floatRadix x
\end{code}
-