Re: [FUN] CodeGolf: solve equation x^x=C

[Philippe Verdy <verdy_p@...>]

Note that the idea of the table may not be good, by my idea of exploring bits of precisions with a binary search can be implemented easily by a recursive function. In which case it becomes possible to explore the whole 52 bits of precision in the result in at most log2(52) recursions.

Le jeu. 27 juin 2019 à 17:51, Coda Highland <chighland@gmail.com> a écrit :

On Thu, Jun 27, 2019 at 10:47 AM Philippe Verdy <verdy_p@wanadoo.fr> wrote:

excellent ! (note that your did not include the function header "function f(x)" and trailer "end" and the code "=x" to print the result on the Lua console).

Oh right, I meant to write print(x) instead of return x, that way it doesn't have to be a function. I just forgot that was my plan when I started writing it.

It works because the range from 0 to 395 is small enough and it assumes that math.random() will return an exact value.

This can create an infinite loop if this condition x*x=C is never reached exactly, because:

- random() will not explore all the possible bits, as random() does not return all the possible values for the 52 bits of numbers in (0,1).

- even if you have the best approximation possible of x, x^x=C may still be wrong (and there's no upper bound of the relative error on the value of x).

I knew it was terrible when I submitted it. :P

/s/ Adam