• progress towards PERF: df.loc is 100x slower for CategoricalIndex than for normal Index #20395
• xref PERF: __contains__ method for Categorical #21022
• tests added / passed
• benchmark added / passed
• passes git diff upstream/master -u -- "*.py" | flake8 --diff
• whatsnew entry

Currently, membership checks in CategoricalIndex is very slow as explained in #21022. This PR fixes the issue for CategoricalIndex, while #21022 contains the fix for Categorical. The difference between the two cases is the use of _engine for CategoricalIndex, which makes this even faster than the Catagorical solution in #21022.

Tests exist already and can be found in tests/indexes/test_category.py::TestCategoricalIndex::test_contains.

ASV:

      before           after         ratio
     [0c65c57a]       [986779ab]
-      2.49±0.2ms       3.26±0.2μs     0.00  categoricals.Contains.time_contains

SOME BENCHMARKS HAVE CHANGED SIGNIFICANTLY.