Fix various issues in Index.intersection

python/cudf/cudf/core/_base_index.py

@@ -608,19 +608,43 @@ def intersection(self, other, sort=False):
                     (1, 'Blue')],
                 )
         """
+        if not can_convert_to_column(other):
+            raise TypeError("Input must be Index or array-like")
+
         if not isinstance(other, BaseIndex):
-            other = cudf.Index(other, name=self.name)
+            other = cudf.Index(
+                other,
+                name=getattr(other, "name", self.name),
+            )
 
         if sort not in {None, False}:
             raise ValueError(
                 f"The 'sort' keyword only takes the values of "
                 f"None or False; {sort} was passed."
             )
 
-        if self.equals(other):
+        if self.equals(other) or not len(self):
+            dtypes = [self.dtype, other.dtype]
+            common_dtype = cudf.utils.dtypes.find_common_type(dtypes)
+            if cudf.get_option(
+                "mode.pandas_compatible"
+            ) and common_dtype == cudf.dtype("object"):
+                common_dtype = "str"
             if self.has_duplicates:
-                return self.unique()._get_reconciled_name_object(other)
-            return self._get_reconciled_name_object(other)
+                return (
+                    self.unique()
+                    ._get_reconciled_name_object(other)
+                    .astype(common_dtype)
+                )
+            return self._get_reconciled_name_object(other).astype(common_dtype)
+        elif not len(other):
+            dtypes = [self.dtype, other.dtype]
+            common_dtype = cudf.utils.dtypes.find_common_type(dtypes)
+            if cudf.get_option(
+                "mode.pandas_compatible"
+            ) and common_dtype == cudf.dtype("object"):
+                common_dtype = "str"
+            return other._get_reconciled_name_object(self).astype(common_dtype)
 
         res_name = _get_result_name(self.name, other.name)
 

python/cudf/cudf/core/index.py

@@ -681,7 +681,9 @@ def _union(self, other, sort=None):
     @_cudf_nvtx_annotate
     def _intersection(self, other, sort=False):
         if not isinstance(other, RangeIndex):
-            return super()._intersection(other, sort=sort)
+            return self._try_reconstruct_range_index(
+                super()._intersection(other, sort=sort)
+            )
 
         if not len(self) or not len(other):
             return RangeIndex(0)
@@ -722,7 +724,7 @@ def _intersection(self, other, sort=False):
         if sort is None:
             new_index = new_index.sort_values()
 
-        return new_index
+        return self._try_reconstruct_range_index(new_index)
 
     @_cudf_nvtx_annotate
     def difference(self, other, sort=None):

python/cudf/cudf/core/join/_join_helpers.py

@@ -74,6 +74,10 @@ def _match_join_keys(
             common_type = ltype.categories.dtype
         else:
             common_type = rtype.categories.dtype
+        if cudf.get_option(
+            "mode.pandas_compatible"
+        ) and common_type == cudf.dtype("object"):
+            common_type = "str"
         return lcol.astype(common_type), rcol.astype(common_type)
 
     if is_dtype_equal(ltype, rtype):

python/cudf/cudf/tests/test_index.py

@@ -11,6 +11,7 @@
 import pytest
 
 import cudf
+from cudf.api.types import is_bool_dtype
 from cudf.core._compat import PANDAS_GE_133, PANDAS_GE_200
 from cudf.core.index import (
     CategoricalIndex,
@@ -2099,25 +2100,48 @@ def test_union_index(idx1, idx2, sort):
         (pd.Index([0, 1, 2, 30], name=pd.NA), pd.Index([30, 0, 90, 100])),
         (pd.Index([0, 1, 2, 30], name="a"), [90, 100]),
         (pd.Index([0, 1, 2, 30]), pd.Index([0, 10, 1.0, 11])),
-        (pd.Index(["a", "b", "c", "d", "c"]), pd.Index(["a", "c", "z"])),
+        (
+            pd.Index(["a", "b", "c", "d", "c"]),
+            pd.Index(["a", "c", "z"], name="abc"),
+        ),
         (
             pd.Index(["a", "b", "c", "d", "c"]),
             pd.Index(["a", "b", "c", "d", "c"]),
         ),
         (pd.Index([True, False, True, True]), pd.Index([10, 11, 12, 0, 1, 2])),
         (pd.Index([True, False, True, True]), pd.Index([True, True])),
+        (pd.RangeIndex(0, 10, name="a"), pd.Index([5, 6, 7], name="b")),
+        (pd.Index(["a", "b", "c"], dtype="category"), pd.Index(["a", "b"])),
+        (pd.Index(["a", "b", "c"], dtype="category"), pd.Index([1, 2, 3])),
+        (pd.Index([0, 1, 2], dtype="category"), pd.RangeIndex(0, 10)),
+        (pd.Index(["a", "b", "c"], name="abc"), []),
+        (pd.Index([], name="abc"), pd.RangeIndex(0, 4)),
+        (pd.Index([1, 2, 3]), pd.Index([1, 2], dtype="category")),
+        (pd.Index([]), pd.Index([1, 2], dtype="category")),
     ],
 )
 @pytest.mark.parametrize("sort", [None, False])
-def test_intersection_index(idx1, idx2, sort):
+@pytest.mark.parametrize("pandas_compatible", [True, False])
+def test_intersection_index(idx1, idx2, sort, pandas_compatible):
     expected = idx1.intersection(idx2, sort=sort)
 
-    idx1 = cudf.from_pandas(idx1) if isinstance(idx1, pd.Index) else idx1
-    idx2 = cudf.from_pandas(idx2) if isinstance(idx2, pd.Index) else idx2
-
-    actual = idx1.intersection(idx2, sort=sort)
-
-    assert_eq(expected, actual, exact=False)
+    with cudf.option_context("mode.pandas_compatible", pandas_compatible):
+        idx1 = cudf.from_pandas(idx1) if isinstance(idx1, pd.Index) else idx1
+        idx2 = cudf.from_pandas(idx2) if isinstance(idx2, pd.Index) else idx2
+
+        actual = idx1.intersection(idx2, sort=sort)
+
+        # TODO: Resolve the bool vs ints mixed issue
+        # once pandas has a direction on this issue
+        # https://github.com/pandas-dev/pandas/issues/44000
+        assert_eq(
+            expected,
+            actual,
+            exact=False
+            if (is_bool_dtype(idx1.dtype) and not is_bool_dtype(idx2.dtype))
+            or (not is_bool_dtype(idx1.dtype) or is_bool_dtype(idx2.dtype))
+            else True,
+        )
 
 
 @pytest.mark.parametrize(