Fix SparseDtype comparison

Author: tqa236

pandas/core/dtypes/dtypes.py

@@ -1705,17 +1705,15 @@ def __eq__(self, other: object) -> bool:
 
         if isinstance(other, type(self)):
             subtype = self.subtype == other.subtype
-            if self._is_na_fill_value:
+            if self._is_na_fill_value or other._is_na_fill_value:
                 # this case is complicated by two things:
                 # SparseDtype(float, float(nan)) == SparseDtype(float, np.nan)
                 # SparseDtype(float, np.nan)     != SparseDtype(float, pd.NaT)
                 # i.e. we want to treat any floating-point NaN as equal, but
                 # not a floating-point NaN and a datetime NaT.
-                fill_value = (
-                    other._is_na_fill_value
-                    and isinstance(self.fill_value, type(other.fill_value))
-                    or isinstance(other.fill_value, type(self.fill_value))
-                )
+                fill_value = isinstance(
+                    self.fill_value, type(other.fill_value)
+                ) or isinstance(other.fill_value, type(self.fill_value))
             else:
                 with warnings.catch_warnings():
                     # Ignore spurious numpy warning

pandas/tests/arrays/sparse/test_dtype.py

@@ -68,6 +68,14 @@ def test_nans_equal():
     assert b == a
 
 
+def test_nans_not_equal():
+    # GH 54770
+    a = SparseDtype(float, 0)
+    b = SparseDtype(float, pd.NA)
+    assert not a == b
+    assert not b == a
+
+
 with warnings.catch_warnings():
     msg = "Allowing arbitrary scalar fill_value in SparseDtype is deprecated"
     warnings.filterwarnings("ignore", msg, category=FutureWarning)