BUG: 0/0 with arrow backend is not "NA"

[b-phi]

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Reproducible Example

import pyarrow as pa
import pandas as pd

s = pd.Series([0], dtype=pd.ArrowDtype(pa.float64()))
(s / s).isna()

Issue Description

Dividing by zero with the arrow backend produces float('nan') which is not detected as NA by pandas when it is inside an arrow series.

In [25]: s / s
Out[25]:
0    NaN
dtype: double[pyarrow]

In [25]: (s / s).isna()
Out[25]:
0    False
dtype: bool

In [26]: (s / s).apply(pd.isna)
Out[26]:
0    True
dtype: bool

In [28]: pd.isna(float('nan'))
Out[28]: True

In [30]: pd.Series([float('nan')]).isna()
Out[30]:
0    True
dtype: bool

Expected Behavior

What is considered a NaN should not be dependent on the dtype backend used.

Installed Versions

INSTALLED VERSIONS ------------------ commit : d9cdd2ee5a58015ef6f4d15c7226110c9aab8140 python : 3.10.10.final.0 python-bits : 64 OS : Darwin OS-release : 23.5.0 Version : Darwin Kernel Version 23.5.0: Wed May 1 20:09:52 PDT 2024; root:xnu-10063.121.3~5/RELEASE_X86_64 machine : x86_64 processor : i386 byteorder : little LC_ALL : None LANG : en_US.UTF-8 LOCALE : en_US.UTF-8 pandas : 2.2.2 numpy : 2.0.0 pytz : 2024.1 dateutil : 2.9.0.post0 setuptools : 70.1.1 pip : 24.1.1 Cython : None pytest : 8.2.1 hypothesis : None sphinx : 7.3.7 blosc : None feather : None xlsxwriter : None lxml.etree : None html5lib : None pymysql : None psycopg2 : 2.9.9 jinja2 : 3.1.4 IPython : 8.24.0 pandas_datareader : None adbc-driver-postgresql: None adbc-driver-sqlite : None bs4 : 4.12.3 bottleneck : None dataframe-api-compat : None fastparquet : None fsspec : 2024.5.0 gcsfs : None matplotlib : None numba : None numexpr : None odfpy : None openpyxl : None pandas_gbq : None pyarrow : 16.1.0 pyreadstat : None python-calamine : None pyxlsb : None s3fs : 2024.5.0 scipy : 1.13.1 sqlalchemy : None tables : None tabulate : 0.9.0 xarray : None xlrd : None zstandard : None tzdata : 2024.1 qtpy : None pyqt5 : None

[asishm]

xref https://github.com/pandas-dev/pandas/issues/32265. See also #58988 and the comment chain https://github.com/pandas-dev/pandas/pull/58988/files#r1636855759

I wouldnt consider float64, Float64 and double[pyarrow] as the same dtype but different backends in the current state of pandas (there is a separate PDEP out there that talks about creating unified pandas dtypes)

[WillAyd]

Yes technically even going back to IEEE 757 0/0 is NaN; the Float64 data type does not consider NaN to be a missing value (i.e. NA)

What you expect is reasonable given the history of pandas, but the future of it is uncertain. @asishm has linked the proper discussion; I think in the long term the behavior of the OP is correct but we are just missing a isnan method if you truly cared to detect NaN

[b-phi]

Thank you for the discussion links. Some way to detect the nan beyond np.isnan(df) would certainly cover our use case. The discrepancy between series.isna() and series.apply(pd.isna) is also quite confusing.