BUG: DatetimeIndex intersection with non-anchored freq

pandas/core/indexes/datetimelike.py

@@ -637,6 +637,13 @@ def _can_fast_intersect(self, other: Self) -> bool:
  # Because freq is not None, we must then be monotonic decreasing
  return False
 
+ # for non-anchored frequencies, need to check that the two
+ # indexes actually share a common point
+ # GH#44025
+ diff = other[0] - self[0]
+ if diff != Timedelta(0) and diff.total_seconds() % 86400 != 0:
+ return False
+
  # this along with matching freqs ensure that we "line up",
  # so intersection will preserve freq
  # Note we are assuming away Ticks, as those go through _range_intersect

pandas/tests/indexes/datetimes/test_setops.py

@@ -7,6 +7,7 @@
 import numpy as np
 import pytest
 
+from pandas._libs.tslibs.timedeltas import Timedelta
 import pandas.util._test_decorators as td
 
 import pandas as pd
@@ -757,3 +758,16 @@ def test_intersection_non_nano_rangelike():
  freq="D",
  )
  tm.assert_index_equal(result, expected)
+
+
+def test_cday_intersection_empty():
+ # GH#44025
+ off = pd.offsets.CDay(1, normalize=False)
+ ts = Timestamp("2021-10-13 09:00")
+ ts2 = ts + Timedelta("1 hour")
+
+ dti1 = date_range(start=ts, periods=10, freq=off)
+ dti2 = date_range(start=ts2, periods=10, freq=off)
+ result = dti1.intersection(dti2)
+ expected = DatetimeIndex([], dtype="datetime64[ns]")
+ tm.assert_index_equal(result, expected)