PERF: MultiIndex.equals for equal length indexes

[lukemanley]

• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/v2.3.0.rst file if fixing a bug or adding a new feature.

Avoids densifying the levels of the multiindex to check for equality.

from asv_bench.benchmarks.multiindex_object import Equals

b = Equals()
b.setup()
%timeit b.time_equals_deepcopy()

# 56.4 ms ± 1.03 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)   -> main
# 3.77 ms ± 58.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)  -> PR

[mroeschke]

Could we just use is_dtype_equal?

[lukemanley]

The equality rules for numpy dtypes are not as strict as is_dtype_equal:

In [1]: import pandas as pd

In [2]: import numpy as np

In [3]: idx = pd.Index([1])

In [4]: idx.astype("int64").equals(idx.astype("int32"))
Out[4]: True

In [5]: pd.core.dtypes.common.is_dtype_equal(np.int64, np.int32)
Out[5]: False

[mroeschke]

Thanks @lukemanley