[Haskell-cafe] Fractional sqrt

[Novák Zoltán]

Hello,

I would like to use the sqrt function on Fractional numbers.
(mysqrt :: (Fractional a) => a->a)

Half of the problem is solved by:

Prelude> :t (realToFrac.sqrt)
(realToFrac.sqrt) :: (Fractional b, Real a, Floating a) => a -> b

For the other half I tried:

Prelude> :t (realToFrac.sqrt.realToFrac)
(realToFrac.sqrt.realToFrac) :: (Fractional b, Real a) => a -> b

Prelude> :t (realToFrac.sqrt.fromRational.toRational)
(realToFrac.sqrt.fromRational.toRational) :: (Fractional b, Real a) => a -> b

Prelude> :t (realToFrac.sqrt.realToFrac.fromRational.toRational)
(realToFrac.sqrt.realToFrac.fromRational.toRational) :: (Fractional b,
 Real a) => a -> b

I have to admit that I do not fully understand the Haskell numerical tower... 
Now I'm using the Newton method:

mysqrt :: (Fractional a) => a -> a
mysqrt x = (iterate (\y -> (x / y + y) / 2.0 ) 1.0) !!2000

But I want a faster solution. (Not by replacing 2000 with 100... :)

				Zoltan