BUG: weekday incorrect for dates before 0000-03-01

[MarcoGorelli]

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

In [1]: pd.Timestamp('0000-03-01').weekday()
Out[1]: 2

In [2]: pd.Timestamp('0000-02-29').weekday()
Out[2]: 2

Issue Description

pandas thinks that before Wednesday there was another Wednesday - my guess is that this was written by a French pupil trying to get an extra half-day off? 😄

Expected Behavior

I'd expect

In [1]: pd.Timestamp('0000-03-01').weekday()
Out[1]: 2

In [2]: pd.Timestamp('0000-02-29').weekday()
Out[2]: 1

At least, that's what Rust's chrono gives:

use chrono::{NaiveDate};

fn main() {
    let date_str = "0000-02-29";
    let date = NaiveDate::parse_from_str(date_str, "%Y-%m-%d").unwrap();
    let weekday_abbrev = date.format("%a").to_string();
    println!("date: {:?}", date);
    println!("Weekday (abbreviated): {}", weekday_abbrev);
}

outputs

date: 0000-02-29
Weekday (abbreviated): Tue

Likewise, https://calculat.io/en/date/what-day-of-the-week-is/29-february-0000 gives it as Tuesday

Installed Versions

INSTALLED VERSIONS

commit : 965ceca
python : 3.10.6.final.0
python-bits : 64
OS : Linux
OS-release : 5.10.102.1-microsoft-standard-WSL2
Version : #1 SMP Wed Mar 2 00:30:59 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_GB.UTF-8
LOCALE : en_GB.UTF-8

pandas : 2.0.2
numpy : 1.24.3
pytz : 2023.3
dateutil : 2.8.2
setuptools : 67.6.1
pip : 23.0.1
Cython : None
pytest : 7.3.1
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.13.2
pandas_datareader: None
bs4 : 4.12.2
bottleneck : None
brotli : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : 3.7.1
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 12.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
snappy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None
None

[MarcoGorelli]

From https://en.wikipedia.org/wiki/Determination_of_the_day_of_the_week#Sakamoto.27s_methods, it looks like the current method is only accurate if the year is greater than 1752

[mcgeestocks]

take

[jorisvandenbossche]

Just as confirmation with another tool, also Arrow (date.h) gives the same result as chrono:

In [69]: arr = pa.array(["0000-02-29", "0000-03-01"]).cast(pa.timestamp("us"))

In [70]: pc.day_of_week(arr)
Out[70]: 
<pyarrow.lib.Int64Array object at 0x7f01133a4b20>
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