[issue27761] Private _nth_root function loses accuracy

[Mark Dickinson]

Mark Dickinson added the comment:

> What else can I do? Since I'm only dealing with integer powers, should I 
> try using my own ipow(y, n) for testing?

I'd expect that a square-and-multiply-style pow would be less accurate than math.pow, in general, simply because of the number of floating-point operations involved.

But I don't think there's a real problem here so long as you don't have an expectation of getting super-accurate (e.g., correctly rounded or faithfully rounded) results; testing that results are accurate to within 10 ulps or so is probably good enough.

If you want an actual correctly-rounded nth root just for testing purposes, it's certainly possible to construct one with integer arithmetic, but an easier alternative might simply be to use MPFR's "mpfr_root" function (as wrapped by gmpy2) to generate test values.

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<http://bugs.python.org/issue27761>
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