chore: import upstream snapshot with attribution

test/auto_parallel/spmd_rules/test_elementwise_rule.py

@@ -0,0 +1,800 @@
+# Copyright (c) 2023 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import unittest
+
+from paddle.distributed.auto_parallel.static.dist_attribute import (
+    DistTensorSpec,
+    TensorDistAttr,
+)
+from paddle.distributed.fleet import auto
+from paddle.framework import core
+
+
+class TestElementwiseSPMDRule(unittest.TestCase):
+    def setUp(self):
+        self.unary_rule = core.get_phi_spmd_rule("relu")
+        self.binary_rule = core.get_phi_spmd_rule("add")
+
+        x_shape = [64, 36]
+        y_shape = [64, 36]
+        process_mesh = auto.ProcessMesh(mesh=[0, 1, 2, 3])
+
+        x_tensor_dist_attr = TensorDistAttr()
+        x_tensor_dist_attr.dims_mapping = [1, 0]
+        x_tensor_dist_attr.process_mesh = process_mesh
+        self.x_dist_tensor_spec = DistTensorSpec(x_shape, x_tensor_dist_attr)
+
+        y_tensor_dist_attr = TensorDistAttr()
+        y_tensor_dist_attr.dims_mapping = [0, -1]
+        y_tensor_dist_attr.process_mesh = process_mesh
+        self.y_dist_tensor_spec = DistTensorSpec(y_shape, y_tensor_dist_attr)
+
+        self.out_dist_tensor_spec = DistTensorSpec(self.x_dist_tensor_spec)
+
+        self.attrs = []
+
+    def test_single_mesh_dim(self):
+        # [0, -1], [-1, -1] --> [0, -1], [0, -1], [0, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, -1])
+        result_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1])
+
+        # [0, -1], [-1, 0] --> [0, -1], [0, -1], [0, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, 0])
+        result_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1])
+
+        # [-1, -1], [-1, -1] --> [-1, -1], [-1, -1], [-1, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, -1])
+
+        result_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [-1, -1])
+
+        # [-1, 0]--> [-1, 0], [-1, 0]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, 0])
+
+        result_dist_attrs = self.unary_rule.infer_forward(
+            self.x_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, 0])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [-1, 0])
+
+    def test_single_mesh_dim_broadcast(self):
+        self.x_dist_tensor_spec.shape = [64, 36, 12]
+        self.y_dist_tensor_spec.shape = [12]
+
+        # [0, -1, -1], [-1] --> [0, -1, -1], [-1], [0, -1, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(len(resulted_dist_attrs), 2)
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [0, -1, -1]
+        )
+
+        # [-1, 0, -1], [-1] --> [-1, 0, -1], [-1], [-1, 0, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, 0, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, 0, -1])
+        self.assertEqual((inferred_input_dist_attrs[1].dims_mapping), [-1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, 0, -1]
+        )
+
+        # [-1, -1, 0], [-1] --> [-1, -1, 0], [0], [-1, -1, 0]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, -1, 0])
+        self.y_dist_tensor_spec.set_dims_mapping([-1])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, -1, 0])
+        self.assertEqual((inferred_input_dist_attrs[1].dims_mapping), [0])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, -1, 0]
+        )
+
+        # [-1, -1, -1], [0] --> [-1, -1, 0], [0], [-1, -1, 0]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, -1, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([0])
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, -1, 0])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, -1, 0]
+        )
+
+        self.x_dist_tensor_spec.shape = [64, 36, 12]
+        self.y_dist_tensor_spec.shape = [1, 12]
+        # [-1, 0, -1], [-1, -1] --> [-1, 0, -1], [-1, -1], [-1, 0, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, 0, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, 0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1, -1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, 0, -1]
+        )
+
+        self.x_dist_tensor_spec.shape = [64, 1, 1, 12]
+        self.y_dist_tensor_spec.shape = [64, 32, 12]
+        # [0, -1, -1, -1], [-1, -1, -1] --> [0, -1, -1, -1], [-1, -1, -1], [0, -1, -1, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1, -1, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, -1, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(
+            inferred_input_dist_attrs[0].dims_mapping, [0, -1, -1, -1]
+        )
+        self.assertEqual(
+            inferred_input_dist_attrs[1].dims_mapping, [-1, -1, -1]
+        )
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [0, -1, -1, -1]
+        )
+
+        # [-1, -1, -1, -1], [0, -1, -1] --> [-1, -1, -1, -1], [0, -1, -1], [-1, 0, -1, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, -1, -1, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([0, -1, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(
+            inferred_input_dist_attrs[0].dims_mapping, [-1, -1, -1, -1]
+        )
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1, -1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, -0, -1, -1]
+        )
+
+    def test_multi_mesh_dim(self):
+        process_mesh = auto.ProcessMesh([[0, 1, 2], [3, 4, 5]])
+        self.x_dist_tensor_spec.set_process_mesh(process_mesh)
+        self.y_dist_tensor_spec.set_process_mesh(process_mesh)
+        self.x_dist_tensor_spec.shape = [96, 24, 48]
+        self.y_dist_tensor_spec.shape = [96, 24, 48]
+
+        # [0, 1, -1], [-1, -1, -1] --> [0, 1, -1], [0, 1, -1], [0, 1, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, 1, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, -1, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(len(resulted_dist_attrs), 2)
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, 1, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, 1, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, 1, -1])
+
+        # [0, -1, -1], [-1, 1, 0] --> [0, 1, -1], [0, 1, -1], [0, 1, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, 1, 0])
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, 1, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, 1, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, 1, -1])
+
+    def test_multi_mesh_dim_broadcast(self):
+        process_mesh = auto.ProcessMesh([[0, 1, 2], [3, 4, 5]])
+        self.x_dist_tensor_spec.set_process_mesh(process_mesh)
+        self.y_dist_tensor_spec.set_process_mesh(process_mesh)
+        self.x_dist_tensor_spec.shape = [96, 24, 48]
+        self.y_dist_tensor_spec.shape = [48]
+
+        # [0, -1, -1], [1] --> [0, -1, 1], [1], [0, -1, 1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([1])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(len(resulted_dist_attrs), 2)
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1, 1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1, 1])
+
+        # [0, 1, -1], [0] --> [0, 1, -1], [-1], [0, 1, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, 1, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([0])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, 1, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, 1, -1])
+
+        self.x_dist_tensor_spec.shape = [96, 1, 1, 48]
+        self.y_dist_tensor_spec.shape = [96, 24, 48]
+        # [-1, -1, -1, 1], [0, -1, 1] --> [-1, -1, -1, 1], [0, -1, 1], [-1, 0, -1, 1]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, -1, -1, 1])
+        self.y_dist_tensor_spec.set_dims_mapping([0, -1, 1])
+
+        resulted_dist_attrs = self.binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(
+            inferred_input_dist_attrs[0].dims_mapping, [-1, -1, -1, 1]
+        )
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1, 1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, 0, -1, 1]
+        )
+
+    def test_backward_single_mesh_dim(self):
+        # [0, -1] --> [0, -1], [0, -1], [0, -1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([0, -1])
+        result_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1])
+
+        # [-1, -1] --> [-1, -1], [-1, -1], [-1, -1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([-1, -1])
+
+        result_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [-1, -1])
+
+        # [-1, 0]--> [-1, 0], [-1, 0] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([-1, 0])
+
+        result_dist_attrs = self.unary_rule.infer_backward(
+            self.x_dist_tensor_spec, self.out_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, 0])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [-1, 0])
+
+    def test_backward_single_mesh_dim_broadcast(self):
+        self.x_dist_tensor_spec.shape = [64, 36, 12]
+        self.y_dist_tensor_spec.shape = [12]
+        self.out_dist_tensor_spec.shape = [64, 36, 12]
+
+        # [0, -1, -1] --> [0, -1, -1], [-1], [0, -1, -1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([0, -1, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(len(resulted_dist_attrs), 2)
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [0, -1, -1]
+        )
+
+        # [-1, 0, -1] --> [-1, 0, -1], [-1], [-1, 0, -1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([-1, 0, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, 0, -1])
+        self.assertEqual((inferred_input_dist_attrs[1].dims_mapping), [-1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, 0, -1]
+        )
+
+        # [-1, -1, 0] --> [-1, -1, 0], [0], [-1, -1, 0] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([-1, -1, 0])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, -1, 0])
+        self.assertEqual((inferred_input_dist_attrs[1].dims_mapping), [0])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, -1, 0]
+        )
+
+        self.x_dist_tensor_spec.shape = [64, 36, 12]
+        self.y_dist_tensor_spec.shape = [1, 12]
+        self.out_dist_tensor_spec.shape = [64, 36, 12]
+        # [-1, 0, -1] --> [-1, 0, -1], [-1, -1], [-1, 0, -1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([-1, 0, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, 0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1, -1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, 0, -1]
+        )
+
+        self.x_dist_tensor_spec.shape = [64, 1, 1, 12]
+        self.y_dist_tensor_spec.shape = [64, 32, 12]
+        self.out_dist_tensor_spec.shape = [64, 64, 32, 12]
+        # [0, -1, -1, -1] --> [0, -1, -1, -1], [-1, -1, -1], [0, -1, -1, -1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([0, -1, -1, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(
+            inferred_input_dist_attrs[0].dims_mapping, [0, -1, -1, -1]
+        )
+        self.assertEqual(
+            inferred_input_dist_attrs[1].dims_mapping, [-1, -1, -1]
+        )
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [0, -1, -1, -1]
+        )
+
+        # [-1, 0, -1, -1] --> [-1, -1, -1, -1], [0, -1, -1], [-1, 0, -1, -1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([-1, 0, -1, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(
+            inferred_input_dist_attrs[0].dims_mapping, [-1, -1, -1, -1]
+        )
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1, -1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, -0, -1, -1]
+        )
+
+    def test_backward_multi_mesh_dim(self):
+        process_mesh = auto.ProcessMesh([[0, 1, 2], [3, 4, 5]])
+        self.x_dist_tensor_spec.set_process_mesh(process_mesh)
+        self.y_dist_tensor_spec.set_process_mesh(process_mesh)
+        self.x_dist_tensor_spec.shape = [96, 24, 48]
+        self.y_dist_tensor_spec.shape = [96, 24, 48]
+        self.out_dist_tensor_spec.shape = [96, 24, 48]
+
+        # [0, 1, -1] --> [0, 1, -1], [0, 1, -1], [0, 1, -1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([0, 1, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(len(resulted_dist_attrs), 2)
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, 1, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, 1, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, 1, -1])
+
+    def test_backward_multi_mesh_dim_broadcast(self):
+        process_mesh = auto.ProcessMesh([[0, 1, 2], [3, 4, 5]])
+        self.x_dist_tensor_spec.set_process_mesh(process_mesh)
+        self.y_dist_tensor_spec.set_process_mesh(process_mesh)
+        self.x_dist_tensor_spec.shape = [96, 24, 48]
+        self.y_dist_tensor_spec.shape = [48]
+        self.out_dist_tensor_spec.shape = [96, 24, 48]
+
+        # [0, -1, 1] --> [0, -1, 1], [1], [0, -1, 1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([0, -1, 1])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(len(resulted_dist_attrs), 2)
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1, 1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1, 1])
+
+        # [0, 1, -1] --> [0, 1, -1], [-1], [0, 1, -1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([0, 1, -1])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, 1, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, 1, -1])
+
+        self.x_dist_tensor_spec.shape = [96, 1, 1, 48]
+        self.y_dist_tensor_spec.shape = [96, 24, 48]
+        self.out_dist_tensor_spec.shape = [96, 96, 24, 48]
+
+        # [-1, 0, -1, 1] --> [-1, -1, -1, 1], [0, -1, 1], [-1, 0, -1, 1] (output --> inputs, output)
+        self.out_dist_tensor_spec.set_dims_mapping([-1, 0, -1, 1])
+
+        resulted_dist_attrs = self.binary_rule.infer_backward(
+            self.x_dist_tensor_spec,
+            self.y_dist_tensor_spec,
+            self.out_dist_tensor_spec,
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(
+            inferred_input_dist_attrs[0].dims_mapping, [-1, -1, -1, 1]
+        )
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1, 1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, 0, -1, 1]
+        )
+
+    def test_single_mesh_dim_greater_than(self):
+        binary_rule = core.get_phi_spmd_rule("greater_than")
+        # [0, -1], [-1, -1] --> [0, -1], [0, -1], [0, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, -1])
+        result_dist_attrs = binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        self.assertEqual(len(result_dist_attrs), 2)
+
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1])
+
+        # [0, -1], [-1, 0] --> [0, -1], [0, -1], [0, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, 0])
+        result_dist_attrs = binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        self.assertEqual(len(result_dist_attrs), 2)
+
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1])
+
+    def test_single_mesh_dim_broadcast_greater_than(self):
+        binary_rule = core.get_phi_spmd_rule("greater_than")
+        self.x_dist_tensor_spec.shape = [1, 64]
+        self.y_dist_tensor_spec.shape = [64]
+
+        # [-1, 0], [-1] --> [-1, 0], [0], [-1, 0]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, 0])
+        self.y_dist_tensor_spec.set_dims_mapping([-1])
+
+        resulted_dist_attrs = binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+
+        self.assertEqual(len(resulted_dist_attrs), 2)
+
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, 0])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [-1, 0])
+
+    def test_single_mesh_dim_less_than(self):
+        binary_rule = core.get_phi_spmd_rule("less_than")
+        # [0, -1], [-1, -1] --> [0, -1], [0, -1], [0, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, -1])
+        result_dist_attrs = binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        self.assertEqual(len(result_dist_attrs), 2)
+
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1])
+
+        # [0, -1], [-1, 0] --> [0, -1], [0, -1], [0, -1]
+        self.x_dist_tensor_spec.set_dims_mapping([0, -1])
+        self.y_dist_tensor_spec.set_dims_mapping([-1, 0])
+        result_dist_attrs = binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = result_dist_attrs[0]
+        inferred_output_dist_attrs = result_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1])
+
+    def test_single_mesh_dim_broadcast_less_than(self):
+        binary_rule = core.get_phi_spmd_rule("less_than")
+        self.x_dist_tensor_spec.shape = [1, 64]
+        self.y_dist_tensor_spec.shape = [64]
+
+        # [-1, 0], [-1] --> [-1, 0], [0], [-1, 0]
+        self.x_dist_tensor_spec.set_dims_mapping([-1, 0])
+        self.y_dist_tensor_spec.set_dims_mapping([-1])
+
+        resulted_dist_attrs = binary_rule.infer_forward(
+            self.x_dist_tensor_spec, self.y_dist_tensor_spec
+        )
+
+        self.assertEqual(len(resulted_dist_attrs), 2)
+
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(len(inferred_input_dist_attrs), 2)
+        self.assertEqual(len(inferred_output_dist_attrs), 1)
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, 0])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [-1, 0])
+
+    def test_multi_mesh_dim_with_partial(self):
+        process_mesh = auto.ProcessMesh([[0, 1, 2], [3, 4, 5]])
+        self.multiply_rule = core.get_phi_spmd_rule("multiply")
+        x_shape = [96, 24, 48]
+        y_shape = [24, 48]
+
+        # [0, -1, -1] partial_dim=[1], [-1, 1] --> [0, -1, 1] partial_dim=[], [-1, 1], [0, -1, 1] partial_dim=[]
+        x_tensor_dist_attr = TensorDistAttr()
+        x_tensor_dist_attr.process_mesh = process_mesh
+        x_tensor_dist_attr.dims_mapping = [0, -1, -1]
+        x_tensor_dist_attr._set_partial_dims([1])
+        x_dist_tensor_spec = DistTensorSpec(x_shape, x_tensor_dist_attr)
+
+        y_tensor_dist_attr = TensorDistAttr()
+        y_tensor_dist_attr.process_mesh = process_mesh
+        y_tensor_dist_attr.dims_mapping = [-1, 1]
+        y_dist_tensor_spec = DistTensorSpec(y_shape, y_tensor_dist_attr)
+
+        resulted_dist_attrs = self.multiply_rule.infer_forward(
+            x_dist_tensor_spec, y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [0, -1, 1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1, 1])
+        self.assertEqual(inferred_output_dist_attrs[0].dims_mapping, [0, -1, 1])
+
+        self.assertEqual(inferred_input_dist_attrs[0]._is_partial(), False)
+        self.assertEqual(inferred_input_dist_attrs[1]._is_partial(), False)
+        self.assertEqual(inferred_output_dist_attrs[0]._is_partial(), False)
+
+        # [-1, -1, -1], [-1, 1] partial_dim=[0] --> [-1, -1, 1], [-1, 1] partial_dim=[0], [-1, -1, 1] partial_dim=[0]
+        x_tensor_dist_attr = TensorDistAttr()
+        x_tensor_dist_attr.process_mesh = process_mesh
+        x_tensor_dist_attr.dims_mapping = [-1, -1, -1]
+        x_dist_tensor_spec = DistTensorSpec(x_shape, x_tensor_dist_attr)
+
+        y_tensor_dist_attr = TensorDistAttr()
+        y_tensor_dist_attr.process_mesh = process_mesh
+        y_tensor_dist_attr.dims_mapping = [-1, 1]
+        y_tensor_dist_attr._set_partial_dims([0])
+        y_dist_tensor_spec = DistTensorSpec(y_shape, y_tensor_dist_attr)
+
+        resulted_dist_attrs = self.multiply_rule.infer_forward(
+            x_dist_tensor_spec, y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, -1, 1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [-1, 1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, -1, 1]
+        )
+
+        self.assertEqual(inferred_input_dist_attrs[0]._is_partial(), False)
+        self.assertEqual(inferred_input_dist_attrs[1]._is_partial(), True)
+        self.assertEqual(inferred_input_dist_attrs[1]._partial_dims(), {0})
+        self.assertEqual(inferred_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(inferred_output_dist_attrs[0]._partial_dims(), {0})
+
+        # [-1, 0, -1] partial_dim=[1], [-1, 0] partial_dim=[1] --> [-1, 0, -1] partial_dim=[1], [0, -1] partial_dim=[], [-1, 0, -1] partial_dim=[1]
+        x_tensor_dist_attr = TensorDistAttr()
+        x_tensor_dist_attr.process_mesh = process_mesh
+        x_tensor_dist_attr.dims_mapping = [-1, 0, -1]
+        x_tensor_dist_attr._set_partial_dims([1])
+        x_dist_tensor_spec = DistTensorSpec(x_shape, x_tensor_dist_attr)
+
+        y_tensor_dist_attr = TensorDistAttr()
+        y_tensor_dist_attr.process_mesh = process_mesh
+        y_tensor_dist_attr.dims_mapping = [-1, 0]
+        y_tensor_dist_attr._set_partial_dims([1])
+        y_dist_tensor_spec = DistTensorSpec(y_shape, y_tensor_dist_attr)
+
+        resulted_dist_attrs = self.multiply_rule.infer_forward(
+            x_dist_tensor_spec, y_dist_tensor_spec
+        )
+        inferred_input_dist_attrs = resulted_dist_attrs[0]
+        inferred_output_dist_attrs = resulted_dist_attrs[1]
+
+        self.assertEqual(inferred_input_dist_attrs[0].dims_mapping, [-1, 0, -1])
+        self.assertEqual(inferred_input_dist_attrs[1].dims_mapping, [0, -1])
+        self.assertEqual(
+            inferred_output_dist_attrs[0].dims_mapping, [-1, 0, -1]
+        )
+
+        self.assertEqual(inferred_input_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(inferred_input_dist_attrs[0]._partial_dims(), {1})
+        self.assertEqual(inferred_input_dist_attrs[1]._is_partial(), False)
+        self.assertEqual(inferred_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(inferred_output_dist_attrs[0]._partial_dims(), {1})
+
+
+if __name__ == "__main__":
+    unittest.main()