[Eager grad] Refactor partial grad logic (#40693)

* Refactor partial_grad/backward logic

* Add DuplicateCheck and polish code

* Refactor partial_grad/backward more clearly

* Refactor GeneralGrad by SingleInstance

python/paddle/fluid/tests/unittests/test_imperative_double_grad.py

@@ -116,6 +116,54 @@ class TestEagerGrad(TestCase):
             self.func_simple_example_eager_grad_not_allow_unused()
         self.func_simple_example_eager_grad_not_allow_unused()
 
+    def func_simple_example_eager_grad_duplicate_input(self):
+        np.random.seed(2021)
+        paddle.set_device('cpu')
+        np_x = np.random.random((3, 3))
+        np_y = np.random.random((3, 1))
+        np_z = np.random.random((3, 1))
+        x = paddle.to_tensor(np_x, dtype="float64", stop_gradient=False)
+        y = paddle.to_tensor(np_y, dtype="float64", stop_gradient=False)
+        z = paddle.to_tensor(np_z, dtype="float64", stop_gradient=False)
+        out_z = paddle.nn.functional.sigmoid(z)
+        out = paddle.matmul(x, y)
+
+        try:
+            # duplicate input will arise RuntimeError errors
+            dx = fluid.dygraph.grad(out, [x, x])
+        except RuntimeError as e:
+            error_msg = cpt.get_exception_message(e)
+            assert error_msg.find("duplicate") > 0
+
+    def test_simple_example_eager_grad_duplicate_input(self):
+        with _test_eager_guard():
+            self.func_simple_example_eager_grad_duplicate_input()
+        self.func_simple_example_eager_grad_duplicate_input()
+
+    def func_simple_example_eager_grad_duplicate_output(self):
+        np.random.seed(2021)
+        paddle.set_device('cpu')
+        np_x = np.random.random((3, 3))
+        np_y = np.random.random((3, 1))
+        np_z = np.random.random((3, 1))
+        x = paddle.to_tensor(np_x, dtype="float64", stop_gradient=False)
+        y = paddle.to_tensor(np_y, dtype="float64", stop_gradient=False)
+        z = paddle.to_tensor(np_z, dtype="float64", stop_gradient=False)
+        out_z = paddle.nn.functional.sigmoid(z)
+        out = paddle.matmul(x, y)
+
+        try:
+            # duplicate output will arise RuntimeError errors
+            dx = fluid.dygraph.grad([out, out], [x])
+        except RuntimeError as e:
+            error_msg = cpt.get_exception_message(e)
+            assert error_msg.find("duplicate") > 0
+
+    def test_simple_example_eager_grad_duplicate_output(self):
+        with _test_eager_guard():
+            self.func_simple_example_eager_grad_duplicate_output()
+        self.func_simple_example_eager_grad_duplicate_output()
+
 
 class TestDygraphDoubleGrad(TestCase):
     def setUp(self):