completion.py

# Copyright (c) 2021 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 copy
import logging

from paddle.fluid import core

from .utils import is_naive_data_parallel, get_logger
from .utils import is_gradient_clip_op, __no_shape_var_type__
from .operators import find_compatible_distributed_operator_impls
from .dist_context import _node_id
from .dist_attribute import TensorDistributedAttribute
from .dist_attribute import OperatorDistributedAttribute
from .process_mesh import ProcessMesh
from .process_group import get_world_process_group
from paddle.distributed.fleet.meta_optimizers.common import OpRole


def compute_compatible_process_mesh(process_mesh_list):
    """Compute the compatible process mesh given a list of process meshes."""
    if not process_mesh_list:
        return None

    def _compute_compatible_process_mesh_two(pm1, pm2):
        if pm1 is None:
            return True, pm2
        if pm2 is None:
            return True, pm1
        if pm1 == pm2:
            return True, pm1
        if pm1.processes == pm2.processes:
            if len(pm1.topology) >= len(pm2.topology):
                return True, pm1
            else:
                return True, pm2
        process_set1 = set(pm1.processes)
        process_set2 = set(pm2.processes)
        if process_set1.issubset(process_set2):
            return True, pm2
        if process_set2.issubset(process_set1):
            return True, pm1
        return False, None

    compatible_result = None
    for process_mesh in process_mesh_list:
        compatible, compatible_result = _compute_compatible_process_mesh_two(
            compatible_result, process_mesh
        )
        if not compatible:
            return None
    return copy.deepcopy(compatible_result)


def compute_compatible_dim_mapping(dim_mapping_list):
    """Compute the compatible dim mapping given a list of dim mapping."""
    if not dim_mapping_list:
        return None

    def _compute_compatible_dim_mapping_two(dm1, dm2):
        if dm1 == -1:
            return True, dm2
        if dm2 == -1:
            return True, dm1
        if dm1 == dm2:
            return True, dm1
        return False, None

    compatible_result = -1
    for mapping in dim_mapping_list:
        compatible, compatible_result = _compute_compatible_dim_mapping_two(
            compatible_result, mapping
        )
        if not compatible:
            return None
    return compatible_result


def compute_compatible_dims_mapping(dims_mapping_list):
    """Compute the compatible dims mapping given a list of dims mapping.
    Each of dims mapping is also a list.
    """
    if not dims_mapping_list:
        return None
    length = len(dims_mapping_list[0])
    for dims_mapping in dims_mapping_list:
        if dims_mapping is None:
            return None
        if len(dims_mapping) != length:
            return None
    compatible_result = []
    for dim_mappings in zip(*dims_mapping_list):
        compatible_dim_mapping = compute_compatible_dim_mapping(
            list(dim_mappings)
        )
        if compatible_dim_mapping is None:
            return None
        compatible_result.append(compatible_dim_mapping)
    return compatible_result


def merge_process_mesh_two(pm1, pm2):
    process_set1 = set()
    process_set2 = set()
    if pm1 is None and pm2 is None:
        return None
    if pm1 is not None:
        process_set1 = set(pm1.processes)
    if pm2 is not None:
        process_set2 = set(pm2.processes)
    merged_process_set = process_set1.union(process_set2)
    merged_process_mesh = ProcessMesh(list(merged_process_set))
    return merged_process_mesh


def _validate_dims_mapping(dims_mapping, process_mesh):
    if dims_mapping is None:
        return False
    for i in range(len(dims_mapping)):
        if dims_mapping[i] < -1 or dims_mapping[i] >= len(
            process_mesh.topology
        ):
            return False
    for i in range(len(process_mesh.topology)):
        if dims_mapping.count(i) > 1:
            return False
    return True


class Completer:
    def __init__(self, dist_context):
        assert dist_context is not None
        self._dist_context = dist_context
        self._has_prepared = False
        self._logger = get_logger(logging.INFO, "Completer")

    def _update_tensor_node_dims_mapping(self, tensor_node, fwd=True):
        changed = False
        if (not tensor_node.is_var()) or (tensor_node.var() is None):
            return False
        tensor_desc = tensor_node.var()
        # Skip reader tensor
        if tensor_desc.type() in __no_shape_var_type__:
            return False
        tensor_dist_attr = self._dist_context.get_tensor_dist_attr_for_graph(
            tensor_node
        )
        assert tensor_dist_attr is not None
        if tensor_dist_attr.is_annotated("dims_mapping"):
            return False
        tensor_dims_mapping = tensor_dist_attr.dims_mapping
        if fwd:
            dims_mapping_list = []
            for pred_op_node in tensor_node.inputs:
                if pred_op_node.op() is not None:
                    if (
                        pred_op_node.op().type() == "create_py_reader"
                        or pred_op_node.op().type()
                        == "create_double_buffer_reader"
                        or pred_op_node.op().type() == "read"
                    ):
                        continue
                    op_dist_attr = (
                        self._dist_context.get_op_dist_attr_for_graph(
                            pred_op_node
                        )
                    )
                    if (
                        op_dist_attr.process_mesh
                        == tensor_dist_attr.process_mesh
                    ):
                        op_dims_mapping = op_dist_attr.get_output_dims_mapping(
                            tensor_desc.name()
                        )
                        dims_mapping_list.append(op_dims_mapping)
            dims_mapping_list.append(tensor_dims_mapping)
            compatible_dims_mapping = compute_compatible_dims_mapping(
                dims_mapping_list
            )
            if not _validate_dims_mapping(
                compatible_dims_mapping, tensor_dist_attr.process_mesh
            ):
                return False
            if (compatible_dims_mapping is not None) and (
                compatible_dims_mapping != tensor_dims_mapping
            ):
                tensor_dist_attr.dims_mapping = compatible_dims_mapping
                changed = True
        else:
            dims_mapping_list = []
            for succ_op_node in tensor_node.outputs:
                if succ_op_node.op() is not None:
                    if (
                        succ_op_node.op().type() == "create_py_reader"
                        or succ_op_node.op().type()
                        == "create_double_buffer_reader"
                        or succ_op_node.op().type() == "read"
                    ):
                        continue
                    op_dist_attr = (
                        self._dist_context.get_op_dist_attr_for_graph(
                            succ_op_node
                        )
                    )
                    if (
                        op_dist_attr.process_mesh
                        == tensor_dist_attr.process_mesh
                    ):
                        op_dims_mapping = op_dist_attr.get_input_dims_mapping(
                            tensor_desc.name()
                        )
                        dims_mapping_list.append(op_dims_mapping)
            dims_mapping_list.append(tensor_dims_mapping)
            compatible_dims_mapping = compute_compatible_dims_mapping(
                dims_mapping_list
            )
            if not _validate_dims_mapping(
                compatible_dims_mapping, tensor_dist_attr.process_mesh
            ):
                return False
            if (compatible_dims_mapping is not None) and (
                compatible_dims_mapping != tensor_dims_mapping
            ):
                tensor_dist_attr.dims_mapping = compatible_dims_mapping
                changed = True
        return changed

    def _update_op_node_dims_mapping(self, op_node, fwd=True):
        changed = False
        if (not op_node.is_op()) or (op_node.op() is None):
            return False
        # Skip reader op
        op_desc = op_node.op()
        if (
            op_desc.type() == "create_py_reader"
            or op_desc.type() == "create_double_buffer_reader"
            or op_desc.type() == "while"
            or op_desc.type() == "read"
        ):
            return False
        dist_op = self._dist_context.get_dist_op_for_graph(op_node)
        op_dist_attr = dist_op.dist_attr
        original_op_dist_attr = copy.deepcopy(op_dist_attr)
        if fwd:
            for tensor_node in op_node.inputs:
                if tensor_node.is_var() and tensor_node.var() is not None:
                    if tensor_node.var().type() == core.VarDesc.VarType.READER:
                        continue
                    tensor_desc = tensor_node.var()
                    if op_dist_attr.is_annotated_input_dims_mapping(
                        tensor_desc.name()
                    ):
                        continue
                    tensor_dist_attr = (
                        self._dist_context.get_tensor_dist_attr_for_graph(
                            tensor_node
                        )
                    )
                    if (
                        op_dist_attr.process_mesh
                        == tensor_dist_attr.process_mesh
                    ):
                        tensor_dims_mapping = tensor_dist_attr.dims_mapping
                        op_dims_mapping = op_dist_attr.get_input_dims_mapping(
                            tensor_desc.name()
                        )
                        compatible_dims_mapping = (
                            compute_compatible_dims_mapping(
                                [op_dims_mapping, tensor_dims_mapping]
                            )
                        )
                        if not _validate_dims_mapping(
                            compatible_dims_mapping, op_dist_attr.process_mesh
                        ):
                            continue
                        if (compatible_dims_mapping is not None) and (
                            compatible_dims_mapping != op_dims_mapping
                        ):
                            op_dist_attr.set_input_dims_mapping(
                                tensor_desc.name(), compatible_dims_mapping
                            )
                            changed = True
            # Find the most compatible implemenetations from the distributed operator
            op_dist_impls = find_compatible_distributed_operator_impls(
                dist_op, fwd=True
            )
            if op_dist_impls is not None:
                not_compatible = True
                backup_op_dist_attr = copy.deepcopy(op_dist_attr)
                backup_changed = changed
                for op_dist_impl in op_dist_impls:
                    dim_changed = op_dist_impl.update_dims_mapping(dist_op)
                    if dim_changed:
                        changed = True
                    if (
                        op_dist_impl.is_auto_compatible(dist_op)
                        and dist_op.validate_dist_attr()
                    ):
                        if op_dist_impl.type == "elementwise":
                            op_dist_attr.impl_type = "default"
                        else:
                            op_dist_attr.impl_type = op_dist_impl.type
                        # op_dist_attr.impl_type = op_dist_impl.type
                        op_dist_attr.impl_idx = op_dist_impl.idx
                        not_compatible = False
                        break
                    else:
                        dist_op.dist_attr = backup_op_dist_attr
                        changed = backup_changed
                if not_compatible:
                    dist_op.dist_attr = original_op_dist_attr
                    changed = False
            else:
                dist_op.dist_attr = original_op_dist_attr
                changed = False
        else:
            for tensor_node in op_node.outputs:
                if tensor_node.is_var() and tensor_node.var() is not None:
                    if tensor_node.var().type() == core.VarDesc.VarType.READER:
                        continue
                    tensor_desc = tensor_node.var()
                    if op_dist_attr.is_annotated_output_dims_mapping(
                        tensor_desc.name()
                    ):
                        continue
                    tensor_dist_attr = (
                        self._dist_context.get_tensor_dist_attr_for_graph(
                            tensor_node
                        )
                    )
                    if (
                        op_dist_attr.process_mesh
                        == tensor_dist_attr.process_mesh
                    ):
                        tensor_dims_mapping = tensor_dist_attr.dims_mapping
                        op_dims_mapping = op_dist_attr.get_output_dims_mapping(
                            tensor_desc.name()
                        )
                        compatible_dims_mapping = (
                            compute_compatible_dims_mapping(
                                [op_dims_mapping, tensor_dims_mapping]
                            )
                        )
                        if not _validate_dims_mapping(
                            compatible_dims_mapping, op_dist_attr.process_mesh
                        ):
                            continue
                        if (compatible_dims_mapping is not None) and (
                            compatible_dims_mapping != op_dims_mapping
                        ):
                            op_dist_attr.set_output_dims_mapping(
                                tensor_desc.name(), compatible_dims_mapping
                            )
                            changed = True
            # Find the most compatible implemenetations from the distributed operator
            op_dist_impls = find_compatible_distributed_operator_impls(
                dist_op, fwd=False
            )
            if op_dist_impls is not None:
                not_compatible = True
                backup_op_dist_attr = copy.deepcopy(op_dist_attr)
                backup_changed = changed
                for op_dist_impl in op_dist_impls:
                    dim_changed = op_dist_impl.update_dims_mapping(dist_op)
                    if dim_changed:
                        changed = True
                    if (
                        op_dist_impl.is_auto_compatible(dist_op)
                        and dist_op.validate_dist_attr()
                    ):
                        if op_dist_impl.type == "elementwise":
                            op_dist_attr.impl_type = "default"
                        else:
                            op_dist_attr.impl_type = op_dist_impl.type
                        # op_dist_attr.impl_type = op_dist_impl.type
                        op_dist_attr.impl_idx = op_dist_impl.idx
                        not_compatible = False
                        break
                    else:
                        dist_op.dist_attr = backup_op_dist_attr
                        changed = backup_changed
                if not_compatible:
                    dist_op.dist_attr = original_op_dist_attr
                    changed = False
            else:
                dist_op.dist_attr = original_op_dist_attr
                changed = False
        return changed

    def _update_dims_mapping_between_graphs(self):
        changed = False
        for parent_node, child_node in self._node_pairs_between_graphs:
            parent_node_dist_attr = self._dist_context.get_dist_attr_for_graph(
                parent_node
            )
            child_node_dist_attr = self._dist_context.get_dist_attr_for_graph(
                child_node
            )
            if (
                parent_node_dist_attr.process_mesh
                != child_node_dist_attr.process_mesh
            ):
                continue
            parent_node_dims_mapping = parent_node_dist_attr.dims_mapping
            child_node_dims_mapping = child_node_dist_attr.dims_mapping
            compatible_dims_mapping = compute_compatible_dims_mapping(
                [parent_node_dims_mapping, child_node_dims_mapping]
            )
            if not _validate_dims_mapping(
                compatible_dims_mapping, parent_node_dist_attr.process_mesh
            ):
                return False
            if (compatible_dims_mapping is not None) and (
                compatible_dims_mapping != parent_node_dims_mapping
            ):
                parent_node_dist_attr.dims_mapping = compatible_dims_mapping
                changed = True
            if (compatible_dims_mapping is not None) and (
                compatible_dims_mapping != child_node_dims_mapping
            ):
                child_node_dist_attr.dims_mapping = compatible_dims_mapping
                changed = True
        return changed

    def _update_dims_mapping_for_special(self):
        # Set the dims_mapping of a tensor to the dims_mapping inside the op which produces it
        op_nodes = self._dist_context._serial_ordered_op_nodes
        # NOTE: this list may be changed if Paddle changes the existing rules.
        related_reader_ops = [
            "create_py_reader",
            "create_double_buffer_reader",
            "read",
        ]
        for op_node in op_nodes:
            if (
                op_node.op() is not None
                and op_node.op().type() in related_reader_ops
            ):
                continue
            op_dist_attr = self._dist_context.get_dist_attr_for_graph(op_node)
            for tensor_node in op_node.outputs:
                if tensor_node.is_var() and tensor_node.var() is not None:
                    if tensor_node.var().type() == core.VarDesc.VarType.READER:
                        continue
                    tensor_desc = tensor_node.var()
                    tensor_dist_attr = (
                        self._dist_context.get_tensor_dist_attr_for_graph(
                            tensor_node
                        )
                    )
                    if (
                        op_dist_attr.process_mesh
                        == tensor_dist_attr.process_mesh
                    ):
                        op_dims_mapping = op_dist_attr.get_output_dims_mapping(
                            tensor_desc.name()
                        )
                        tensor_dist_attr.dims_mapping = op_dims_mapping

    def _update_dims_mapping(self):
        # Complete dims_mapping for each node
        reach_fix_point = False
        while not reach_fix_point:
            changed = False
            for is_fwd in [True, False]:
                all_nodes = (
                    self._dist_context.serial_ordered_nodes
                    if is_fwd
                    else reversed(self._dist_context.serial_ordered_nodes)
                )
                for node in all_nodes:
                    if node.is_var() and node.var() is not None:
                        tensor_changed = self._update_tensor_node_dims_mapping(
                            node, fwd=is_fwd
                        )
                        if tensor_changed:
                            changed = True
                    if node.is_op() and node.op() is not None:
                        op_changed = self._update_op_node_dims_mapping(
                            node, fwd=is_fwd
                        )
                        if op_changed:
                            changed = True
                graph_changed = self._update_dims_mapping_between_graphs()
                if graph_changed:
                    changed = True
            if changed:
                reach_fix_point = False
            else:
                reach_fix_point = True
        # NOTE: this will be removed after changing the reshard rule
        self._update_dims_mapping_for_special()

    def _update_process_mesh_by_nearest(self, op_node, nearest_op_node):
        op_dist_attr = self._dist_context.get_dist_attr_for_graph(op_node)
        # Set the process mesh of the op node by its nearest op node
        if not op_dist_attr.is_annotated("process_mesh"):
            process_mesh = op_dist_attr.process_mesh
            nearest_op_dis_attr = self._dist_context.get_dist_attr_for_graph(
                nearest_op_node
            )
            nearest_process_mesh = nearest_op_dis_attr.process_mesh
            compatible_process_mesh = compute_compatible_process_mesh(
                [process_mesh, nearest_process_mesh]
            )
            if (
                compatible_process_mesh is not None
                and process_mesh != compatible_process_mesh
            ):
                op_dist_attr.process_mesh = compatible_process_mesh
        # Skip the process_mesh setting of inputs and outputs of while_op
        if op_dist_attr.op_type == "while":
            return
        # Set the process mesh of the op node's leaf-inputs
        for tensor_node in op_node.inputs:
            if tensor_node.is_var() and tensor_node.var() is not None:
                tensor_dist_attr = (
                    self._dist_context.get_tensor_dist_attr_for_graph(
                        tensor_node
                    )
                )
                if tensor_dist_attr.is_annotated("process_mesh"):
                    continue
                # Skip the non-leaf var node
                if len(tensor_node.inputs) != 0:
                    continue
                compatible_process_mesh = compute_compatible_process_mesh(
                    [tensor_dist_attr.process_mesh, op_dist_attr.process_mesh]
                )
                if (
                    compatible_process_mesh is not None
                    and tensor_dist_attr.process_mesh != compatible_process_mesh
                ):
                    tensor_dist_attr.process_mesh = compatible_process_mesh
                # Set the process mesh of the op node's outputs
        for tensor_node in op_node.outputs:
            if tensor_node.is_var() and tensor_node.var() is not None:
                tensor_dist_attr = (
                    self._dist_context.get_tensor_dist_attr_for_graph(
                        tensor_node
                    )
                )
                if tensor_dist_attr.is_annotated("process_mesh"):
                    continue
                compatible_process_mesh = compute_compatible_process_mesh(
                    [tensor_dist_attr.process_mesh, op_dist_attr.process_mesh]
                )
                if (
                    compatible_process_mesh is not None
                    and tensor_dist_attr.process_mesh != compatible_process_mesh
                ):
                    tensor_dist_attr.process_mesh = compatible_process_mesh

    def _update_process_mesh_for_specials(self):
        def _find_nearest_tensor_node_before(nodes, idx, var_name):
            for node in reversed(nodes[:idx]):
                if (
                    node.is_var()
                    and node.var() is not None
                    and node.var().name() == var_name
                ):
                    return node

        def _find_nearest_tensor_node_after(nodes, idx, var_name):
            for node in nodes[idx + 1 :]:
                if (
                    node.is_var()
                    and node.var() is not None
                    and node.var().name() == var_name
                ):
                    return node

        def _find_nodes_related_to_cond(source_node):
            related_nodes = []
            visited = set()
            frontier = list()
            frontier.append(source_node)
            # BFS
            while len(frontier) != 0:
                cur = frontier[0]
                frontier = frontier[1:]
                if _node_id(cur) in visited:
                    continue
                # TODO: need more restrictions
                neighbors = cur.inputs + cur.outputs
                for node in neighbors:
                    if node.is_var() and node.var() is not None:
                        if (
                            node.var().type() != core.VarDesc.VarType.READER
                            and len(node.var().shape()) == 1
                        ):
                            frontier.append(node)
                            related_nodes.append(node)
                    if node.is_op() and node.op() is not None:
                        flag = True
                        if (
                            node.op().type() == "create_py_reader"
                            or node.op().type() == "create_double_buffer_reader"
                            or node.op().type() == "read"
                        ):
                            flag = False
                        for tensor_node in node.inputs:
                            if (
                                tensor_node.is_var()
                                and tensor_node.var() is not None
                            ):
                                if (
                                    tensor_node.var().type()
                                    in __no_shape_var_type__
                                    or len(tensor_node.var().shape()) != 1
                                ):
                                    flag = False
                                    break
                        for tensor_node in node.outputs:
                            if (
                                tensor_node.is_var()
                                and tensor_node.var() is not None
                            ):
                                if (
                                    tensor_node.var().type()
                                    in __no_shape_var_type__
                                    or len(tensor_node.var().shape()) != 1
                                ):
                                    flag = False
                                    break
                        if flag:
                            frontier.append(node)
                            related_nodes.append(node)
                visited.add(_node_id(cur))
            return related_nodes

        def _make_dims_mapping_replicate(dist_attr):
            if isinstance(dist_attr, TensorDistributedAttribute):
                for i, _ in enumerate(dist_attr.dims_mapping):
                    dist_attr.dims_mapping[i] = -1
            if isinstance(dist_attr, OperatorDistributedAttribute):
                for arg_name in dist_attr.inputs_dist_attrs.keys():
                    new_dims_mapping = []
                    dims_mapping = dist_attr.get_input_dims_mapping(arg_name)
                    for _ in dims_mapping:
                        new_dims_mapping.append(-1)
                    dist_attr.set_input_dims_mapping(arg_name, new_dims_mapping)
                for arg_name in dist_attr.outputs_dist_attrs.keys():
                    new_dims_mapping = []
                    dims_mapping = dist_attr.get_output_dims_mapping(arg_name)
                    for _ in dims_mapping:
                        new_dims_mapping.append(-1)
                    dist_attr.set_output_dims_mapping(
                        arg_name, new_dims_mapping
                    )

        # Amend the process meshes related to while_op
        for while_op_node, while_op_node_idx in self._while_op_nodes.values():
            sub_graph_id = while_op_node.op()._block_attr_id("sub_block")
            sub_graph = self._dist_context.serial_graph.get_sub_graph(
                sub_graph_id
            )
            sub_graph_nodes = list(sub_graph.all_nodes())
            while_dist_op = self._dist_context.get_dist_op_for_graph(
                while_op_node
            )
            while_op_dist_attr = while_dist_op.dist_attr

            # Step 1: set the process mesh of while_op to the merged process mesh of its subblock
            merged_process_mesh = while_op_dist_attr.process_mesh
            for node in sub_graph_nodes:
                if (node.is_var() and node.var() is not None) or (
                    node.is_op() and node.op() is not None
                ):
                    dist_attr = self._dist_context.get_dist_attr_for_graph(node)
                    merged_process_mesh = merge_process_mesh_two(
                        merged_process_mesh, dist_attr.process_mesh
                    )
            while_op_dist_attr.process_mesh = merged_process_mesh
            _make_dims_mapping_replicate(while_op_dist_attr)

            # Step 2: set the related nodes of while_op to the process mesh of while_op
            # Step 2.1: Find related nodes of cond var the graph of while_op
            cond_tensor_related_nodes = []
            cond_tensor_name = while_op_node.op().input("Condition")[0]
            cond_tensor_node = None
            for node in while_op_node.inputs:
                if (
                    node.is_var()
                    and node.var() is not None
                    and node.var().name() == cond_tensor_name
                ):
                    cond_tensor_node = node
                    cond_tensor_related_nodes.append(cond_tensor_node)
                    break

            cond_tensor_related_nodes.extend(
                _find_nodes_related_to_cond(cond_tensor_node)
            )

            # Step 2.2: Find related nodes of cond var in the subgraph of while_op
            cond_tensor_node = None
            for node in reversed(sub_graph_nodes):
                if (
                    node.is_var()
                    and node.var() is not None
                    and node.var().name() == cond_tensor_name
                    and len(node.outputs) == 0
                ):
                    cond_tensor_node = node
                    break

            cond_tensor_related_nodes.extend(
                _find_nodes_related_to_cond(cond_tensor_node)
            )
            # Step 2.3: Add the StepScops output of while_op
            stepscopes_tensor_name = while_op_node.op().output("StepScopes")[0]
            stepscopes_tensor_node = None
            for output_node in while_op_node.outputs:
                if (
                    output_node.is_var()
                    and output_node.var() is not None
                    and output_node.var().name() == stepscopes_tensor_name
                ):
                    stepscopes_tensor_node = output_node
            cond_tensor_related_nodes.append(stepscopes_tensor_node)
            # Step 2.4: Set the process meshes of all nodes related to cond var to the process mesh of while op
            for node in cond_tensor_related_nodes:
                tensor_dist_attr = self._dist_context.get_dist_attr_for_graph(
                    node
                )
                tensor_dist_attr.process_mesh = merged_process_mesh
                _make_dims_mapping_replicate(tensor_dist_attr)

            # Step 3: set the process meshes of the inputs in while_op to the process meshes of the outside input nodes
            while_op_inputs_dist_attrs = while_op_dist_attr.inputs_dist_attrs
            for (
                tensor_name,
                tensor_dist_attr,
            ) in while_op_inputs_dist_attrs.items():
                nearest_tensor_node = _find_nearest_tensor_node_before(
                    self._dist_context.serial_ordered_nodes,
                    while_op_node_idx,
                    tensor_name,
                )
                nearest_tensor_dist_attr = (
                    self._dist_context.get_dist_attr_for_graph(
                        nearest_tensor_node
                    )
                )
                tensor_dist_attr.process_mesh = (
                    nearest_tensor_dist_attr.process_mesh
                )

            # Step 4: set the process meshes of the outputs in while_op to the process meshes of the outside output nodes
            while_op_outputs_dist_attrs = while_op_dist_attr.outputs_dist_attrs
            for (
                tensor_name,
                tensor_dist_attr,
            ) in while_op_outputs_dist_attrs.items():
                nearest_tensor_node = _find_nearest_tensor_node_before(
                    self._dist_context.serial_ordered_nodes,
                    while_op_node_idx,
                    tensor_name,
                )
                if nearest_tensor_node is None:
                    nearest_tensor_node = _find_nearest_tensor_node_after(
                        self._dist_context.serial_ordered_nodes,
                        while_op_node_idx,
                        tensor_name,
                    )
                nearest_tensor_dist_attr = (
                    self._dist_context.get_dist_attr_for_graph(
                        nearest_tensor_node
                    )
                )
                tensor_dist_attr.process_mesh = (
                    nearest_tensor_dist_attr.process_mesh
                )

        # Amend the process meshes related to array
        for array_node_list in self._array_nodes.values():
            merged_process_mesh = None
            for array_node in array_node_list:
                dist_attr = self._dist_context.get_dist_attr_for_graph(
                    array_node
                )
                merged_process_mesh = merge_process_mesh_two(
                    merged_process_mesh, dist_attr.process_mesh
                )
            for array_node in array_node_list:
                dist_attr = self._dist_context.get_dist_attr_for_graph(
                    array_node
                )
                dist_attr.process_mesh = merged_process_mesh
                _make_dims_mapping_replicate(dist_attr)

    def _update_process_mesh_between_graphs(self):
        for parent_node, child_node in self._node_pairs_between_graphs:
            parent_node_dist_attr = self._dist_context.get_dist_attr_for_graph(
                parent_node
            )
            child_node_dist_attr = self._dist_context.get_dist_attr_for_graph(
                child_node
            )
            parent_node_dist_attr.process_mesh = (
                child_node_dist_attr.process_mesh
            )
            compatible_process_mesh = compute_compatible_process_mesh(
                [
                    parent_node_dist_attr.process_mesh,
                    child_node_dist_attr.process_mesh,
                ]
            )
            if (
                compatible_process_mesh is not None
                and parent_node_dist_attr.process_mesh
                != compatible_process_mesh
            ):
                parent_node_dist_attr.process_mesh = compatible_process_mesh
            if (
                compatible_process_mesh is not None
                and child_node_dist_attr.process_mesh != compatible_process_mesh
            ):
                child_node_dist_attr.process_mesh = compatible_process_mesh

    def _update_process_mesh(self):
        ordered_op_nodes = self._dist_context._serial_ordered_op_nodes

        # Step 1: Set the annotated process meshes from tensors to the first ops using them
        ordered_tensor_nodes = self._dist_context._serial_ordered_tensor_nodes
        for tensor_node in ordered_tensor_nodes:
            tensor_dist_attr = (
                self._dist_context.get_tensor_dist_attr_for_graph(tensor_node)
            )
            if not tensor_dist_attr.is_annotated("process_mesh"):
                continue
            first_op_node = None
            for op_node in ordered_op_nodes:
                # TODO: Need a better rule for the control flow ops.
                # For now, do not set the process mesh of while_op from its inputs
                if op_node.op().type() == "while":
                    continue
                for input_tensor_node in op_node.inputs:
                    if _node_id(tensor_node) == _node_id(input_tensor_node):
                        first_op_node = op_node
                        break
                if first_op_node is not None:
                    break
            if first_op_node is None:
                continue
            op_dist_attr = self._dist_context.get_dist_attr_for_graph(
                first_op_node
            )
            if op_dist_attr is not None and not op_dist_attr.is_annotated(
                "process_mesh"
            ):
                compatible_process_mesh = compute_compatible_process_mesh(
                    [tensor_dist_attr.process_mesh, op_dist_attr.process_mesh]
                )
                if (
                    compatible_process_mesh is not None
                    and op_dist_attr.process_mesh != compatible_process_mesh
                ):
                    op_dist_attr.process_mesh = compatible_process_mesh

        # Step 2: set the process meshes of ops with the nearest op before them
        # Step 2.1: find the first op node which has the process mesh
        idx_of_first_op_node_has_process_mesh = -1
        for idx, op_node in enumerate(ordered_op_nodes):
            op_dist_attr = self._dist_context.get_dist_attr_for_graph(op_node)
            if (
                op_dist_attr.process_mesh is not None
                and idx_of_first_op_node_has_process_mesh == -1
            ):
                idx_of_first_op_node_has_process_mesh = idx
                # Reuse the following method to set the related tensors for same op node
                self._update_process_mesh_by_nearest(op_node, op_node)
        # Step 2.2: set the process meshes of ops by the nearest op node after the first op node
        if idx_of_first_op_node_has_process_mesh + 1 > len(ordered_op_nodes):
            return None
        for idx, op_node in enumerate(
            ordered_op_nodes[idx_of_first_op_node_has_process_mesh + 1 :]
        ):
            original_idx = idx_of_first_op_node_has_process_mesh + idx + 1
            nearest_op_node = ordered_op_nodes[original_idx - 1]
            nearest_op_dist_attr = self._dist_context.get_dist_attr_for_graph(
                nearest_op_node
            )
            op_dist_attr = self._dist_context.get_dist_attr_for_graph(op_node)
            assert nearest_op_dist_attr.process_mesh is not None
            self._update_process_mesh_by_nearest(op_node, nearest_op_node)
        # Step 2.3: set the process meshes of ops by the nearest op node before the first op node
        nearest_op_node = ordered_op_nodes[
            idx_of_first_op_node_has_process_mesh
        ]
        for op_node in ordered_op_nodes[:idx_of_first_op_node_has_process_mesh]:
            self._update_process_mesh_by_nearest(op_node, nearest_op_node)

        # Step 3: adjust the process meshes for special ops
        self._update_process_mesh_for_specials()

        # Step 4: adjust the process meshes between graphs
        self._update_process_mesh_between_graphs()

    def _prepare(self):
        if self._has_prepared:
            return
        self._while_op_nodes = {}
        self._array_nodes = {}
        self._node_pairs_between_graphs = []
        all_nodes = self._dist_context.serial_ordered_nodes
        for idx, node in enumerate(all_nodes):
            if node.is_op():
                if node.op().type() == "while":
                    self._while_op_nodes[_node_id(node)] = (node, idx)
                if node.op().type() == "read_from_array":
                    array_var_name = node.op().input("X")[0]
                    if self._array_nodes.get(array_var_name, None) is None:
                        self._array_nodes[array_var_name] = []
                    self._array_nodes[array_var_name].append(node)
                    # Add the array input node
                    self._array_nodes[array_var_name].append(node.inputs[0])
                if node.op().type() == "write_to_array":
                    array_var_name = node.op().output("Out")[0]
                    if self._array_nodes.get(array_var_name, None) is None:
                        self._array_nodes[array_var_name] = []
                    self._array_nodes[array_var_name].append(node)
                    self._array_nodes[array_var_name].append(node.outputs[0])
            if node.is_var() and node.var() is not None:
                if node.node.graph_id() != 0:
                    for before_node in reversed(all_nodes[:idx]):
                        if (
                            before_node.is_var()
                            and before_node.var() is not None
                            and before_node.node.graph_id()
                            == node.node.graph_id() - 1
                            and before_node.var().name() == node.var().name()
                        ):
                            self._node_pairs_between_graphs.append(
                                (before_node, node)
                            )
                    for after_node in all_nodes[idx + 1 :]:
                        if (
                            after_node.is_var()
                            and after_node.var() is not None
                            and after_node.node.graph_id()
                            == node.node.graph_id() - 1
                            and after_node.var().name() == node.var().name()
                        ):
                            self._node_pairs_between_graphs.append(
                                (after_node, node)
                            )
        self._has_prepared = True

    def complete_forward_annotation(self, serial_main_program=None):
        """Complete annotation for the partial annotated serial_main_program.
        Arguments:
            serial_main_program: partial annotated serial_main_program.
        Returns:e
            serial_main_program: completed annotated serial_main_program.
        """

        if serial_main_program is None:
            serial_main_program = self._dist_context.serial_main_program
        else:
            self._dist_context._serial_main_program = serial_main_program

        if not is_naive_data_parallel(self._dist_context):
            self._dist_context.initialize(with_graph=True)
            self._prepare()
            self._update_process_mesh()
            self._update_dims_mapping()
            # Copy the corresponding distributed attribute from graph to serial_main_program
            self._dist_context.copy_dist_attr_from_graph_to_program()
        else:
            self._logger.info("Default data parallel will be set.")
            self._dist_context.initialize(with_graph=False)
            # A fast and special completion for data parallel
            self._update_dist_attr_for_dp()

        # NOTE:[HighOrderGrad] update vars and ops distributed attribute in high order gradient
        self._complete_high_order_grad_annotation(serial_main_program)
        # Do the validation check and amend some completion
        self._dist_context.amend_dist_attr_for_program()
        self._dist_context.validate_dist_attr_for_program()
        return serial_main_program

    def _update_dist_attr_for_dp(self):
        # TODO: we must ensure the world process group contains all ranks
        ranks = get_world_process_group().ranks
        process_mesh = ProcessMesh(ranks)

        dist_tensors = self._dist_context._dist_tensors_for_program
        for dist_tensor in dist_tensors.values():
            dist_tensor.dist_attr.process_mesh = process_mesh

        dist_ops = self._dist_context._dist_ops_for_program
        for dist_op in dist_ops.values():
            serial_op = dist_op.serial_op
            op_dist_attr = dist_op.dist_attr
            op_dist_attr.process_mesh = process_mesh
            original_op_dist_attr = copy.deepcopy(op_dist_attr)

            for arg_name in serial_op.input_arg_names:
                serial_tensor = dist_op.get_serial_input(arg_name)
                if not serial_tensor.is_parameter:
                    dist_tensor = (
                        self._dist_context.get_dist_tensor_for_program(
                            serial_tensor
                        )
                    )
                    op_dist_attr = dist_op.dist_attr
                    op_dist_attr.process_mesh = (
                        dist_tensor.dist_attr.process_mesh
                    )
                    op_dist_attr.set_input_dims_mapping(
                        arg_name, dist_tensor.dist_attr.dims_mapping
                    )

            op_dist_impls = find_compatible_distributed_operator_impls(
                dist_op, fwd=True
            )
            if op_dist_impls is not None:
                not_compatible = True
                backup_op_dist_attr = copy.deepcopy(op_dist_attr)
                for op_dist_impl in op_dist_impls:
                    op_dist_impl.update_dims_mapping(dist_op)
                    if (
                        op_dist_impl.is_auto_compatible(dist_op)
                        and dist_op.validate_dist_attr()
                    ):
                        op_dist_attr.impl_type = op_dist_impl.type
                        op_dist_attr.impl_idx = op_dist_impl.idx
                        not_compatible = False
                        break
                    else:
                        dist_op.dist_attr = backup_op_dist_attr
                if not_compatible:
                    dist_op.dist_attr = original_op_dist_attr
            else:
                dist_op.dist_attr = original_op_dist_attr

            for arg_name in serial_op.output_arg_names:
                op_dist_attr = dist_op.dist_attr
                serial_tensor = dist_op.get_serial_output(arg_name)
                dist_tensor = self._dist_context.get_dist_tensor_for_program(
                    serial_tensor
                )
                dist_tensor.dist_attr.dims_mapping = (
                    op_dist_attr.get_output_dims_mapping(arg_name)
                )

    def _complete_tensor_dist_attr_by_op(self, serial_main_program=None):
        if serial_main_program is None:
            serial_main_program = self._dist_context.serial_main_program
        else:
            self._dist_context._serial_main_program = serial_main_program

        self._dist_context.initialize()

        self._prepare()

        has_set_dist_attr = set()

        all_nodes = self._dist_context.serial_ordered_nodes
        for node in all_nodes:
            if node.is_op():
                if node.op().type() in ["while"]:
                    continue
                dist_op = self._dist_context.get_dist_op_for_graph(node)
                op_dist_attr = dist_op.dist_attr
                for tensor_node in node.inputs:
                    if tensor_node.is_var() and tensor_node.var() is not None:
                        # Skip the non-leaf var node
                        if len(tensor_node.inputs) != 0:
                            continue
                        tensor_desc = tensor_node.var()
                        tensor_name = tensor_desc.name()
                        tensor = dist_op.get_serial_input(tensor_name)
                        # Use the first op to set the tensor dist attr
                        if tensor_name in has_set_dist_attr:
                            continue
                        tensor_dist_attr = (
                            self._dist_context.get_tensor_dist_attr_for_graph(
                                tensor_node
                            )
                        )
                        tensor_dist_attr.process_mesh = (
                            op_dist_attr.process_mesh
                        )
                        tensor_dist_attr.dims_mapping = (
                            op_dist_attr.get_input_dims_mapping(tensor_name)
                            if tensor.is_parameter
                            else [-1 for i in tensor_desc.shape()]
                        )
                        has_set_dist_attr.add(tensor_name)
                for tensor_node in node.outputs:
                    if tensor_node.is_var() and tensor_node.var() is not None:
                        tensor_name = tensor_node.var().name()
                        if tensor_name in has_set_dist_attr:
                            continue
                        tensor_dist_attr = (
                            self._dist_context.get_tensor_dist_attr_for_graph(
                                tensor_node
                            )
                        )
                        tensor_dist_attr.process_mesh = (
                            op_dist_attr.process_mesh
                        )
                        tensor_dist_attr.dims_mapping = (
                            op_dist_attr.get_output_dims_mapping(tensor_name)
                        )
                        has_set_dist_attr.add(tensor_name)

        self._update_process_mesh_for_specials()

        self._update_process_mesh_between_graphs()

        self._update_dims_mapping_for_special()

        self._update_dims_mapping_between_graphs()

        # Copy the corresponding distributed attribute from graph to serial_main_program
        self._dist_context.copy_dist_attr_from_graph_to_program()

        # Do the validation check and amend some completion
        self._dist_context.amend_dist_attr_for_program()

        self._dist_context.validate_dist_attr_for_program()

    def _complete_high_order_grad_annotation(self, serial_main_program=None):
        """
        NOTE:
            [HighOrderGrad] Complete the annotation of vars and ops only for high order gradient.
            This function is temporary to support high order gradient, and will be removed in the future.
        """

        if serial_main_program is None:
            serial_main_program = self._dist_context.serial_main_program
        else:
            self._dist_context._serial_main_program = serial_main_program

        def _is_grad_var_name(name):
            if "@GRAD" in name:
                return True
            return False

        def _get_op_by_id(ops, id):
            for op in ops:
                if op.desc.original_id() == id:
                    return op
            return None

        ops = list(serial_main_program.global_block().ops)
        vars = serial_main_program.global_block().vars
        dist_op_context = self._dist_context.dist_op_context
        grad_var_to_var = dist_op_context.grad_var_to_var

        appended_grad_times = 0
        for idx in range(0, len(ops)):
            op = ops[idx]
            if int(op.attr('op_role')) == int(
                core.op_proto_and_checker_maker.OpRole.Forward
            ):
                continue

            if int(op.attr('op_role')) == int(
                core.op_proto_and_checker_maker.OpRole.Backward
            ) and int(ops[idx - 1].attr('op_role')) == int(
                core.op_proto_and_checker_maker.OpRole.Forward
            ):
                appended_grad_times += 1

            if int(op.attr('op_role')) == int(
                int(core.op_proto_and_checker_maker.OpRole.Backward)
                | int(core.op_proto_and_checker_maker.OpRole.Loss)
            ):
                assert op.type == "fill_constant"
                break

            # complete the annotation of grad op (xxx_grad op or sum op)
            # xxx_grad op will have a corresponding forward op in grad_op_id_to_op_id
            grad_op = ops[idx]
            if (
                grad_op.desc.original_id()
                in dist_op_context.grad_op_id_to_op_id
            ):
                # TODO support the case where one forward op corresponding to multiple xxx_grad op
                forward_op = _get_op_by_id(
                    ops,
                    dist_op_context.grad_op_id_to_op_id[
                        grad_op.desc.original_id()
                    ],
                )
                assert forward_op is not None

                fwd_op_dist_attr = (
                    self._dist_context.get_op_dist_attr_for_program(forward_op)
                )
                fwd_op_process_mesh = fwd_op_dist_attr.process_mesh
                grad_op_dist_attr = OperatorDistributedAttribute()
                grad_op_dist_attr.process_mesh = fwd_op_process_mesh

                for input_name in grad_op.input_arg_names:
                    if (
                        input_name not in forward_op.input_arg_names
                        and input_name not in forward_op.output_arg_names
                    ):
                        if input_name in grad_var_to_var[appended_grad_times]:
                            fwd_name = grad_var_to_var[appended_grad_times][
                                input_name
                            ]
                            ref_dims_mapping = (
                                fwd_op_dist_attr.get_output_dims_mapping(
                                    fwd_name
                                )
                            )
                        else:
                            input_var = vars[input_name]
                            ref_dims_mapping = self._dist_context.get_tensor_dist_attr_for_program(
                                input_var
                            ).dims_mapping
                    else:
                        if fwd_op_dist_attr.get_input_dims_mapping(input_name):
                            ref_dims_mapping = (
                                fwd_op_dist_attr.get_input_dims_mapping(
                                    input_name
                                )
                            )
                        else:
                            ref_dims_mapping = (
                                fwd_op_dist_attr.get_output_dims_mapping(
                                    input_name
                                )
                            )
                    assert (
                        ref_dims_mapping is not None
                    ), "[{}] 's dims mapping is NONE".format(input_name)
                    grad_op_dist_attr.set_input_dims_mapping(
                        input_name, ref_dims_mapping
                    )

                for output_name in grad_op.output_arg_names:
                    assert output_name in grad_var_to_var[appended_grad_times]
                    fwd_name = grad_var_to_var[appended_grad_times][output_name]
                    ref_dims_mapping = fwd_op_dist_attr.get_input_dims_mapping(
                        fwd_name
                    )
                    # var
                    output_var = vars[output_name]
                    tensor_dist_attr = TensorDistributedAttribute()
                    tensor_dist_attr.dims_mapping = ref_dims_mapping
                    tensor_dist_attr.process_mesh = fwd_op_process_mesh
                    self._dist_context.set_tensor_dist_attr_for_program(
                        output_var, tensor_dist_attr
                    )
                    # op
                    grad_op_dist_attr.set_output_dims_mapping(
                        output_name, ref_dims_mapping
                    )

                self._dist_context.set_op_dist_attr_for_program(
                    grad_op, grad_op_dist_attr
                )

            # grad ops that have not a corresponding mapping in grad_op_id_to_op_id
            else:

                if grad_op.type == 'sum':
                    assert all(map(_is_grad_var_name, grad_op.input_arg_names))
                    output_name = grad_op.output_arg_names[0]
                    assert (
                        output_name in grad_var_to_var[appended_grad_times]
                    ), "sum op's output '{}' has no corresponding var".format(
                        output_name
                    )
                    ref_fwd_var_name = grad_var_to_var[appended_grad_times][
                        output_name
                    ]
                    ref_fwd_var = vars[ref_fwd_var_name]
                    ref_fwd_dist_attr = (
                        self._dist_context.get_tensor_dist_attr_for_program(
                            ref_fwd_var
                        )
                    )
                    ref_fwd_dims_mapping = ref_fwd_dist_attr.dims_mapping
                    ref_fwd_process_mesh = ref_fwd_dist_attr.process_mesh
                    # output
                    tensor_dist_attr = TensorDistributedAttribute()
                    tensor_dist_attr.dims_mapping = ref_fwd_dims_mapping
                    tensor_dist_attr.process_mesh = ref_fwd_process_mesh
                    output_var = vars[output_name]
                    self._dist_context.set_tensor_dist_attr_for_program(
                        output_var, tensor_dist_attr
                    )
                    # op
                    grad_op_dist_attr = OperatorDistributedAttribute()
                    grad_op_dist_attr.process_mesh = ref_fwd_process_mesh
                    for var_name in grad_op.input_arg_names:
                        grad_op_dist_attr.set_input_dims_mapping(
                            var_name, ref_fwd_dims_mapping
                        )
                    grad_op_dist_attr.set_output_dims_mapping(
                        output_name, ref_fwd_dims_mapping
                    )

                elif grad_op.type == 'fill_any_like':
                    ref_var_name = grad_op.input_arg_names[0]
                    ref_var = vars[ref_var_name]
                    ref_dist_attr = (
                        self._dist_context.get_tensor_dist_attr_for_program(
                            ref_var
                        )
                    )
                    ref_dims_mapping = ref_dist_attr.dims_mapping
                    ref_process_mesh = ref_dist_attr.process_mesh
                    # output
                    tensor_dist_attr = TensorDistributedAttribute()
                    tensor_dist_attr.dims_mapping = ref_dims_mapping
                    tensor_dist_attr.process_mesh = ref_process_mesh
                    output_var_name = grad_op.output_arg_names[0]
                    output_var = vars[output_var_name]
                    self._dist_context.set_tensor_dist_attr_for_program(
                        output_var, tensor_dist_attr
                    )
                    # op
                    grad_op_dist_attr = OperatorDistributedAttribute()
                    grad_op_dist_attr.process_mesh = ref_process_mesh
                    grad_op_dist_attr.set_input_dims_mapping(
                        ref_var_name, ref_dims_mapping
                    )
                    grad_op_dist_attr.set_output_dims_mapping(
                        output_var_name, ref_dims_mapping
                    )

                elif grad_op.type in ['shape', 'fill_constant']:
                    continue

                else:
                    raise ValueError(
                        "got unexpect op [{}]".format(str(grad_op.type))
                    )

                self._dist_context.set_op_dist_attr_for_program(
                    grad_op, grad_op_dist_attr
                )

    def complete_backward_annotation(self, serial_main_program=None):
        """Complete the annotation of vars and ops in the backward phase for parallel program."""

        if serial_main_program is None:
            serial_main_program = self._dist_context.serial_main_program
        else:
            self._dist_context._serial_main_program = serial_main_program

        def _is_grad_var_name(name):
            if "@GRAD" in name:
                return True
            return False

        def _get_forward_varname_from_grad_varname(grad_var_name):
            assert _is_grad_var_name(
                grad_var_name
            ), "[{}] is not a grad varnme.".format(grad_var_name)
            return grad_var_name[: grad_var_name.find("@GRAD")]

        def _get_op_by_id(ops, id):
            for op in ops:
                if op.desc.original_id() == id:
                    return op
            return None

        first_backward_op_idx = -1
        for idx, op in enumerate(serial_main_program.global_block().ops):
            if int(op.attr('op_role')) == int(
                int(core.op_proto_and_checker_maker.OpRole.Backward)
                | int(core.op_proto_and_checker_maker.OpRole.Loss)
            ):
                assert op.type == "fill_constant"
                first_backward_op_idx = idx
                break

        assert (
            first_backward_op_idx >= 0
        ), "No backward procedure found in this program."

        ops = list(serial_main_program.global_block().ops)
        vars = serial_main_program.global_block().vars
        dist_op_context = self._dist_context.dist_op_context
        grad_var_to_var = dist_op_context.grad_var_to_var[
            len(dist_op_context.grad_var_to_var)
        ]

        for idx in range(first_backward_op_idx, len(ops)):

            # complete the initial grad loss op
            if idx == first_backward_op_idx:
                assert ops[idx].type == "fill_constant"
                assert (
                    len(ops[idx].input_arg_names) == 0
                ), "first backward op should has only ONE output, but got [{}]".format(
                    len(ops[idx].input_arg_names)
                )
                assert (
                    len(ops[idx].output_arg_names) == 1
                ), "first backward op should has only ONE output, but got [{}]".format(
                    len(ops[idx].output_arg_names)
                )

                grad_var = vars[ops[idx].output_arg_names[0]]
                forward_var_name = _get_forward_varname_from_grad_varname(
                    grad_var.name
                )
                forward_var = vars[forward_var_name]

                # TODO complete other attribte for grad var
                tensor_dist_attr = TensorDistributedAttribute()
                process_mesh = (
                    self._dist_context.get_tensor_dist_attr_for_program(
                        forward_var
                    ).process_mesh
                )
                dims_mapping = (
                    self._dist_context.get_tensor_dist_attr_for_program(
                        forward_var
                    ).dims_mapping
                )
                tensor_dist_attr.dims_mapping = dims_mapping
                tensor_dist_attr.process_mesh = process_mesh
                self._dist_context.set_tensor_dist_attr_for_program(
                    grad_var, tensor_dist_attr
                )

                op_dist_attr = OperatorDistributedAttribute()
                op_dist_attr.process_mesh = process_mesh
                op_dist_attr.set_output_dims_mapping(
                    grad_var.name, dims_mapping
                )
                self._dist_context.set_op_dist_attr_for_program(
                    ops[idx], op_dist_attr
                )
                continue

            # complete the annotation of grad op (xxx_grad op or sum op)
            # xxx_grad op will have a corresponding forward op in grad_op_id_to_op_id
            grad_op = ops[idx]
            if (
                grad_op.desc.original_id()
                in dist_op_context.grad_op_id_to_op_id
            ):
                # TODO support the case where one forward op corresponding to multiple xxx_grad op
                forward_op = _get_op_by_id(
                    ops[:first_backward_op_idx],
                    dist_op_context.grad_op_id_to_op_id[
                        grad_op.desc.original_id()
                    ],
                )
                assert forward_op is not None

                if grad_op.type == "concat" and forward_op.type == "split":
                    forward_op_dist_attr = (
                        self._dist_context.get_op_dist_attr_for_program(
                            forward_op
                        )
                    )
                    output_var = vars[grad_op.desc.output('Out')[0]]
                    split_input_var_name = forward_op.input("X")[0]
                    ref_dims_mapping = (
                        forward_op_dist_attr.get_input_dims_mapping(
                            split_input_var_name
                        )
                    )
                    ref_mesh = forward_op_dist_attr.process_mesh

                    grad_op_dist_attr = OperatorDistributedAttribute()
                    for input_name in grad_op.input_arg_names:
                        grad_op_dist_attr.set_input_dims_mapping(
                            input_name, ref_dims_mapping
                        )

                    output_var_dist_attr = TensorDistributedAttribute()
                    output_var_dist_attr.dims_mapping = ref_dims_mapping
                    output_var_dist_attr.process_mesh = ref_mesh
                    self._dist_context.set_tensor_dist_attr_for_program(
                        output_var, output_var_dist_attr
                    )

                    grad_op_dist_attr.set_output_dims_mapping(
                        output_var.name, ref_dims_mapping
                    )
                    grad_op_dist_attr.process_mesh = ref_mesh
                    self._dist_context.set_op_dist_attr_for_program(
                        grad_op, grad_op_dist_attr
                    )
                    grad_op_dist_attr.impl_type = fwd_op_dist_attr.impl_type
                    grad_op_dist_attr.impl_idx = fwd_op_dist_attr.impl_idx

                    continue

                fwd_op_dist_attr = (
                    self._dist_context.get_op_dist_attr_for_program(forward_op)
                )
                fwd_op_process_mesh = fwd_op_dist_attr.process_mesh
                grad_op_dist_attr = OperatorDistributedAttribute()
                grad_op_dist_attr.process_mesh = fwd_op_process_mesh

                for input_name in grad_op.input_arg_names:
                    if (
                        input_name not in forward_op.input_arg_names
                        and input_name not in forward_op.output_arg_names
                    ):
                        if input_name in grad_var_to_var:
                            fwd_name = grad_var_to_var[input_name]
                            ref_dims_mapping = (
                                fwd_op_dist_attr.get_output_dims_mapping(
                                    fwd_name
                                )
                            )
                        else:
                            input_var = vars[input_name]
                            ref_dims_mapping = self._dist_context.get_tensor_dist_attr_for_program(
                                input_var
                            ).dims_mapping
                    else:
                        if fwd_op_dist_attr.get_input_dims_mapping(input_name):
                            ref_dims_mapping = (
                                fwd_op_dist_attr.get_input_dims_mapping(
                                    input_name
                                )
                            )
                        else:
                            ref_dims_mapping = (
                                fwd_op_dist_attr.get_output_dims_mapping(
                                    input_name
                                )
                            )
                    assert (
                        ref_dims_mapping is not None
                    ), "[{}] 's dims mapping is NONE".format(input_name)
                    grad_op_dist_attr.set_input_dims_mapping(
                        input_name, ref_dims_mapping
                    )

                for output_name in grad_op.output_arg_names:
                    assert output_name in grad_var_to_var
                    fwd_name = grad_var_to_var[output_name]
                    ref_dims_mapping = fwd_op_dist_attr.get_input_dims_mapping(
                        fwd_name
                    )
                    # var
                    output_var = vars[output_name]
                    tensor_dist_attr = TensorDistributedAttribute()
                    tensor_dist_attr.dims_mapping = ref_dims_mapping
                    tensor_dist_attr.process_mesh = fwd_op_process_mesh
                    self._dist_context.set_tensor_dist_attr_for_program(
                        output_var, tensor_dist_attr
                    )
                    # op
                    grad_op_dist_attr.set_output_dims_mapping(
                        output_name, ref_dims_mapping
                    )

                grad_op_dist_attr.impl_type = fwd_op_dist_attr.impl_type
                grad_op_dist_attr.impl_idx = fwd_op_dist_attr.impl_idx
                self._dist_context.set_op_dist_attr_for_program(
                    grad_op, grad_op_dist_attr
                )

            # grad ops that have not a corresponding mapping in grad_op_id_to_op_id
            else:
                if grad_op.type == 'sum':
                    assert all(map(_is_grad_var_name, grad_op.input_arg_names))
                    output_name = grad_op.output_arg_names[0]
                    assert (
                        output_name in grad_var_to_var
                    ), "sum op's output '{}' has no corresponding var".format(
                        output_name
                    )
                    ref_fwd_var_name = grad_var_to_var[output_name]
                    ref_fwd_var = vars[ref_fwd_var_name]
                    ref_fwd_dist_attr = (
                        self._dist_context.get_tensor_dist_attr_for_program(
                            ref_fwd_var
                        )
                    )
                    ref_fwd_dims_mapping = ref_fwd_dist_attr.dims_mapping
                    ref_fwd_process_mesh = ref_fwd_dist_attr.process_mesh

                    # output
                    tensor_dist_attr = TensorDistributedAttribute()
                    tensor_dist_attr.dims_mapping = ref_fwd_dims_mapping
                    tensor_dist_attr.process_mesh = ref_fwd_process_mesh
                    output_var = vars[output_name]
                    self._dist_context.set_tensor_dist_attr_for_program(
                        output_var, tensor_dist_attr
                    )

                    # op
                    grad_op_dist_attr = OperatorDistributedAttribute()
                    grad_op_dist_attr.process_mesh = ref_fwd_process_mesh
                    for var_name in grad_op.input_arg_names:
                        grad_op_dist_attr.set_input_dims_mapping(
                            var_name, ref_fwd_dims_mapping
                        )
                    grad_op_dist_attr.set_output_dims_mapping(
                        output_name, ref_fwd_dims_mapping
                    )
                    grad_op_dist_attr.impl_type = "default"
                    grad_op_dist_attr.impl_idx = 0

                elif grad_op.type == 'fill_any_like':
                    ref_var_name = grad_op.input_arg_names[0]
                    ref_var = vars[ref_var_name]
                    ref_dist_attr = (
                        self._dist_context.get_tensor_dist_attr_for_program(
                            ref_var
                        )
                    )
                    ref_dims_mapping = ref_dist_attr.dims_mapping
                    ref_process_mesh = ref_dist_attr.process_mesh
                    # output
                    tensor_dist_attr = TensorDistributedAttribute()
                    tensor_dist_attr.dims_mapping = ref_dims_mapping
                    tensor_dist_attr.process_mesh = ref_process_mesh
                    output_var_name = grad_op.output_arg_names[0]
                    output_var = vars[output_var_name]
                    self._dist_context.set_tensor_dist_attr_for_program(
                        output_var, tensor_dist_attr
                    )
                    # op
                    grad_op_dist_attr = OperatorDistributedAttribute()
                    grad_op_dist_attr.process_mesh = ref_process_mesh
                    grad_op_dist_attr.set_input_dims_mapping(
                        ref_var_name, ref_dims_mapping
                    )
                    grad_op_dist_attr.set_output_dims_mapping(
                        output_var_name, ref_dims_mapping
                    )

                else:
                    raise ValueError(
                        "got unexpect op [{}]".format(str(grad_op.type))
                    )

                self._dist_context.set_op_dist_attr_for_program(
                    grad_op, grad_op_dist_attr
                )

    def complete_update_annotation(self, serial_main_program):
        """Complete the annotation of vars and ops in the update phase for parallel program."""
        # Copy the dist tensors and dist ops annotated by users from the default context
        # global mesh
        from paddle.distributed.auto_parallel.process_group import (
            get_world_process_group,
        )

        world_ranks = get_world_process_group().ranks

        # Notice: serial_main_program is actually a dist_main_program of current rank,
        # and must be passed into this function.
        # TODO: We should fix this behavior.

        ops = list(serial_main_program.global_block().ops)
        vars = serial_main_program.global_block().vars
        learning_rate_completed = False

        for idx in range(len(ops)):

            # complete the annotation of the optimizer op.
            # TODO to add attribute for moment var
            op = ops[idx]
            if int(op.attr('op_role')) == int(OpRole.Optimize):
                if is_gradient_clip_op(op):
                    if op.type in [
                        "sum",
                        "sqrt",
                        "fill_constant",
                        "elementwise_max",
                        "elementwise_div",
                    ]:
                        op_dist_attr = OperatorDistributedAttribute()
                        op_dist_attr.process_mesh = world_ranks
                        for in_name in op.input_arg_names:
                            in_var = vars[in_name]
                            in_dist_attr = self._dist_context.get_tensor_dist_attr_for_program(
                                in_var
                            )
                            op_dist_attr.set_input_dist_attr(
                                in_name, in_dist_attr
                            )
                        for out_name in op.output_arg_names:
                            out_var = vars[out_name]
                            out_dist_attr = TensorDistributedAttribute()
                            out_dist_attr.process_mesh = world_ranks
                            out_dist_attr.dims_mapping = [
                                -1 for _ in range(len(out_var.shape))
                            ]
                            self._dist_context.set_tensor_dist_attr_for_program(
                                out_var, out_dist_attr
                            )
                            op_dist_attr.set_output_dist_attr(
                                out_name, out_dist_attr
                            )
                    else:
                        in_var = vars[op.input("X")[0]]
                        in_dist_attr = (
                            self._dist_context.get_tensor_dist_attr_for_program(
                                in_var
                            )
                        )
                        assert in_dist_attr is not None
                        ref_process_mesh = in_dist_attr.process_mesh
                        ref_dims_mapping = in_dist_attr.dims_mapping

                        if (
                            op.type == "cast"
                            and ops[idx + 1].type == "elementwise_mul"
                        ):
                            ref_var = vars[ops[idx + 1].input("X")[0]]
                            ref_dist_attr = self._dist_context.get_tensor_dist_attr_for_program(
                                ref_var
                            )
                            assert ref_dist_attr is not None
                            ref_process_mesh = ref_dist_attr.process_mesh

                        out_var = vars[op.output("Out")[0]]
                        out_dist_attr = TensorDistributedAttribute()
                        out_dist_attr.process_mesh = ref_process_mesh
                        if out_var.shape == in_var.shape:
                            out_dist_attr.dims_mapping = ref_dims_mapping
                        else:
                            assert (
                                len(out_var.shape) == 1
                                and out_var.shape[0] == 1
                            )
                            out_dist_attr.dims_mapping = [-1]
                        self._dist_context.set_tensor_dist_attr_for_program(
                            out_var, out_dist_attr
                        )

                        op_dist_attr = OperatorDistributedAttribute()
                        op_dist_attr.process_mesh = ref_process_mesh
                        op_dist_attr.set_input_dist_attr(
                            in_var.name, in_dist_attr
                        )
                        op_dist_attr.set_output_dist_attr(
                            out_var.name, out_dist_attr
                        )

                    self._dist_context.set_op_dist_attr_for_program(
                        op, op_dist_attr
                    )

                if "Grad" in op.input_names and "Param" in ops[idx].input_names:
                    assert (
                        len(op.input("Param")) == 1
                    ), "Only support one-to-one now."
                    assert (
                        len(op.input("Grad")) == 1
                    ), "Only support one-to-one now."
                    param = vars[op.input("Param")[0]]
                    grad_var = vars[op.input("Grad")[0]]

                    param_dist_attr = (
                        self._dist_context.get_tensor_dist_attr_for_program(
                            param
                        )
                    )
                    assert param_dist_attr is not None
                    ref_process_mesh = (
                        self._dist_context.get_tensor_dist_attr_for_program(
                            param
                        ).process_mesh
                    )
                    assert ref_process_mesh is not None
                    ref_dims_mapping = (
                        self._dist_context.get_tensor_dist_attr_for_program(
                            param
                        ).dims_mapping
                    )
                    assert ref_dims_mapping is not None
                    op_dist_attr = OperatorDistributedAttribute()
                    op_dist_attr.process_mesh = ref_process_mesh
                    op_dist_attr.set_input_dims_mapping(
                        grad_var.name, ref_dims_mapping
                    )
                    op_dist_attr.set_input_dims_mapping(
                        param.name, ref_dims_mapping
                    )
                    op_dist_attr.set_output_dims_mapping(
                        param.name, ref_dims_mapping
                    )
                    learning_var = vars[op.input("LearningRate")[0]]
                    op_dist_attr.set_input_dims_mapping(learning_var.name, [-1])
                    op_dist_attr.set_output_dims_mapping(
                        learning_var.name, [-1]
                    )

                    if not learning_rate_completed:
                        learning_rate_completed = True
                        var_dist_attr = TensorDistributedAttribute()
                        var_dist_attr.process_mesh = world_ranks
                        var_dist_attr.dims_mapping = [-1]
                        self._dist_context.set_tensor_dist_attr_for_program(
                            learning_var, var_dist_attr
                        )

                    for input_name in op.desc.input_names():

                        if input_name in [
                            'Param',
                            'Grad',
                            'LearningRate',
                            "SkipUpdate",
                            "Beta1Tensor",
                            "Beta2Tensor",
                            "EpsilonTensor",
                        ]:
                            continue
                        if len(op.desc.input(input_name)) == 0:
                            continue

                        assert len(op.desc.input(input_name)) == 1
                        input_var = vars[op.desc.input(input_name)[0]]
                        input_var_attr = TensorDistributedAttribute()

                        if "Beta1Pow" in input_name or "Beta2Pow" in input_name:
                            input_var_attr.dims_mapping = [-1]
                            op_dist_attr.set_input_dims_mapping(
                                input_var.name, [-1]
                            )
                            op_dist_attr.set_output_dims_mapping(
                                input_var.name, [-1]
                            )
                        else:
                            input_var_attr.dims_mapping = ref_dims_mapping
                            op_dist_attr.set_input_dims_mapping(
                                input_var.name, ref_dims_mapping
                            )
                            op_dist_attr.set_output_dims_mapping(
                                input_var.name, ref_dims_mapping
                            )

                        input_var_attr.process_mesh = ref_process_mesh
                        self._dist_context.set_tensor_dist_attr_for_program(
                            input_var, input_var_attr
                        )

                    self._dist_context.set_op_dist_attr_for_program(
                        op, op_dist_attr
                    )
                    continue

    def complete_prim_annotation(self, serial_main_program=None):
        """
        fill default data parallel annotation for program with primitive operators.

        Arguments:
            serial_main_program: partial annotated serial_main_program.
        Returns:
            serial_main_program: completed annotated serial_main_program.
        """
        if serial_main_program is None:
            serial_main_program = self._dist_context.serial_main_program
        else:
            self._dist_context._serial_main_program = serial_main_program

        self._dist_context._is_initialized = True
        self._dist_context._init_dist_attr_for_program()
        self._init_global_mesh_for_program()
        # Do the validation check and amend some completion
        self._dist_context.amend_dist_attr_for_program()
        self._dist_context.validate_dist_attr_for_program()

    def _init_global_mesh_for_program(self):
        # Copy the dist tensors and dist ops annotated by users from the default context
        # global mesh
        from paddle.distributed.auto_parallel.process_group import (
            get_world_process_group,
        )

        world_ranks = get_world_process_group().ranks

        for block in self._dist_context._serial_main_program.blocks:
            for tensor in block.vars.values():
                # Copy the distributed tensors in the default context
                dist_tensor = self._dist_context.get_dist_tensor_for_program(
                    tensor
                )
                assert dist_tensor is not None
                dist_tensor.dist_attr.process_mesh = world_ranks
            for op in block.ops:
                # Copy the distributed operators in the default context
                dist_op = self._dist_context.get_dist_op_for_program(op)
                assert dist_op is not None
                dist_op.dist_attr.process_mesh = world_ranks

                # Find the most compatible implemenetations from the distributed operator
                op_dist_impls = find_compatible_distributed_operator_impls(
                    dist_op, fwd=True
                )
                if op_dist_impls is not None:
                    backup_op_dist_attr = copy.deepcopy(dist_op.dist_attr)
                    for op_dist_impl in op_dist_impls:
                        dim_changed = op_dist_impl.update_dims_mapping(dist_op)
                        if op_dist_impl.is_auto_compatible(dist_op):
                            if op_dist_impl.type == "elementwise":
                                dist_op.dist_attr.impl_type = "default"
                            else:
                                dist_op.dist_attr.impl_type = op_dist_impl.type
                            # op_dist_attr.impl_type = op_dist_impl.type
                            dist_op.dist_attr.impl_idx = op_dist_impl.idx
                            break
                        else:
                            dist_op.dist_attr = backup_op_dist_attr