diff --git a/paddle/fluid/distributed/auto_parallel/spmd_rules/common.cc b/paddle/fluid/distributed/auto_parallel/spmd_rules/common.cc
index f1b8a60a169f9ea4073d49879fbcf8b8d61299f1..dc740da070bfb8b46292dec8b83c41a598b05c6e 100644
--- a/paddle/fluid/distributed/auto_parallel/spmd_rules/common.cc
+++ b/paddle/fluid/distributed/auto_parallel/spmd_rules/common.cc
@@ -12,6 +12,8 @@ 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. */
 
+#include <glog/logging.h>
+
 #include "paddle/fluid/distributed/auto_parallel/spmd_rules/common.h"
 
 namespace paddle {
@@ -42,7 +44,7 @@ std::unordered_map<std::string, int64_t> ShardingMergeForTensors(
   int64_t merge_dim;
 
   for (auto& pair : tensor_axes_to_dim_pairs) {
-    for (int i = 0; i < pair.second.size(); i++) {
+    for (size_t i = 0; i < pair.second.size(); ++i) {
       auto tensor_axis = pair.first.substr(i, 1);
       auto mesh_dim = pair.second[i];
 
@@ -71,7 +73,7 @@ std::unordered_map<std::string, int64_t> ShardingMergeForTensors(
       VLOG(4) << "Sharding Conflict: Mesh_Dim [" << it.first
               << "] are Sharding Multiple Tensor Axis: [" << it.second
               << "]. The Axis: [" << it.second[0] << "] is Picked.";
-      for (int i = 1; i < it.second.size(); i++) {
+      for (size_t i = 1; i < it.second.size(); ++i) {
         axis_to_dim_map[it.second.substr(i, 1)] = -1;
       }
     }
@@ -113,7 +115,7 @@ TensorDistAttr CopyTensorDistAttrForOutput(
   new_dist_attr.set_process_mesh(src_dist_attr.process_mesh());
   new_dist_attr.set_batch_dim(src_dist_attr.batch_dim());
   new_dist_attr.set_dynamic_dims(src_dist_attr.dynamic_dims());
-  new_dist_attr.set_annotated(false);
+  // new_dist_attr.set_annotated(false); TODO unset field is false by default.
   return new_dist_attr;
 }
 
@@ -122,8 +124,8 @@ std::vector<int64_t> ResoluteOutputPartialDimension(
     const std::string& tensor_axes) {
   std::vector<int64_t> partial_on_dims;
 
-  for (auto& it : in_axis_to_dim_map) {
-    if (out_axis.find(it.first) != std::string::npos) {
+  for (auto& it : axis_to_dim_map) {
+    if (tensor_axes.find(it.first) == std::string::npos) {
       if (it.second > -1) {
         partial_on_dims.push_back(it.second);
       }
@@ -132,6 +134,20 @@ std::vector<int64_t> ResoluteOutputPartialDimension(
   return partial_on_dims;
 }
 
+std::string GetBroadcastAxes(const int64_t& tenosr_ndim,
+                             const int64_t& broadcast_ndim,
+                             const std::string& alphabet) {
+  PADDLE_ENFORCE_GE(
+      alphabet.size(),
+      broadcast_ndim,
+      phi::errors::InvalidArgument(
+          "size of alphabet [%d] is less than broadcast ndim [%d]",
+          alphabet.size(),
+          broadcast_ndim));
+  return alphabet.substr(0, broadcast_ndim)
+      .substr(broadcast_ndim - tenosr_ndim, tenosr_ndim);
+}
+
 }  // namespace auto_parallel
 }  // namespace distributed
 }  // namespace paddle
diff --git a/paddle/fluid/distributed/auto_parallel/spmd_rules/common.h b/paddle/fluid/distributed/auto_parallel/spmd_rules/common.h
index 2465998c9229125a54c49d77de4d86bdeba6707f..41d031106a4c348c278c3589c68baf6dfc142df3 100644
--- a/paddle/fluid/distributed/auto_parallel/spmd_rules/common.h
+++ b/paddle/fluid/distributed/auto_parallel/spmd_rules/common.h
@@ -19,14 +19,18 @@ limitations under the License. */
 #include <string>
 #include <vector>
 
-#include "paddle/fluid/distributed/auto_parallel/spmd_rules/dist_tensor_spec.h"
 #include "paddle/fluid/framework/type_defs.h"
+#include "paddle/fluid/platform/enforce.h"
 #include "paddle/phi/core/distributed/auto_parallel/dist_attr.h"
 
+#include "paddle/fluid/distributed/auto_parallel/spmd_rules/dist_tensor_spec.h"
+
 namespace paddle {
 namespace distributed {
 namespace auto_parallel {
 
+using paddle::framework::Attribute;
+
 class SPMDRuleBase {
  public:
   virtual ~SPMDRuleBase() {}
@@ -64,10 +68,10 @@ class SPMDRuleBase {
   const Attribute& GetAttr(const std::string& name,
                            const paddle::framework::AttributeMap& attrs) const {
     auto iter = attrs.find(name);
-    PADDLE_ENFORCE_NE(
-        iter,
-        attrs.end(),
-        platform::errors::NotFound("(%s) is not found in AttributeMap."));
+    PADDLE_ENFORCE_NE(iter,
+                      attrs.end(),
+                      paddle::platform::errors::NotFound(
+                          "(%s) is not found in AttributeMap."));
     return iter->second;
   }
 };
@@ -96,6 +100,15 @@ std::vector<int64_t> ResoluteOutputPartialDimension(
     const std::unordered_map<std::string, int64_t>& axis_to_dim_map,
     const std::string& tensor_axes);
 
+// Generate the axis notation of tensor for the einsum notation of a broadcast
+// operation(alignment star from the rightmost axis). tenosr_ndim: the size of
+// the tensor. broadcast_ndim: the maxium size of tensors in this broadcast
+// operation. alphabet: the characters used to represent the axes of tensor.
+// length of alphabet should >= broadcast_ndim.
+std::string GetBroadcastAxes(const int64_t& tenosr_ndim,
+                             const int64_t& broadcast_ndim,
+                             const std::string& alphabet);
+
 }  // namespace auto_parallel
 }  // namespace distributed
 }  // namespace paddle