BUG: NumericIndex should not support float16 dtype

pandas/core/indexes/numeric.py

@@ -74,8 +74,8 @@ class NumericIndex(Index):
     Notes
     -----
     An NumericIndex instance can **only** contain numpy int64/32/16/8, uint64/32/16/8 or
-    float64/32/16 dtype. In particular, ``NumericIndex`` *can not* hold Pandas numeric
-    dtypes (:class:`Int64Dtype`, :class:`Int32Dtype` etc.).
+    float64/32 dtype. In particular, ``NumericIndex`` *can not* hold numpy float16
+    dtype or Pandas numeric dtypes (:class:`Int64Dtype`, :class:`Int32Dtype` etc.).
     """
 
     _typ = "numericindex"
@@ -174,6 +174,10 @@ def _ensure_array(cls, data, dtype, copy: bool):
             raise ValueError("Index data must be 1-dimensional")
 
         subarr = np.asarray(subarr)
+        if subarr.dtype == "float16":
+            # float16 not supported (no indexing engine)
+            subarr = subarr.astype("float32")
+
         return subarr
 
     @classmethod
@@ -198,6 +202,9 @@ def _ensure_dtype(cls, dtype: Dtype | None) -> np.dtype | None:
             return cls._default_dtype
 
         dtype = pandas_dtype(dtype)
+        if dtype == np.float16:
+            # float16 not supported (no indexing engine)
+            dtype = np.dtype(np.float32)
         assert isinstance(dtype, np.dtype)
 
         if cls._is_backward_compat_public_numeric_index:

pandas/tests/indexes/numeric/test_numeric.py

@@ -552,6 +552,20 @@ def test_constructor_32bit(self, dtype):
         assert index.dtype == np.int64
 
 
+class TestFloat16Index:
+    # float 16 indexes not supported
+    # GH 49535
+    def test_array(self):
+        arr = np.array([1, 2, 3], dtype=np.float16)
+        result = NumericIndex(arr)
+
+        expected = NumericIndex([1, 2, 3], dtype=np.float32)
+        tm.assert_index_equal(result, expected, check_exact=True)
+
+        result = NumericIndex([1, 2, 3], dtype=np.float16)
+        tm.assert_index_equal(result, expected, check_exact=True)
+
+
 class TestUIntNumericIndex(NumericInt):
 
     _index_cls = NumericIndex