BUG: fixes weekday for dates before 1752

doc/source/whatsnew/v2.1.0.rst

@@ -364,9 +364,11 @@ Datetimelike
 - Bug in :func:`date_range` when ``freq`` was a :class:`DateOffset` with ``nanoseconds`` (:issue:`46877`)
 - Bug in :meth:`Timestamp.date`, :meth:`Timestamp.isocalendar`, :meth:`Timestamp.timetuple`, and :meth:`Timestamp.toordinal` were returning incorrect results for inputs outside those supported by the Python standard library's datetime module (:issue:`53668`)
 - Bug in :meth:`Timestamp.round` with values close to the implementation bounds returning incorrect results instead of raising ``OutOfBoundsDatetime`` (:issue:`51494`)
+- Bug in :meth:`Timestamp.weekday` with days incorrectly calculating before year 1752 (:issue:`53738`)
 - Bug in :meth:`arrays.DatetimeArray.map` and :meth:`DatetimeIndex.map`, where the supplied callable operated array-wise instead of element-wise (:issue:`51977`)
 - Bug in constructing a :class:`Series` or :class:`DataFrame` from a datetime or timedelta scalar always inferring nanosecond resolution instead of inferring from the input (:issue:`52212`)
 - Bug in parsing datetime strings with weekday but no day e.g. "2023 Sept Thu" incorrectly raising ``AttributeError`` instead of ``ValueError`` (:issue:`52659`)
+-
 
 Timedelta
 ^^^^^^^^^

pandas/_libs/tslibs/ccalendar.pyx

@@ -2,7 +2,6 @@
 """
 Cython implementations of functions resembling the stdlib calendar module
 """
-
 cimport cython
 from numpy cimport (
     int32_t,
@@ -19,7 +18,7 @@ cdef int32_t* days_per_month_array = [
     31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31,
     31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
 
-cdef int* sakamoto_arr = [0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4]
+cdef int* em = [0, 0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334]
 
 # The first 13 entries give the month days elapsed as of the first of month N
 # (or the total number of days in the year for N=13) in non-leap years.
@@ -76,11 +75,22 @@ cpdef int32_t get_days_in_month(int year, Py_ssize_t month) noexcept nogil:
 
 @cython.wraparound(False)
 @cython.boundscheck(False)
-@cython.cdivision
+@cython.cdivision(True)
+cdef long quot(long a , long b) noexcept nogil:
+    cdef long x
+    x = a/b
+    if (a < 0):
+        x -= (a % b != 0)
+    return x
+
+
+@cython.wraparound(False)
+@cython.boundscheck(False)
+@cython.cdivision(True)
 cdef int dayofweek(int y, int m, int d) noexcept nogil:
     """
     Find the day of week for the date described by the Y/M/D triple y, m, d
-    using Sakamoto's method, from wikipedia.
+    using Gauss' method, from wikipedia.
 
     0 represents Monday.  See [1]_.
 
@@ -103,16 +113,25 @@ cdef int dayofweek(int y, int m, int d) noexcept nogil:
     [1] https://docs.python.org/3/library/calendar.html#calendar.weekday
 
     [2] https://en.wikipedia.org/wiki/\
-    Determination_of_the_day_of_the_week#Sakamoto.27s_methods
+    Determination_of_the_day_of_the_week#Gauss's_algorithm
     """
     cdef:
-        int day
-
-    y -= m < 3
-    day = (y + y / 4 - y / 100 + y / 400 + sakamoto_arr[m - 1] + d) % 7
-    # convert to python day
-    return (day + 6) % 7
-
+        long c
+        int g
+        int f
+        int e
+
+    if (m < 3):
+        y -= 1
+
+    c = quot(y, 100)
+    g = y - quot(y, 100) * 100
+    f = 5 * (c - quot(c, 4) * 4)
+    e = em[m]
+
+    if (m > 2):
+        e -= 1
+    return (-1 + d + e + f + g + g/4) % 7
 
 cdef bint is_leapyear(int64_t year) noexcept nogil:
     """

pandas/tests/scalar/timestamp/test_timestamp.py

@@ -14,6 +14,7 @@
     tzlocal,
     tzutc,
 )
+from hypothesis import given
 import numpy as np
 import pytest
 import pytz
@@ -36,6 +37,7 @@
     Timestamp,
 )
 import pandas._testing as tm
+from pandas._testing._hypothesis import DATETIME_IN_PD_TIMESTAMP_RANGE_NO_TZ
 
 from pandas.tseries import offsets
 from pandas.tseries.frequencies import to_offset
@@ -223,6 +225,31 @@ def test_resolution(self):
         assert dt.as_unit("ms").resolution == Timedelta(milliseconds=1)
         assert dt.as_unit("s").resolution == Timedelta(seconds=1)
 
+    @pytest.mark.parametrize(
+        "date_string, expected_true, expected_false",
+        [
+            ("0000-2-29", 1, 2),
+            ("0000-3-1", 2, 3),
+            ("1582-10-14", 3, 4),
+            ("1582-10-15", 4, 5),
+            ("1752-01-01", 5, 6),
+            ("2023-06-18", 6, 0),
+        ],
+    )
+    def test_dow_historic(self, date_string, expected_true, expected_false):
+        # GH 53738
+        dt = Timestamp(date_string)
+        dow = dt.weekday()
+        assert dow == expected_true
+        assert not dow == expected_false
+
+    @given(DATETIME_IN_PD_TIMESTAMP_RANGE_NO_TZ)
+    def test_dow_sanity(self, dt):
+        # GH 53738
+        expected = dt.weekday()
+        result = datetime(dt.year, dt.month, dt.day).weekday()
+        assert result == expected
+
 
 class TestTimestamp:
     def test_default_to_stdlib_utc(self):