BUG: Fix NaT comparisons with Timedelta (#26039)

doc/source/whatsnew/v0.25.0.rst

@@ -273,7 +273,7 @@ Datetimelike
 Timedelta
 ^^^^^^^^^
 
--
+- Bug with comparisons between :class:`Timedelta` and ``NaT`` raising ``TypeError`` (:issue:`26039`)
 -
 -
 

pandas/_libs/tslibs/timedeltas.pyx

@@ -779,13 +779,17 @@ cdef class _Timedelta(timedelta):
                     return PyObject_RichCompare(np.array([self]), other, op)
                 return PyObject_RichCompare(other, self, reverse_ops[op])
             else:
-                if op == Py_EQ:
-                    return False
-                elif op == Py_NE:
-                    return True
-                raise TypeError('Cannot compare type {cls} with type {other}'
-                                .format(cls=type(self).__name__,
-                                        other=type(other).__name__))
+                if other is NaT:
+                    return PyObject_RichCompare(other, self, reverse_ops[op])
+                else:
+                    if op == Py_EQ:
+                        return False
+                    elif op == Py_NE:
+                        return True
+                    raise TypeError('Cannot compare type {cls} with '
+                                    'type {other}'
+                                    .format(cls=type(self).__name__,
+                                            other=type(other).__name__))
 
         return cmp_scalar(self.value, ots.value, op)
 

pandas/tests/scalar/timedelta/test_arithmetic.py

@@ -689,3 +689,37 @@ def test_rdivmod_invalid(self):
     def test_td_op_timedelta_timedeltalike_array(self, op, arr):
         with pytest.raises(TypeError):
             op(arr, Timedelta('1D'))
+
+
+class TestTimedeltaCompare():
+    """
+    Tests for Timedelta comparisons.
+    """
+
+    def test_timedelta_nat_comparisons(self):
+        # GH 26039
+        td = pd.Timedelta(0)
+
+        result = td > NaT
+        assert result is False
+
+        result = td >= NaT
+        assert result is False
+
+        result = td < NaT
+        assert result is False
+
+        result = td <= NaT
+        assert result is False
+
+        result = NaT > td
+        assert result is False
+
+        result = NaT >= td
+        assert result is False
+
+        result = NaT < td
+        assert result is False
+
+        result = NaT <= td
+        assert result is False