Hello. The following code hangs:

import fnmatch
fnmatch.fnmatchcase("a" * 32, "*" * 16 + "b")

Measurements show that its execution time rises exponentially with the number of asterisks. Bash and SQLite 3 process this glob instantly.

This is because "fnmatchcase" generates a regular expression with repeated dots:

(?s:.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*b)\\Z

It's equivalent to:

(?s:.*b)\\Z

But works in exponential time. So the solution is to replace multiple asterisks with a single one, so the latter regexp is generated instead.

>So the solution is to replace multiple asterisks with a single one
No, this is not a solution. This glob also hangs:

fnmatch.fnmatchcase("a" * 32, "*a" * 16 + "b")

And again, Bash and SQLite 3 work perfectly.

Note that doctest has the same kind of potential problem with matching ellipsis (0 or more characters) in expected output blocks.  Backtracking isn't needed at all to resolve patterns of that limited kind, but I don't think Python's re module supports enough gimmicks to disable backtracking.

So instead doctest has its own

_ellipsis_match()

function to do it in worst-case linear time.

"The trick" with this kind of pattern is that a `*` should consume as little as possible to allow the next fixed portion to match.  Apply that at every stage, and it succeeds or it doesn't.  Backtracking can't change that outcome.  For, e.g., the shell pattern:

a*bc*d*

a regexp to do this without backtracking would be like this, IF Python's re engine supported "atomic groups" (but it doesn't):

a(?>.*?bc)(?>.*?d).*\Z

The same effect can be gotten in a more convoluted way, via positive lookahead assertions and backreferencing (which Python's re engine does support):

a(?=(.*?bc))\1(?=(.*?d))\2.*\Z

Assertions are "one and done":  if the overall match fails, assertions don't try alternatives.

So that's _a_ way to proceed.  I'm unclear on that it's worth it, though.  Stuff like "*a*a*a*a*a*a*" is just hard to swallow as a shell pattern that would occur in real life.

Changed version to 3.9, because anything done would change the regexp generated, and fnmatch.translate()` makes that regexp visible.

New changeset b9c46a2c2d7fc68457bff641f78932d66f5e5f59 by Tim Peters in branch 'master':
bpo-40480 "fnmatch" exponential execution time (GH-19908)
https://github.com/python/cpython/commit/b9c46a2c2d7fc68457bff641f78932d66f5e5f59

This change has caused a problem for coverage.py.  The full details are here: https://github.com/nedbat/coveragepy/issues/988#issuecomment-626926513

Coverage.py combines fnmatch-produced regexes by joining them with pipes into one larger regex.  The \<g1> group in the regexes now makes that larger regex invalid.

Ned, would it be possible to rewrite code of the form:

    if giant pasted regexp matches:
    
to:

    if any(p matches for p in patterns):

That should work under any version of Python.

There's no guarantee that regexps _can_ be pasted together and still work, so I can't call this change "a bug".  That pasting regexps together "worked" before was an implementation accident.

I'd be happy to change it anyway, except I know of no way to use Python's re engine without backreferences that can avoid exponential-time behavior in some cases.  In some other regexp engines, yes (e.g., as the code comments note, in those that support "atomic grouping"), but not in Python's.  Nor does Python's re engine support reusing backreference names or numbers.

So I know of no way to restore the ability to paste regexps together that wouldn't reintroduce the possiblity of exponential time failure :-(

one way might be to give the groups "unique" names (perhaps hashing the input string?)  ((this is what I attempted to do in a little bit of code which tried to "backport" (group)*+ and (group)++))

I don't want something probabilistic.  Fix it or don't ;-)

One thing that would work, but at the cost of non-determinism:  do the same as now, but obtain the number part of the group name by applying next() to a module-global private instance of itertools.count().  That will keep the numbers increasing "forever", and across calls.  The point to using .count() is that it's atomic (i.e., won't repeat a number if multiple threads happen to be constructing regexps simultaneously).

It's a darned silly amount of effort, though ;-)

New changeset b1b4c790e7d3b5f4244450aefe3d8f01710c13f7 by Tim Peters in branch 'master':
bpo-40480: restore ability to join fnmatch.translate() results (GH-20049)
https://github.com/python/cpython/commit/b1b4c790e7d3b5f4244450aefe3d8f01710c13f7

Wow, thanks Tim. To be honest, I was coming around to your original point of view that it was too much to promise that these regexes could be combined the way I'm doing it.  If we have to undo this latest change, I can live with it.

Ned, I'm happy to do this. While the ability to join wasn't documented, it's not an unreasonable expectation. I'm not sure it's possible to fail _unless_ the regexps use named groups (and/or numbered backreferences) - and nobody in their right mind would expect regexps for such simple patterns to do such a thing ;-)

So chances seem decent the regression your user stumbled into wouldn't be the only one to pop up.  The fix was actually quite easy (and thanks to Anthony for nudging me in that direction!).  The annoying part was writing a test given that the precise group names generated are no longer predictable :-(