Steven D'Aprano added the comment: On Sun, Aug 14, 2016 at 08:29:39AM +0000, Mark Dickinson wrote: > Steven: can you explain why you think your code *should* be giving > exact results for exact powers? Do you have an error analysis that > says that should be the case?
No error analysis, only experimental results. > One issue here is that libm pow functions vary hugely in quality, so > any algorithm that depends on ** or math.pow is going to be hard to > prove anything about. pow() is just the starting point. An earlier version of the function started with an initial guess of x for the nth root of x, but it was very slow, and sometimes failed to converge in any reasonable time. By swapping to an initial guess calculated with pow(), I cut the number of iterations down to a much smaller number. Because I'm not to worried about being super-fast, the nth root function goes through the following steps: - use y = pow(x, 1/n) for an initial guess; - if y**n == x, return y; - improve the guess with the "Nth root algorithm"; - if that doesn't converge after a while, return y; - finally, compare the epsilons abs(y**n - x) for the initial guess and improved version, returning whichever gives the smaller epsilon. So I'm confident that nth_root() should never be worse than pow(). > I think the tests should simply be weakened: it's unreasonable to > expect perfect results in this case. Okay. I'll weaken the tests. ---------- _______________________________________ Python tracker <rep...@bugs.python.org> <http://bugs.python.org/issue27761> _______________________________________ _______________________________________________ Python-bugs-list mailing list Unsubscribe: https://mail.python.org/mailman/options/python-bugs-list/archive%40mail-archive.com
