[Haskell-cafe] Re: Debugging Newton's method for square roots
Jón Fairbairn
jon.fairbairn at cl.cam.ac.uk
Sun Oct 15 08:55:01 EDT 2006
Vraj Mohan <r.vrajmohan at gmail.com> writes:
> I am new to Haskell and need help in debugging my code.
>
> I wrote the following function for calculating square roots using Newton's
> method:
>
> my_sqrt :: Float -> Float
> my_sqrt x = improve 1 x
> where improve y x = if abs (y * y - x) < epsilon
> then y
> else improve ((y + (x/y))/ 2) x
> epsilon = 0.00001
>
>
>
> This works for several examples that I tried out but goes into an infinite loop
> for my_sqrt 96.
Generally it's better to separate out the different parts of
the algorithm. So
sqrt_step x candidate = (candidate + x/candidate)/2
Now you can try
take 20 $ iterate (sqrt_step 2) 1
and watch the convergence. When you're happy with that, you
can use something like “head . dropWhile unconverged”.
> (The equivalent code is well-behaved on MIT Scheme)
Is it? Is there equivalent code to “my_sqrt :: Float ->
Float”? (that might be pertinent).
--
Jón Fairbairn Jon.Fairbairn at cl.cam.ac.uk
http://www.chaos.org.uk/~jf/Stuff-I-dont-want.html (updated 2006-09-13)
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