BUG: Inconsistent equal comparison for datetime and string

[jeff-hernandez]

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• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd

data = [
    {"f_0": "2015-07-01", "f_2": "08335394550"},
    {"f_0": "2015-07-02", "f_2": "+49 (0) 0345 300033"},
    {"f_0": "2015-07-03", "f_2": "+49(0)2598 04457"},
    {"f_0": "2015-07-04", "f_2": "0741470003"},
    {"f_0": "2015-07-05", "f_2": "04181 83668"},
]

dtypes = dict(f_0='datetime64[ns]', f_2='string')
df = pd.DataFrame(data=data).astype(dtypes)
df['f_0'].eq(df['f_2'])

OverflowError: signed integer is greater than maximum

Issue Description

Applying an equal comparison between datetime and string columns can result in different behaviors. In the example above, the comparison results in an overflow error, whereas in the example below, the comparison results in the expected boolean column. Both examples compare the same data types but yield different behaviors.

data = [
    {"f_0": "2015-07-01", "f_2": "a"},
    {"f_0": "2015-07-02", "f_2": "b"},
    {"f_0": "2015-07-03", "f_2": "c"},
    {"f_0": "2015-07-04", "f_2": "d"},
    {"f_0": "2015-07-05", "f_2": "e"},
]

dtypes = dict(f_0='datetime64[ns]', f_2='string')
df = pd.DataFrame(data=data).astype(dtypes)
df['f_0'].eq(df['f_2'])

0    False
1    False
2    False
3    False
4    False
dtype: bool

Expected Behavior

I'd expect the output to also be a boolean column.

import pandas as pd

data = [
    {"f_0": "2015-07-01", "f_2": "08335394550"},
    {"f_0": "2015-07-02", "f_2": "+49 (0) 0345 300033"},
    {"f_0": "2015-07-03", "f_2": "+49(0)2598 04457"},
    {"f_0": "2015-07-04", "f_2": "0741470003"},
    {"f_0": "2015-07-05", "f_2": "04181 83668"},
]

dtypes = dict(f_0='datetime64[ns]', f_2='string')
df = pd.DataFrame(data=data).astype(dtypes)
df['f_0'].eq(df['f_2'])

0    False
1    False
2    False
3    False
4    False
dtype: bool

Installed Versions

INSTALLED VERSIONS

commit : 66e3805
python : 3.8.12.final.0
python-bits : 64
OS : Darwin
OS-release : 21.2.0
Version : Darwin Kernel Version 21.2.0: Sun Nov 28 20:28:54 PST 2021; root:xnu-8019.61.5~1/RELEASE_X86_64
machine : x86_64
processor : i386
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.3.5
numpy : 1.20.3
pytz : 2021.3
dateutil : 2.8.2
pip : 21.3.1
setuptools : 58.0.4
Cython : None
pytest : 6.2.5
hypothesis : None
sphinx : 4.2.0
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.0.3
IPython : 7.28.0
pandas_datareader: None
bs4 : 4.10.0
bottleneck : None
fsspec : 2021.11.1
fastparquet : 0.5.0
gcsfs : None
matplotlib : 3.2.2
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 6.0.1
pyxlsb : None
s3fs : None
scipy : 1.7.3
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
numba : 0.54.1

[Compro-Prasad]

Catching OverflowError at

pandas/pandas/core/arrays/datetimes.py

Line 2209 in b2da0a7

except ValueError as err:

would be helpful.