BUG: nan comparisons behave differently on identical objects

[vyasr]

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Reproducible Example

>>> import pandas as pd
>>> import numpy as np
>>> idx = pd.Index([np.nan])
>>> idx > idx
array([ True])
>>> idx > idx.copy()
array([False])

Issue Description

When an index contains np.nan, it compares differently to itself than to any other index object containing np.nan (including a copy of itself). This seems likely to be caused by some internal check for identity (other is self) that is taking precedence over element-wise comparisons.

Expected Behavior

NaN should follow IEEE 754, so we should see

>>> idx > idx
array([False])

without needing a copy.

Installed Versions

INSTALLED VERSIONS

commit : 4bfe3d0
python : 3.8.13.final.0
python-bits : 64
OS : Linux
OS-release : 4.15.0-76-generic
Version : #86-Ubuntu SMP Fri Jan 17 17:24:28 UTC 2020
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : None
LOCALE : en_US.UTF-8
pandas : 1.4.2
numpy : 1.21.6
pytz : 2022.1
dateutil : 2.8.2
pip : 22.1.1
setuptools : 62.3.2
Cython : 0.29.30
pytest : 7.1.2
hypothesis : 6.46.7
sphinx : 4.5.0
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.8.0
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.0.3
IPython : 8.3.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : None
brotli :
fastparquet : None
fsspec : 2022.5.0
gcsfs : None
markupsafe : 2.1.1
matplotlib : None
numba : 0.55.1
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 7.0.0
pyreadstat : None
pyxlsb : None
s3fs : 2022.5.0
scipy : 1.8.1
snappy :
sqlalchemy : 1.4.36
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
zstandard : None

[mroeschke]

cc @jbrockmendel possibly traced back to #43555

[simonjayhawkins]

cc @jbrockmendel possibly traced back to #43555

can confirm. first bad commit: [e9d0a58] REF: Share Index comparison and arithmetic methods (#43555)

[jbrockmendel]

Yah, looks like the trouble is in

            elif op in {operator.ne, operator.lt, operator.gt}:
                arr = np.zeros(len(self), dtype=bool)
                if self._can_hold_na and not isinstance(self, ABCMultiIndex):
                    arr[self.isna()] = True
                return arr

the setting arr[self.isna()] = True should only be for operator.ne