I found another performance issue in _power_exact:

>>> Decimal(4) ** Decimal("-1.2e-999999999")
^CTraceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/stefan/pydev/cpython/Lib/decimal.py", line 2343, in __pow__
    ans = self._power_exact(other, context.prec + 1)
  File "/home/stefan/pydev/cpython/Lib/decimal.py", line 2098, in _power_exact
    ten_pow = 10**-ye
KeyboardInterrupt



This one is in the power operation in line 2098. There are several
other places where huge integer powers are calculated if 'ye' is
sufficiently large.

Thanks for the report;  I'll try to find some time to look at this.

This isn't the first time that I've thought that it might be better just to abandon the aim of getting correctly-rounded results for pow.

Here's a patch. Stefan, could you please review?

Here's a slightly improved version that adds guards against computing 10**ye for large ye in the case y < 0, ye > 0.

New changeset c3fe54781244 by Mark Dickinson in branch 'default':
Issue #12080: Fix a performance issue in Decimal._power_exact that causes some corner-case Decimal.__pow__ calls to take an unreasonably long time.
http://hg.python.org/cpython/rev/c3fe54781244

New changeset 78d79499e7de by Mark Dickinson in branch '2.7':
Issue #12080: Fix a performance issue in Decimal._power_exact that caused some corner-case Decimal.__pow__ calls to take an unreasonably long time.
http://hg.python.org/cpython/rev/78d79499e7de

Fixed for 3.3 and 2.7.

Mark Dickinson <report@bugs.python.org> wrote:
> Here's a patch. Stefan, could you please review?

Mark, sorry for not replying earlier. The patch looks great.

I've also tested the patch in practice: I ran 700,000,000 random tests with
an exponent range of [-999999999, 999999999]. This took three days.

Without the patch, this would have been impossible; the range had to be
restricted to [-9999, 9999].

Unfortunately I got sidetracked reviewing the rest of the function (today
I started out on a mechanical proof of the nth-root part).

I *did* review the changes though, and I think they are correct.