BUG: Rounding timedelta to 3 decimal places does not work correctly and is unstable.

[madeinjapan]

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

from pandas import Timedelta

td = Timedelta('0 days 00:00:00.000500')
td
# Timedelta('0 days 00:00:00.000500')

td.round('ms')
# Timedelta('0 days 00:00:00') <- the round is incorrect

td_new = Timedelta('0 days 00:00:00.000501')    # added .000001
td_new.round('ms')
# Timedelta('0 days 00:00:00.001000')

# With builtin round
round(0.000500, 3)
# 0.001

# Another strange situation with pandas
td_strange = Timedelta('0 days 00:00:00.001500')    # <- change 000500 to 001500
td_strange.round('ms')
# Timedelta('0 days 00:00:00.002000') <- looks OK

# but with
td_strange1 = Timedelta('0 days 00:00:00.002500')    # <- change 001500 to 002500
td_strange1.round('ms')
# Timedelta('0 days 00:00:00.002000') <- looks incorrect

# and with builtin round
round(1.000500, 3)
# 1.0
round(2.000500, 3)
# 2.001

Issue Description

Rounding does not work for values ​​ending in 5. Based on the rounding rules, we round up from 5. Pandas does this in some cases and not in others. Unstable

Expected Behavior

Correct application of rounding rules, or an alternative solution for fast rounding of large data (> 1 million).

Installed Versions

INSTALLED VERSIONS

commit : d9cdd2e
python : 3.11.6.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.22631
machine : AMD64
processor : Intel64 Family 6 Model 186 Stepping 3, GenuineIntel
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : English_United States.1252

pandas : 2.2.2
numpy : 1.25.2
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 65.5.0
pip : 23.2.1
Cython : None
pytest : 7.4.2
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : 8.16.1
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : 3.7.2
numba : None
numexpr : 2.10.0
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.11.1
sqlalchemy : None
tables : 3.9.2
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[mroeschke]

Thanks for the issue but this is the expected behavior. pandas, like python rounding, implements rounding half to even (aka bankers rounding), so closing as the expected behavior

[madeinjapan]

I did not know this. I learned something again. Thanks