Fixed #52234

* Copied fix from https://github.com/ltauro/pandas/tree/nan-not-in-index and applied review comments

Author: ssche

doc/source/whatsnew/v2.1.0.rst

@@ -422,6 +422,7 @@ Indexing
 ^^^^^^^^
 - Bug in :meth:`DataFrame.__setitem__` losing dtype when setting a :class:`DataFrame` into duplicated columns (:issue:`53143`)
 - Bug in :meth:`DataFrame.__setitem__` with a boolean mask and :meth:`DataFrame.putmask` with mixed non-numeric dtypes and a value other than ``NaN`` incorrectly raising ``TypeError`` (:issue:`53291`)
+- Bug when using ``nan`` to index (:issue:`52234`)
 
 Missing
 ^^^^^^^

pandas/_libs/index.pyx

@@ -360,6 +360,8 @@ cdef class IndexEngine:
         values = self.values
         stargets = set(targets)
 
+        na_in_stargets = any(checknull(t) for t in stargets)
+
         n = len(values)
         n_t = len(targets)
         if n > 10_000:
@@ -374,7 +376,7 @@ cdef class IndexEngine:
         if (
                 stargets and
                 len(stargets) < 5 and
-                not any([checknull(t) for t in stargets]) and
+                not na_in_stargets and
                 self.is_monotonic_increasing
         ):
             # if there are few enough stargets and the index is monotonically
@@ -396,7 +398,7 @@ cdef class IndexEngine:
             # otherwise, map by iterating through all items in the index
 
             # short-circuit na check
-            if values.dtype == object:
+            if na_in_stargets:
                 check_na_values = True
                 # keep track of nas in values
                 found_nas = set()

pandas/tests/indexes/base_class/test_indexing.py

@@ -37,6 +37,24 @@ def test_get_indexer_non_unique_dtype_mismatch(self):
         tm.assert_numpy_array_equal(np.array([-1], dtype=np.intp), indexes)
         tm.assert_numpy_array_equal(np.array([0], dtype=np.intp), missing)
 
+    @pytest.mark.parametrize(
+        "idx_values,idx_non_unique",
+        [
+            ([np.nan, 100, 200, 100], [np.nan, 100]),
+            ([np.nan, 100.0, 200.0, 100.0], [np.nan, 100.0]),
+        ],
+    )
+    def test_get_indexer_non_unique_int_index(self, idx_values, idx_non_unique):
+        indexes, missing = Index(idx_values).get_indexer_non_unique(Index([np.nan]))
+        tm.assert_numpy_array_equal(np.array([0], dtype=np.intp), indexes)
+        tm.assert_numpy_array_equal(np.array([], dtype=np.intp), missing)
+
+        indexes, missing = Index(idx_values).get_indexer_non_unique(
+            Index(idx_non_unique)
+        )
+        tm.assert_numpy_array_equal(np.array([0, 1, 3], dtype=np.intp), indexes)
+        tm.assert_numpy_array_equal(np.array([], dtype=np.intp), missing)
+
 
 class TestGetLoc:
     @pytest.mark.slow  # to_flat_index takes a while