BUG: DataFrame.corr clips values when cov=True

[j-hendricks]

Pandas version checks

• 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

In [50]: x = pd.DataFrame({"A": [1, 2, None, 4], "B": [2, 4, None, 9]})

In [51]: x.cov()
Out[51]:
     A    B
A  1.0  1.0
B  1.0  1.0

In [52]: x.dropna().cov()
Out[52]:
          A     B
A  2.333333   5.5
B  5.500000  13.0

Issue Description

Stemming from #61154. DataFrame.corr was clipped between -1 and 1 to handle numerical precision errors. However, this was done regardless of whether cov equals True or False, and should instead only be done when cov=False.

Expected Behavior

import pandas as pd

In [50]: x = pd.DataFrame({"A": [1, 2, None, 4], "B": [2, 4, None, 9]})

In [51]: x.cov()
Out[51]:
A B
A 1.0 1.0
B 1.0 1.0

In [52]: x.dropna().cov()
Out[52]:
A B
A 1.0 1.0
B 1.0 1.0

Installed Versions

commit : cdc9e95
python : 3.10.16
python-bits : 64
OS : Darwin
OS-release : 24.3.0
Version : Darwin Kernel Version 24.3.0: Thu Jan 2 20:24:22 PST 2025; root:xnu-11215.81.4~3/RELEASE_ARM64_T6041
machine : x86_64
processor : i386
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 3.0.0.dev0+2006.gcdc9e952f1
numpy : 1.26.4
dateutil : 2.9.0.post0
pip : 25.0.1
Cython : 3.0.12
sphinx : 8.1.3
IPython : 8.34.0
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.13.3
blosc : None
bottleneck : 1.4.2
fastparquet : 2024.11.0
fsspec : 2025.3.0
html5lib : 1.1
hypothesis : 6.130.4
gcsfs : 2025.3.0
jinja2 : 3.1.6
lxml.etree : 5.3.1
matplotlib : 3.10.1
numba : 0.61.0
numexpr : 2.10.2
odfpy : None
openpyxl : 3.1.5
psycopg2 : 2.9.9
pymysql : 1.4.6
pyarrow : 19.0.1
pyreadstat : 1.2.8
pytest : 8.3.5
python-calamine : None
pytz : 2025.2
pyxlsb : 1.0.10
s3fs : 2025.3.0
scipy : 1.15.2
sqlalchemy : 2.0.40
tables : 3.10.1
tabulate : 0.9.0
xarray : 2024.9.0
xlrd : 2.0.1
xlsxwriter : 3.2.2
zstandard : 0.23.0
tzdata : 2025.2
qtpy : None
pyqt5 : None