BUG: Index.intersection casting to object instead of numeric

doc/source/whatsnew/v1.2.0.rst

@@ -771,6 +771,7 @@ Other
 - Fixed metadata propagation in the :class:`Series.dt`, :class:`Series.str` accessors, :class:`DataFrame.duplicated`, :class:`DataFrame.stack`, :class:`DataFrame.unstack`, :class:`DataFrame.pivot`, :class:`DataFrame.append`, :class:`DataFrame.diff`, :class:`DataFrame.applymap` and :class:`DataFrame.update` methods (:issue:`28283`, :issue:`37381`)
 - Fixed metadata propagation when selecting columns with ``DataFrame.__getitem__`` (:issue:`28283`)
 - Bug in :meth:`Index.union` behaving differently depending on whether operand is an :class:`Index` or other list-like (:issue:`36384`)
+- Bug in :meth:`Index.intersection` with non-matching numeric dtypes casting to ``object`` dtype instead of minimal common dtype (:issue:`38122`)
 - Passing an array with 2 or more dimensions to the :class:`Series` constructor now raises the more specific ``ValueError`` rather than a bare ``Exception`` (:issue:`35744`)
 - Bug in ``dir`` where ``dir(obj)`` wouldn't show attributes defined on the instance for pandas objects (:issue:`37173`)
 - Bug in :meth:`RangeIndex.difference` returning :class:`Int64Index` in some cases where it should return :class:`RangeIndex` (:issue:`38028`)

pandas/core/indexes/base.py

@@ -33,6 +33,7 @@
 from pandas.util._decorators import Appender, cache_readonly, doc
 
 from pandas.core.dtypes.cast import (
+    find_common_type,
     maybe_cast_to_integer_array,
     validate_numeric_casting,
 )
@@ -2826,8 +2827,9 @@ def intersection(self, other, sort=False):
             return self._get_reconciled_name_object(other)
 
         if not is_dtype_equal(self.dtype, other.dtype):
-            this = self.astype("O")
-            other = other.astype("O")
+            dtype = find_common_type([self.dtype, other.dtype])
+            this = self.astype(dtype)
+            other = other.astype(dtype)
             return this.intersection(other, sort=sort)
 
         result = self._intersection(other, sort=sort)

pandas/core/indexes/multi.py

@@ -3713,16 +3713,14 @@ def _convert_can_do_setop(self, other):
         if not isinstance(other, Index):
 
             if len(other) == 0:
-                other = MultiIndex(
-                    levels=[[]] * self.nlevels,
-                    codes=[[]] * self.nlevels,
-                    verify_integrity=False,
-                )
+                return self[:0], self.names
             else:
                 msg = "other must be a MultiIndex or a list of tuples"
                 try:
                     other = MultiIndex.from_tuples(other)
-                except TypeError as err:
+                except (ValueError, TypeError) as err:
+                    # ValueError raised by tupels_to_object_array if we
+                    #  have non-object dtype
                     raise TypeError(msg) from err
         else:
             result_names = get_unanimous_names(self, other)

pandas/tests/indexes/multi/test_setops.py

@@ -2,7 +2,7 @@
 import pytest
 
 import pandas as pd
-from pandas import MultiIndex, Series
+from pandas import Index, MultiIndex, Series
 import pandas._testing as tm
 
 
@@ -294,6 +294,24 @@ def test_intersection(idx, sort):
     # assert result.equals(tuples)
 
 
+def test_intersection_non_object(idx, sort):
+    other = Index(range(3), name="foo")
+
+    result = idx.intersection(other, sort=sort)
+    expected = MultiIndex(levels=idx.levels, codes=[[]] * idx.nlevels, names=None)
+    tm.assert_index_equal(result, expected, exact=True)
+
+    # if we pass a length-0 ndarray (i.e. no name, we retain our idx.name)
+    result = idx.intersection(np.asarray(other)[:0], sort=sort)
+    expected = MultiIndex(levels=idx.levels, codes=[[]] * idx.nlevels, names=idx.names)
+    tm.assert_index_equal(result, expected, exact=True)
+
+    msg = "other must be a MultiIndex or a list of tuples"
+    with pytest.raises(TypeError, match=msg):
+        # With non-zero length non-index, we try and fail to convert to tuples
+        idx.intersection(np.asarray(other), sort=sort)
+
+
 def test_intersect_equal_sort():
     # GH-24959
     idx = pd.MultiIndex.from_product([[1, 0], ["a", "b"]])

pandas/tests/indexes/ranges/test_setops.py

@@ -3,11 +3,40 @@
 import numpy as np
 import pytest
 
-from pandas import Index, Int64Index, RangeIndex
+from pandas import Index, Int64Index, RangeIndex, UInt64Index
 import pandas._testing as tm
 
 
 class TestRangeIndexSetOps:
+    @pytest.mark.parametrize("klass", [RangeIndex, Int64Index, UInt64Index])
+    def test_intersection_mismatched_dtype(self, klass):
+        # check that we cast to float, not object
+        index = RangeIndex(start=0, stop=20, step=2, name="foo")
+        index = klass(index)
+
+        flt = index.astype(np.float64)
+
+        # bc index.equals(flt), we go through fastpath and get RangeIndex back
+        result = index.intersection(flt)
+        tm.assert_index_equal(result, index, exact=True)
+
+        result = flt.intersection(index)
+        tm.assert_index_equal(result, flt, exact=True)
+
+        # neither empty, not-equals
+        result = index.intersection(flt[1:])
+        tm.assert_index_equal(result, flt[1:], exact=True)
+
+        result = flt[1:].intersection(index)
+        tm.assert_index_equal(result, flt[1:], exact=True)
+
+        # empty other
+        result = index.intersection(flt[:0])
+        tm.assert_index_equal(result, flt[:0], exact=True)
+
+        result = flt[:0].intersection(index)
+        tm.assert_index_equal(result, flt[:0], exact=True)
+
     def test_intersection(self, sort):
         # intersect with Int64Index
         index = RangeIndex(start=0, stop=20, step=2)