RuntimeError: Segmentation fault with nth_root

[lfousse]

sage: RealField(53)(0.05).nth_root(7 * 10^8)
---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)

/opt/sage-4.7.2/<ipython console> in <module>()

/opt/sage-4.7.2/local/lib/python2.6/site-packages/sage/rings/real_mpfr.so in sage.rings.real_mpfr.RealNumber.nth_root (sage/rings/real_mpfr.c:23889)()

RuntimeError: Segmentation fault

Apply 12105.patch​ to the Sage repository.

[johanbosman]

The bug is in line 4708 of sage/rings/real_mpfr.pyx:

        if algorithm == 0 and fld.__prec * n < 10000:

The result of that multiplication as a signed int may become negative and actually does so in your example.

[kcrisman]

On Mac I don't get an error, but it hangs and eventually consumes all resources, so fair enough!

This patch gives

sage: timeit("RealField(53)(0.05).nth_root(7 * 10^8)")
625 loops, best of 3: 69.2 µs per loop

One question I have is whether this is the most appropriate test with this precision.

sage: RealField(53)(0.05).nth_root(7 * 10^8) 
0.999999995720382
sage: _^(7*10^8)
0.0499999991341384

Is that good enough?

Otherwise this is fine, passes tests, etc. on 5.0.beta1.

[johanbosman]

It'll be difficult to get a more accurate answer with that precision. Let's turn the last 2 into a 3:

sage: 0.999999995720383^(7*10^8)
0.0500000185630449

[kcrisman]

It'll be difficult to get a more accurate answer with that precision.

Well, that's what I figured, but I'm not a numerical analysis expert. Thanks.

Positive review.