[Haskell-cafe] Fractional sqrt

[Lennart Augustsson]

I don't see a much better way than using something like Newton- 
Raphson and testing for some kind of convergence.  The Fractional  
class can contain many things; for instance it contains rational  
numbers.  So your mysqrt function would have to be able to cope with  
returning arbitrary precision results.  As a first step you should  
specify what mysqrt should return when it can't return the exact  
result.  For instance, what would you like mysqrt (2%1) to return?

	-- Lennart

On Jan 18, 2007, at 18:15 , Novák Zoltán wrote:

> 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
>
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