In 3.8 we add a new function `unicodedata.is_normalized`.  The result is equivalent to `str == unicodedata.normalize(form, str)`, but the implementation uses a version of the "quick check" algorithm from UAX #15 as an optimization to try to avoid having to copy the whole string.  This was added in issue #32285, commit 2810dd7be.

However, it turns out the code doesn't actually implement the same algorithm as UAX #15, and as a result we often miss the optimization and end up having to compute the whole normalized string after all.

Here's a quick demo on my desktop.  We pass a long string made entirely out of a character for which the quick-check algorithm always says `NO`, it's not normalized:

$ build.base/python -m timeit -s 'import unicodedata; s = "\uf900"*500000' -- \
    'unicodedata.is_normalized("NFD", s)'
50 loops, best of 5: 4.39 msec per loop

$ build.base/python -m timeit -s 'import unicodedata; s = "\uf900"*500000' -- \
    's == unicodedata.normalize("NFD", s)'
50 loops, best of 5: 4.41 msec per loop

That's the same 4.4 ms (for a 1 MB string) with or without the attempted optimization.

Here it is after a patch that makes the algorithm run as in the standard:

$ build.dev/python -m timeit -s 'import unicodedata; s = "\uf900"*500000' -- \
    'unicodedata.is_normalized("NFD", s)'
5000000 loops, best of 5: 58.2 nsec per loop

Nearly 5 orders of magnitude faster -- the difference between O(N) and O(1).

The root cause of the issue is that our `is_normalized` static helper, which the new function relies on, was never written as a full implementation of the quick-check algorithm.  The full algorithm can return YES, MAYBE, or NO; but originally this helper's only caller was the implementation of `unicodedata.normalize`, which only cares about YES vs. MAYBE-or-NO.  So the helper often returns MAYBE when the standard algorithm would say NO.

(More precisely, perhaps: it's fine that this helper was never a full implementation... but it didn't say that anywhere, even while referring to the standard algorithm, and as a result set us up for future confusion.)

That's exactly what's happening in the example above: the standard quick-check algorithm would say NO, but our helper says MAYBE.  Which for `unicodedata.is_normalized` means it has to go compute the whole normalized string.

Fix posted, as GH-15558.

Adding cc's for the folks in the thread on #32285, where this function was originally added.

New changeset 2f09413947d1ce0043de62ed2346f9a2b4e5880b by Benjamin Peterson (Greg Price) in branch 'master':
closes bpo-37966: Fully implement the UAX #15 quick-check algorithm. (GH-15558)
https://github.com/python/cpython/commit/2f09413947d1ce0043de62ed2346f9a2b4e5880b

Thanks for that!

New changeset 4dd1c9d9c2bca4744c70c9556b7051f4465ede3e by Miss Islington (bot) in branch '3.8':
closes bpo-37966: Fully implement the UAX GH-15 quick-check algorithm. (GH-15558)
https://github.com/python/cpython/commit/4dd1c9d9c2bca4744c70c9556b7051f4465ede3e

Thanks Greg Price for this nice optimization!