text: import torch
  import operator
  import warnings
  from torch.fx import (
      GraphModule,
  )
  
  from torch.quantization import (
      propagate_qconfig_,
      ObserverBase,
  )
  from torch.fx.graph import (
      Graph,
      Node,
  )
  from torch.fx.node import Argument
  
  from ..qconfig import QConfigAny, qconfig_equals
  from .qconfig_utils import (
      convert_dict_to_ordered_dict,
      generate_qconfig_map,
      get_flattened_qconfig_dict,
  )
  
  from .quantization_patterns import (
      QuantizeHandler,
      CustomModuleQuantizeHandler,
      StandaloneModuleQuantizeHandler,
  )
  
  from .quantization_types import Pattern
  
  from ._equalize import (
      is_equalization_observer,
      node_supports_equalization,
  )
  
  from .graph_module import (
      ObservedGraphModule,
      ObservedStandaloneGraphModule,
  )
  
  from .pattern_utils import (
      MatchResult,
      get_default_output_activation_post_process_map,
  )
  
  from .match_utils import (
      find_matches,
  )
  
  from .utils import (
      _parent_name,
      get_custom_module_class_keys,
      all_node_args_have_no_tensors,
      assert_and_get_unique_device,
      node_bool_tensor_arg_indexes,
      get_new_attr_name_with_prefix,
      NON_QUANTIZABLE_WEIGHT_OPS,
      WEIGHT_INDEX_DICT,
      FUNCTIONAL_OPS_WITH_BIAS,
  )
  
  from ..fuser_method_mappings import DEFAULT_OP_LIST_TO_FUSER_METHOD
  
  from ..quantization_mappings import (
      get_default_qat_module_mappings,
  )
  
  from ..quantize import (
      is_activation_post_process,
      convert
  )
  
  from ..utils import (
      get_combined_dict,
      get_qconfig_dtypes,
      get_swapped_custom_module_class,
      weight_is_quantized,
      activation_is_statically_quantized,
      activation_is_int8_quantized,
      activation_dtype,
      weight_dtype,
  )
  
  from .backend_config_dict import get_fbgemm_backend_config_dict
  from .backend_config_dict import validate_backend_config_dict
  
  from typing import Any, Callable, Dict, List, Optional, Tuple, Union
  
  def is_activation_post_process_node(node: Node, modules: Dict[str, torch.nn.Module]) -> bool:
      return isinstance(node, torch.fx.Node) and node.op == "call_module" and \
          is_activation_post_process(modules[str(node.target)])
  
  def node_arg_is_weight(node: Node, arg: Any) -> bool:
      if isinstance(node, Node) and node.op == 'call_function' and \
              node.target in WEIGHT_INDEX_DICT:
          for i, node_arg in enumerate(node.args):
              if arg is node_arg and i in \
                      WEIGHT_INDEX_DICT[node.target]:  # type: ignore[index]
                  return True
          for kwarg_name, kwarg_value in node.kwargs.items():
              if kwarg_name == 'weight' and arg is kwarg_value:
                  return True
      return False
  
  CONV_OPS_WITH_BIAS = {
      torch.nn.functional.conv1d,
      torch.nn.functional.conv2d,
      torch.nn.functional.conv3d,
  }
  CONV_BIAS_ARG_INDEX = 2
  
  def node_arg_is_bias(node: Node, arg: Any) -> bool:
      if isinstance(node, Node) and node.op == 'call_function':
          if node.target in CONV_OPS_WITH_BIAS:
              for i, node_arg in enumerate(node.args):
                  if arg is node_arg and i == CONV_BIAS_ARG_INDEX:
                      return True
          elif node.target in FUNCTIONAL_OPS_WITH_BIAS:
              for kwarg_name, kwarg_value in node.kwargs.items():
                  if kwarg_name == 'bias' and arg is kwarg_value:
                      return True
      return False
  
  def get_standalone_module_configs(
      node: Node,
      modules: Dict[str, torch.nn.Module],
      prepare_custom_config_dict: Dict[str, Any],
      qconfig: QConfigAny,
  ) -> Tuple[Dict[str, Any], Dict[str, Any]]:
      """
      Returns the standalone module qconfig_dict and prepare_config_dict
      for `node`, assuming that the module pointed to by `node` is
      a standalone modules.
      """
      standalone_module = modules[node.target]  # type: ignore[index]
      standalone_module_name_configs = \
          prepare_custom_config_dict.get("standalone_module_name", [])
      standalone_module_class_configs = \
          prepare_custom_config_dict.get("standalone_module_class", [])
      class_config_map = {x[0]: (x[1], x[2]) for x in standalone_module_class_configs}
      name_config_map = {x[0]: (x[1], x[2]) for x in standalone_module_name_configs}
      config = class_config_map.get(type(standalone_module), (None, None))
      config = name_config_map.get(node.target, config)
      sm_qconfig_dict = {"": qconfig} if config[0] is None else config[0]
      sm_prepare_config_dict = {} if config[1] is None else config[1]
      return sm_qconfig_dict, sm_prepare_config_dict
  
  def qat_swap_modules(
          root: torch.nn.Module,
          additional_qat_module_mapping: Dict[Callable, Callable]) -> None:
      all_mappings = get_combined_dict(
          get_default_qat_module_mappings(), additional_qat_module_mapping)
      convert(root, mapping=all_mappings, inplace=True, remove_qconfig=False)
  
  def update_qconfig_for_qat(
      qconfig_dict: Any,
      additional_qat_module_mapping: Dict[Callable, Callable]
  ) -> Any:
      """
      Update the qconfig_dict to account for module swaps during QAT.
      During QAT we perform a module swap on the nn.Module types to the corresponding nn.qat.modules types.
      """
      all_qat_mappings = get_combined_dict(
          get_default_qat_module_mappings(), additional_qat_module_mapping)
      object_type_dict = qconfig_dict.get("object_type", None)
      new_object_type_dict = object_type_dict.copy()
      for k, v in new_object_type_dict.items():
          if k in all_qat_mappings:
              object_type_dict[all_qat_mappings[k]] = v
      return qconfig_dict
  
  def update_qconfig_for_fusion(
      model: GraphModule,
      qconfig_dict: Any,
  ) -> Any:
      """
      Update the qconfig_dict to account for fused modules such as LinearReLU.
      """
      object_type_dict = qconfig_dict.get("object_type", None)
      if object_type_dict is None:
          return qconfig_dict
  
      modules = dict(model.named_modules())
  
      for node in model.graph.nodes:
          if node.op == 'call_module':
              module_type = type(modules[str(node.target)])
              if module_type not in list(DEFAULT_OP_LIST_TO_FUSER_METHOD.values()):
                  continue
  
              for ops, fuser in DEFAULT_OP_LIST_TO_FUSER_METHOD.items():
                  if module_type == fuser:
                      fused_qconfig = object_type_dict.get(ops[0], None)
  
                      # Raise an error if the modules in the fused module have
                      # different qconfigs specified in the qconfig_dict
                      for op in ops:
                          if not qconfig_equals(object_type_dict.get(op, None), fused_qconfig):
                              raise LookupError("During fusion, we need to specify the same " +
                                                f"qconfigs for both modules in {module_type}.")
  
                      if fused_qconfig is not None:
                          object_type_dict[module_type] = fused_qconfig
  
      return qconfig_dict
  
  def insert_observer(
      node: Node,
      observer: torch.quantization.ObserverBase,
      model: torch.nn.Module,
      modules: Dict[str, torch.nn.Module],
      graph: Graph,
  ) -> Node:
      """
      Attaches `observer` to `model`, and creates a node which calls
      `observer` on the output of `node`.
      """
      model_device = assert_and_get_unique_device(model)
      if model_device:
          observer.to(model_device)
      # add observer module as attribute
      if is_equalization_observer(observer):
          prefix = node.name + '_equalization_process_'
      else:
          prefix = node.name + '_activation_post_process_'
      get_new_observer_name = get_new_attr_name_with_prefix(prefix)
      observer_name = get_new_observer_name(model)
      setattr(model, observer_name, observer)
      modules[observer_name] = observer
      with graph.inserting_after(node):
          new_obs = graph.create_node(
              'call_module', observer_name, (node,), {})
      return new_obs
  
  def get_target_activation_dtype_for_node(
      node: Node,
      qconfig: QConfigAny,
      inputs_seen_counter: int,
      outputs_seen_counter: int,
      input_quantized_idxs: List[int],
      output_quantized_idxs: List[int],
      qhandler: Optional[QuantizeHandler],
      modules: Dict[str, torch.nn.Module],
      cache_for_no_tensor_check: Dict[Node, bool],
  ) -> Optional[torch.dtype]:
      """
      Returns the expected dtype of the input and output of this node after
      convert. If the value is not None, it represents the dtype of the
      Tensor. If the value is None, it means the value is not a Tensor.
  
      Note: this is for activations only, weight dtypes are not handled here.
  
      TODO(future PR, if needed): explicitly spell out the non-Tensor
      dtypes.
      """
      if node.op == 'placeholder':
          if inputs_seen_counter in input_quantized_idxs:
              return torch.quint8
          else:
              # if dtype is fp32 (default), do nothing
              # note: other dtypes are not supported
              return torch.float
  
      elif node.op in ('call_module', 'call_method', 'call_function'):
          args_have_no_tensors = \
              all_node_args_have_no_tensors(
                  node, modules, cache_for_no_tensor_check)
          if args_have_no_tensors:
              return None
  
          # TODO(future PR): consider stopping matching getitem
          is_getitem = node.op == 'call_function' and \
              node.target == operator.getitem
          if is_getitem:
              return torch.float
  
          # get qconfig to determine the eventual dtype of this node
          if qconfig is not None:
              if qhandler is not None and qhandler.input_output_observed():
                  act_dtype, weight_dtype, act_compute_dtype = \
                      get_qconfig_dtypes(qconfig)
                  return act_dtype
              else:
                  return torch.float
          else:
              return torch.float
  
      elif node.op == 'get_attr':
          return torch.float
  
      elif node.op == 'output':
          if outputs_seen_counter in output_quantized_idxs:
              return torch.quint8
          else:
              # if dtype is fp32 (default), do nothing
              # note: other dtypes are not supported
              return torch.float
  
      else:
          raise AssertionError(f'need to handle {node.format_node()}')
  
  def maybe_insert_input_observer_for_arg_or_kwarg(
      node: Union[Node, Any],
      arg: Argument,
      qconfig: QConfigAny,
      model: torch.nn.Module,
      modules: Dict[str, torch.nn.Module],
      graph: Graph,
      node_name_to_target_dtype: Dict[str, Any],
      qhandler: Optional[QuantizeHandler],
      prepare_custom_config_dict: Dict[str, Any],
  ) -> Argument:
      """
      Given a `node` and an `arg`, inserts an input observer between
      `node` and `arg` if necessary.
      """
      # for ops such as torch.cat([x0, x1]),
      # traverse through the list
      if isinstance(arg, (list, tuple)):
          new_arg_to_return = []
          for inner_arg in arg:
              new_inner_arg = maybe_insert_input_observer_for_arg_or_kwarg(
                  node, inner_arg, qconfig, model, modules,
                  graph, node_name_to_target_dtype,
                  qhandler, prepare_custom_config_dict)
              new_arg_to_return.append(new_inner_arg)
          return type(arg)(new_arg_to_return)
  
      if not isinstance(arg, Node):
          return arg
      assert isinstance(arg, Node)
  
      # default (no observer)
      new_arg = arg
  
      is_standalone_module = qhandler is not None and \
          isinstance(qhandler, StandaloneModuleQuantizeHandler)
  
      if not is_standalone_module:
          # regular flow for most nodes, except standalone modules
          is_weight = node_arg_is_weight(node, arg)
          assert qconfig is not None
  
          act_post_process_ctr = qconfig.weight if is_weight else \
              qconfig.activation
  
          is_bias = node_arg_is_bias(node, arg)
          is_activation = not (is_weight or is_bias)
          weight_needs_obs = is_weight and weight_is_quantized(qconfig) and node.target not in NON_QUANTIZABLE_WEIGHT_OPS
          bias_needs_obs = \
              (is_bias and activation_dtype(qconfig) == torch.float16) and \
              weight_dtype(qconfig) == torch.float16
  
          arg_dtype = node_name_to_target_dtype[arg.name]
          node_dtype = node_name_to_target_dtype[node.name]
          dtype_changes_and_second_dtype_not_float = (
              # if the dtypes are different, we need an observer
              (arg_dtype != node_dtype) and
              # except if the second dtype is float, a dequant will be inserted
              # without an observer in convert
              # TODO(future PR): change this so a placeholder is inserted for
              # future dequants, to make the logic easier to understand
              (node_dtype != torch.float) and
              # if arg is a bool tensor or not a tensor, do not insert observer
              (arg_dtype not in (torch.bool, None)) and
              (is_activation and activation_is_statically_quantized(qconfig))
          )
  
          needs_obs = (
              weight_needs_obs or
              bias_needs_obs or
              dtype_changes_and_second_dtype_not_float
          )
  
      else:
          # custom flow for standalone modules
          _sm_qconfig_dict, sm_prepare_config_dict = \
              get_standalone_module_configs(
                  node, modules, prepare_custom_config_dict, qconfig)
  
          sm_input_quantized_idxs = \
              sm_prepare_config_dict.get('input_quantized_idxs', [])
          # for args, this is set to the index of the current arg
          # for kwargs, this is left at None
          cur_input_idx = None
          for arg_idx, arg_to_check in enumerate(node.args):
              if arg_to_check is arg:
                  cur_input_idx = arg_idx
                  break
  
          if cur_input_idx is None:
              needs_obs = False
          else:
              arg_dtype = node_name_to_target_dtype[arg.name]
              node_dtype = torch.quint8 if cur_input_idx in sm_input_quantized_idxs \
                  else torch.float
              needs_obs = (
                  (arg_dtype != node_dtype) and
                  (node_dtype != torch.float)
              )
  
      if needs_obs:
  
          new_obs_mod = act_post_process_ctr()
          existing_obs_node = None
  
          # Before using the new observer, check if an observer
          # of the correct type already exists. If it does, use it.
          # This prevents duplicate observer insertions if a node is
          # used by multiple nodes.
          for maybe_obs_node, _ in arg.users.items():
              if maybe_obs_node.op == 'call_module':
                  maybe_obs_mod = modules[maybe_obs_node.target]  # type: ignore[index]
                  if (
                      type(maybe_obs_mod) == type(new_obs_mod) and
                      node_name_to_target_dtype[maybe_obs_node.name] == node_dtype
                  ):
                      existing_obs_node = maybe_obs_node
                      break
  
          if existing_obs_node is None:
              new_obs_node = insert_observer(
                  arg, new_obs_mod, model, modules, graph)
              # set the type, so the next node can read it
              node_name_to_target_dtype[new_obs_node.name] = node_dtype
              # override this arg to be the observed arg
              new_arg = new_obs_node
          else:
              new_arg = existing_obs_node
  
      return new_arg
  
  
  def maybe_insert_input_observers_for_node(
      node: Node,
      qconfig: QConfigAny,
      model: torch.nn.Module,
      modules: Dict[str, torch.nn.Module],
      graph: Graph,
      node_name_to_target_dtype: Dict[str, Any],
      qhandler: Optional[QuantizeHandler],
      prepare_custom_config_dict: Dict[str, Any],
  ) -> None:
      """
      If needed, inserts observers to the input args and kwargs of `node`.
      Note: modifies `node` inplace.
  
      For example, if cur_node needs an observer after prev_node, we change from
  
        prev_node -> cur_node
  
      To
  
        prev_node -> obs -> cur_node
      """
      if qconfig is None:
          # if quantization is turned off for this node, we do not need
          # to insert input observers
          return
      assert qconfig is not None
  
      # Look through every input arg.  If that arg's target dtype does not
      # match the current node's target dtype, insert an observer.
      new_args = []
      for arg in node.args:
          new_arg = maybe_insert_input_observer_for_arg_or_kwarg(
              node, arg, qconfig, model, modules, graph,
              node_name_to_target_dtype,
              qhandler, prepare_custom_config_dict)
          new_args.append(new_arg)
  
      new_kwargs = {}
      for k, kwarg in node.kwargs.items():
          new_kwarg = maybe_insert_input_observer_for_arg_or_kwarg(
              node, kwarg, qconfig, model, modules, graph,
              node_name_to_target_dtype,
              qhandler, prepare_custom_config_dict)
          new_kwargs[k] = new_kwarg
  
      # assign the new args and kwargs to the node, inplace
      node.args = tuple(new_args)
      node.kwargs = new_kwargs
  
  def maybe_insert_input_equalization_observers_for_node(
      node: Node,
      equalization_qconfig: Any,
      model: torch.nn.Module,
      modules: Dict[str, torch.nn.Module],
      graph: Graph,
      node_name_to_target_dtype: Dict[str, Any],
      is_branch: bool,
  ) -> None:
      """
      If `node` needs to be equalized, find the input/weight observers it needs in
      `equalization_qconfig`, creates them, and inserts it into `graph`.
  
      If `node` does not need an equalization observer, returns None.
      """
      if equalization_qconfig is None or not node_supports_equalization(node, modules):
          return
  
      if is_branch:
          warnings.warn(
              f"Cannot equalize {node} because it is part of a branch."
          )
          return
  
      new_args = []
      for arg in node.args:
          if not isinstance(arg, Node) or node_arg_is_bias(node, arg):
              new_args.append(arg)
              continue
  
          is_weight = node_arg_is_weight(node, arg)
  
          act_eq_process_ctr = equalization_qconfig.weight if is_weight else \
              equalization_qconfig.input_activation
  
          new_eq_obs_mod = act_eq_process_ctr()
          new_eq_obs_node = insert_observer(
              arg, new_eq_obs_mod, model, modules, graph)
  
          # set the type, so the next node can read it
          node_name_to_target_dtype[new_eq_obs_node.name] = node_name_to_target_dtype[arg.name]
  
          new_args.append(new_eq_obs_node)
  
      # assign the new args and kwargs to the node, inplace
      node.args = tuple(new_args)
  
  def maybe_insert_output_observer_for_node(
      node: Node,
      model: torch.nn.Module,
      modules: Dict[str, torch.nn.Module],
      graph: Graph,
      matches: Dict[str, MatchResult],
      node_name_to_target_dtype: Dict[str, Any],
      matched_pattern: Any,
      qhandler: Optional[QuantizeHandler],
  ) -> Optional[Node]:
      """
      If `node` needs an output observer, creates it, inserts it into `graph`
      and returns it.
  
      If `node` does not need an output observer, returns None.
      """
      root_node, matched_nodes, pattern, qhandler, qconfig = matches.get(
          node.name, (None, None, None, None, None))
  
      if qhandler is None:
          return None
  
      assert qconfig is not None
      assert node.op != 'output', 'observer insertion for outputs is handled elsewhere'
  
      is_standalone_module = qhandler is not None and \
          isinstance(qhandler, StandaloneModuleQuantizeHandler)
  
      dtype = node_name_to_target_dtype[node.name]
      should_insert_observer = \
          qhandler.should_insert_observer_for_output(
              qconfig, model.training) and dtype not in (torch.bool, None, torch.float)
      # TODO(future PR): move the following logic to
      # should_insert_observer_for_output
      should_insert_observer = should_insert_observer and \
          activation_is_statically_quantized(qconfig)
  
      # we never insert observers to output of standalone module, we assume
      # if needed, they are inserted inside the standalone module
      should_insert_observer = should_insert_observer and \
          (not is_standalone_module)
  
      if should_insert_observer:
          act_post_process_ctr = qconfig.activation
          if activation_is_int8_quantized(qconfig):
              act_post_process_ctr = \
                  get_default_output_activation_post_process_map().get(
                      matched_pattern,
                      act_post_process_ctr)
          observer = act_post_process_ctr()
          new_obs = insert_observer(node, observer, model, modules, graph)
          # set the type, so the next node can read it
          node_name_to_target_dtype[new_obs.name] = \
              node_name_to_target_dtype[node.name]
          return new_obs
      else:
          return None
  
  def maybe_insert_observers_before_graph_output(
      graph_output_node: Node,
      output_quantized_idxs: List[int],
      node_name_to_target_dtype: Dict[str, torch.dtype],
      qconfig_map: Dict[str, QConfigAny],
      model: torch.nn.Module,
      modules: Dict[str, torch.nn.Module],
      graph: Graph,
  ) -> None:
      """
      If the output needs to be quantized and there are any nodes
      in the output which are not already observed, inserts observers
      for those nodes.
      """
  
      # TODO(future PR): update the output_quantized_idxs API to match
      # arbitrary data structures. There is always a single output, and
      # that output can have arbitrary nesting of values. List[int] is
      # not the right data type for this.
      assert output_quantized_idxs == [0] or output_quantized_idxs == [], \
          'unrecognized format of output_quantized_idxs'
  
      # Currently dequants are inserted in the convert step. So, we only
      # have to do anything if the output is hardcoded to be quantized
      if output_quantized_idxs == []:
          return
      # TODO(future PR): support more dtypes in model outputs, if necessary
      output_target_dtype = torch.quint8
  
      def _recursive_maybe_replace_node_with_obs(
          maybe_node: Argument,
          target_dtype: torch.dtype,
          node_name_to_target_dtype: Dict[str, torch.dtype],
          qconfig_map: Dict[str, QConfigAny],
          model: torch.nn.Module,
          modules: Dict[str, torch.nn.Module],
          graph: Graph,
      ) -> Argument:
          """
          Navigate an arbitrary data structure of lists, tuples, dicts.
          For each container type, recurse on all inputs. Once any Node
          is found, insert an observer if needed and do not recurse further.
  
          For example, given a structure of
  
            {'foo1': [[bar1]], 'foo2': {'foo3': [[[bar3]]]}}
  
          we recurse down to bar1 and bar3, observe them if necessary,
          and if we inserted an observer then replace the original node
          with its observer.
  
          Returns the data structure with all nodes needing observation being
          replaced by their observers.
          """
          if isinstance(maybe_node, Node):
              # check dtype of this node
              this_node_dtype = node_name_to_target_dtype[maybe_node.name]
              if this_node_dtype != target_dtype:
                  # insert observer
                  qconfig = qconfig_map.get(maybe_node.name)
                  # TODO(future PR): see if we need to allow specifying qconfig
                  #   on output nodes, to remove the restriction below.
                  assert qconfig is not None, \
                      'Quantizing the output node without a qconfig is not supported'
                  observer_mod = qconfig.activation()
                  observer_node = insert_observer(
                      maybe_node, observer_mod, model, modules, graph)
                  return observer_node
              else:
                  return maybe_node
          elif isinstance(maybe_node, (list, tuple)):
              results = []
              for inner_node in maybe_node:
                  results.append(_recursive_maybe_replace_node_with_obs(
                      inner_node, target_dtype, node_name_to_target_dtype,
                      qconfig_map, model, modules, graph))
              if isinstance(maybe_node, list):
                  return results
              else:
                  return tuple(results)
          elif isinstance(maybe_node, dict):
              results_dict = {}
              for k, inner_v in maybe_node.items():
                  results_dict[k] = _recursive_maybe_replace_node_with_obs(
                      inner_v, target_dtype, node_name_to_target_dtype,
                      qconfig_map, model, modules, graph)
              return results_dict
          else:
              return results
  
      new_args = []
      for old_arg in graph_output_node.args:
          new_args.append(
              _recursive_maybe_replace_node_with_obs(
                  old_arg, output_target_dtype, node_name_to_target_dtype,
                  qconfig_map, model, modules, graph))
  
      graph_output_node.args = new_args  # type: ignore[assignment]
  
  
  def maybe_propagate_dtype_for_node(
      node: Node,
      target_dtype: torch.dtype,
      node_name_to_target_dtype: Dict[str, torch.dtype],
      matches: Dict[str, MatchResult],
  ) -> None:
      """
      Assigns `target_dtype` to `node`. If `node` is a general tensor shape op
      (see GeneralTensorShapeOpQuantizeHandler in quantization_patterns.py for more details)
      also call this function recursively on
      the first argument, to propagate the dtype to the caller.
      """
      node_name_to_target_dtype[node.name] = target_dtype
      # if this is a copy node, propagate to first arg
      root_node, matched_nodes, pattern, qhandler, qconfig = matches.get(
          node.name, (None, None, None, None, None))
      if qhandler is not None and qhandler.is_general_tensor_shape_op():
          prev_node = node.args[0]
          if isinstance(prev_node, Node):
              maybe_propagate_dtype_for_node(
                  prev_node, target_dtype, node_name_to_target_dtype, matches)
  
  def propagate_dtypes_for_known_nodes(
      graph: Graph,
      node_name_to_target_dtype: Dict[str, torch.dtype],
      matches: Dict[str, MatchResult],
  ) -> None:
      """
      Currently we assume that inputs to the graph are either `torch.float` or
      `torch.quint8`, which is not always correct. For ops such as
      `x.masked_fill(mask, value)`, we know that the dtype of  `mask` is a
      `BoolTensor`. Propagate this information throughout the graph.
  
      Note: not all dtypes in the graph will be correct after this pass, but a
      higher percentage of them will be correct. Hopefully in the future we can
      replace this with a better way to reason about dtypes of tensors.
      """
      for node in graph.nodes:
          bool_arg_idxs = node_bool_tensor_arg_indexes(node)
          for bool_arg_idx in bool_arg_idxs:
              cur_node = node.args[bool_arg_idx]
              maybe_propagate_dtype_for_node(
                  cur_node, torch.bool, node_name_to_target_dtype, matches)
  
  def maybe_make_input_output_share_observers(
      node: Node,
      model: torch.nn.Module,
      modules: Dict[str, torch.nn.Module],
  ) -> bool:
      """
      Ensures that we share an observer
      for all input arguments as well as the output argument. In detail, given
      a graph of
  
        x0 -> obs0 -> op -> x2
                    /
        x1 -> obs1 /
  
      where node obs0 points to observer instance observer0,
      obs1 points to observer1 and obs2 points to observer2, we make nodes obs1
      and ob2 point to observer0.
      Returns: whether the operation succeeded or not
      """
      first_arg = None
      # find the first non-Tensor arg
      for i in range(len(node.args)):
          if isinstance(node.args[i], (Node, list, tuple)):
              first_arg = node.args[i]
              break
  
      # if there is no non-Tensor arg, return directly
      if first_arg is None:
          return False
  
      if isinstance(first_arg, (list, tuple)):
          first_arg_arg = first_arg[0]
      elif isinstance(first_arg, Node):
          first_arg_arg = first_arg
      else:
          return False
  
      # if we have a graph such as
      #   observed_node -> non_observed_node -> cat
      # we need to navigate up to the first observer
      iteration_guard = 0
      while not is_activation_post_process_node(first_arg_arg, modules):
          if not isinstance(first_arg_arg, Node):
              return False
          # did not find an activation_post_process for the op
          if first_arg_arg.op == "placeholder":
              return False
          # trace back the args until we found the first Tensor/Node
          trace_back_node = None
          for i in range(len(first_arg_arg.args)):
              trace_back_node = first_arg_arg.args[i]
              if isinstance(trace_back_node, Node):
                  break
          if trace_back_node is None:
              return False
          first_arg_arg = trace_back_node
  
          iteration_guard += 1
          if iteration_guard > 10000:
              raise AssertionError('Unable to find observer of previous node')
  
      assert isinstance(first_arg_arg, Node)
      target_to_use = first_arg_arg.target
      assert isinstance(target_to_use, str)
      obs_mod_to_use = modules[target_to_use]
  
      if isinstance(first_arg, (list, tuple)):
          # set all other input observer nodes to use that module
          for input_idx, input_arg in enumerate(first_arg):
              if input_idx == 0:
                  continue
              iteration_guard = 0
              while not is_activation_post_process_node(input_arg, modules):
                  input_arg = input_arg.args[0]
                  iteration_guard += 1
                  if iteration_guard > 10000:
                      raise AssertionError('Unable to find observer of previous node')
  
              parent_name, name = _parent_name(input_arg.target)
              setattr(modules[parent_name], name, obs_mod_to_use)
  
      # set the output observer node to use that module
      for output_obs_node, _ in node.users.items():
          assert is_activation_post_process_node(output_obs_node, modules)
          parent_name, name = _parent_name(output_obs_node.target)
          setattr(modules[parent_name], name, obs_mod_to_use)
  
      # TODO(future PR): delete the orphaned observer modules
      return True
  
  def remove_output_observer(
          node: Node,
          model: torch.nn.Module,
          modules: Dict[str, torch.nn.Module]):
      items = list(node.users.items())
      for output_obs_node, _ in items:
          assert is_activation_post_process_node(output_obs_node, modules)
          output_obs_node.replace_all_uses_with(node)
          model.graph.erase_node(output_obs_node)  # type: ignore[union-attr, operator]
  
  def swap_custom_module_to_observed(
          node: Node,
          qconfig: QConfigAny,
          modules: Dict[str, torch.nn.Module],
          prepare_custom_config_dict: Dict[str, Any]):
      custom_module = modules[node.target]  # type: ignore[index]
      custom_module_class_mapping = prepare_custom_config_dict.get(
          "float_to_observed_custom_module_class", {})
      observed_custom_module_class = \
          get_swapped_custom_module_class(
              custom_module, custom_module_class_mapping, qconfig)
      observed_custom_module = \
          observed_custom_module_class.from_float(custom_module)
      parent_name, name = _parent_name(node.target)
      setattr(modules[parent_name], name, observed_custom_module)
  
  def insert_observers_for_model(
      model: GraphModule,
      modules: Dict[str, torch.nn.Module],
      matches: Dict[str, MatchResult],
      qconfig_map: Dict[str, QConfigAny],
      graph: Graph,
      prepare_custom_config_dict: Dict[str, Any],
      equalization_config_map: Dict[str, Any],
      input_quantized_idxs: List[int],
      output_quantized_idxs: List[int],
  ) -> Optional[Node]:
      """
      Inserts observers, using the following high level algorithm:
  
      For each node in the graph:
        1. determine the target dtype of this node in the quantized graph, and save
             it for future steps
        2. determine the target dtype or all args and kwargs of this node
        3. if any arg or kwarg's target dtype does not match the current node's
             dtype, insert an observer
        4. if the current node needs an output observer, insert it
  
      For example:
  
      - starting graph:
          x0 -> linear -> x1
  
      - observed graph after processing x0:
          x0(fp32)
  
      - observed graph after processing linear:
          x0(fp32) -> x0_obs0(int8) -> linear(int8) -> linear_obs0(int8)
  
      - observed graph after processing x1:
          x0(fp32) -> x0_obs0(int8) -> linear(int8) -> linear_obs0(int8) -> x1
  
      After a node is processed, the naive observer placement is guaranteed to be
      complete for that node and all of its predecessors. There can be future
      passes which optimize the graph by deduplicating observers, etc.
      """
  
      node_name_to_target_dtype: Dict[str, Any] = {}
      cache_for_no_tensor_check: Dict[Node, bool] = dict()
  
      inputs_seen_counter = 0
      outputs_seen_counter = 0
      results_node = None
  
      # first, populate the dtype map based only on qconfig and qhandler
      # this assumes:
      # graph inputs are fp32 by default, and int8 where overriden
      # other nodes output dtype is specified by the qconfig
      modules = dict(model.named_modules(remove_duplicate=False))
      for node in model.graph.nodes:
          root_node, matched_nodes, pattern, qhandler, qconfig = matches.get(
              node.name, (None, None, None, None, None))
          node_name_to_target_dtype[node.name] = get_target_activation_dtype_for_node(
              node, qconfig, inputs_seen_counter, outputs_seen_counter,
              input_quantized_idxs, output_quantized_idxs, qhandler,
              modules, cache_for_no_tensor_check)
  
      # Second, for nodes with known input dtypes, propagate them throughout the
      # graph. For example, if there is a call such as
      #   x1 = x0.masked_fill(mask, 1)
      # we propagate the type of mask to be torch.bool
      propagate_dtypes_for_known_nodes(
          model.graph, node_name_to_target_dtype, matches)
  
      # After this point, the current node and all of its arguments
      # have a dtype assigned. Now, we insert observers for inputs
      # of this node (if needed for this node), and the output of this node
      # (if needed for this node).
  
      # Since we are mutating the graph as we go, we iterate over the original
      # nodes before observer insertion, instead of model.graph.nodes.
      nodes_before_observation = list(model.graph.nodes)
  
      for node in nodes_before_observation:
  
          if node.op == 'placeholder':
              # if a graph input is in fp32, it does not need observation
              # if a graph input is in int8, we assume the observation happens
              #   outside of the graph, and no additional observation is needed
              pass
  
          elif node.op in ('call_module', 'call_method', 'call_function', 'output'):
              # check for matches
              root_node, matched_nodes, pattern, qhandler, qconfig = matches.get(
                  node.name, (None, None, None, None, None))
              equalization_qconfig = equalization_config_map.get(node.name, None)
  
              this_node_dtype = node_name_to_target_dtype[node.name]
              output_not_a_tensor = this_node_dtype is None
              # TODO(future PR): consider stopping matching getitem
              is_getitem = node.op == 'call_function' and \
                  node.target == operator.getitem
  
              skip_inserting_observers = (
                  (qconfig is None) or
                  output_not_a_tensor or
                  is_getitem
              ) and (not node.op == 'output')
  
              if not skip_inserting_observers:
                  modules = dict(model.named_modules(remove_duplicate=False))
                  if node.op != 'output':
  
                      # This is currently only used for equalization.
                      # Checks if the current node is in a branch in which the two
                      # first layers are both being quantized.
                      #
                      # ex.       conv2
                      #         /
                      #      x -> conv1
                      #
                      # If this is the case, we will not apply equalization to the
                      # initial two layers.
                      is_quantized_branch = False
                      if (
                          len(node.args) > 0 and
                          isinstance(node.args[0], Node) and
                          len(node.args[0].users) > 1
                      ):
                          for user in node.args[0].users:
                              # Checks if there exists another user being quantized
                              is_user_quantized = (
                                  qconfig_map.get(user.name, None) is not None or
                                  (user.op == 'call_module' and isinstance(modules[str(user.target)], ObserverBase))
                              )
                              if user != node and is_user_quantized:
                                  is_quantized_branch = True
  
                      # this modifies node inplace
                      maybe_insert_input_observers_for_node(
                          node, qconfig, model, modules, graph,
                          node_name_to_target_dtype,
                          qhandler, prepare_custom_config_dict)
  
                      # Insert equalization input observers if needed
                      maybe_insert_input_equalization_observers_for_node(
                          node, equalization_qconfig, model, modules, graph,
                          node_name_to_target_dtype, is_quantized_branch)
  
                      is_last_node_of_pattern = root_node is node
                      is_general_tensor_value_op = \
                          (qhandler is not None and qhandler.is_general_tensor_value_op())
  
                      is_general_tensor_shape_op = \
                          (qhandler is not None and qhandler.is_general_tensor_shape_op())
  
                      if is_last_node_of_pattern and not is_general_tensor_shape_op:
                          # this returns the new observer node if it was needed
                          maybe_output_obs_node = maybe_insert_output_observer_for_node(
                              node, model, modules, graph, matches,
                              node_name_to_target_dtype, pattern, qhandler)
                          if maybe_output_obs_node is not None:
                              # Update users of original node to use the output observer
                              # instead. For example, change
                              #
                              #           next_node
                              #          /
                              #   cur_node -> obs
                              #
                              # to
                              #
                              #                 next_node
                              #                 /
                              #   cur_node -> obs
                              #
                              # We need to save orig users before updating uses because
                              # the list of users will change as we update uses
                              orig_users = list(node.users.keys())
                              for user_node in orig_users:
                                  if user_node is maybe_output_obs_node:
                                      continue
                                  user_node.replace_input_with(node, maybe_output_obs_node)
  
                              # for general tensor value ops, we modify the graph
                              # to make all inputs and outputs use the first input's
                              # observer
                              if is_general_tensor_value_op:
                                  if not maybe_make_input_output_share_observers(node, model, modules):
                                      remove_output_observer(node, model, modules)
  
                              if isinstance(qhandler, CustomModuleQuantizeHandler):
                                  swap_custom_module_to_observed(node, qconfig, modules, prepare_custom_config_dict)
  
                  else:  # output
                      maybe_insert_observers_before_graph_output(
                          node, output_quantized_idxs,
                          node_name_to_target_dtype, qconfig_map,
                          model, modules, graph)
  
          #
          # After this point, the current node has input and output observers
          # that it needs for itself inserted.
          #
  
          # increment the counters, so future inputs and outputs are assigned
          # correct dtypes
          if node.op == 'placeholder':
              inputs_seen_counter += 1
          elif node.op == 'output':
              outputs_seen_counter += 1
              results_node = node
  
      return results_node
  
  def run_prepare_fx_on_standalone_modules(
      model: torch.nn.Module,
      modules: Dict[str, torch.nn.Module],
      matches: Any,
      prepare_custom_config_dict: Dict[str, Any],
  ) -> None:
      """
      Runs prepare_fx on each standalone module. Note: this does
      not modify the graph, it just replaces the unobserved modules with
      their observed versions.
      """
      for (
          node_name,
          (root_node, matched_nodes, pattern, qhandler, qconfig),
      ) in matches.items():
          if qhandler is None:
              continue
          elif not isinstance(qhandler, StandaloneModuleQuantizeHandler):
              continue
  
          sm_qconfig_dict, sm_prepare_config_dict = \
              get_standalone_module_configs(
                  root_node, modules, prepare_custom_config_dict, qconfig)
  
          standalone_module = modules[root_node.target]
          prepare = \
              torch.quantization.quantize_fx._prepare_standalone_module_fx  # type: ignore[attr-defined]
          observed_standalone_module = \
              prepare(standalone_module, sm_qconfig_dict, sm_prepare_config_dict)
          preserved_attributes = \
              set(sm_prepare_config_dict.get("preserved_attributes", []))
          observed_standalone_module = ObservedStandaloneGraphModule(
              observed_standalone_module, observed_standalone_module.graph,
              preserved_attributes)
          parent_name, name = _parent_name(root_node.target)
          setattr(modules[parent_name], name,
                  observed_standalone_module)
          modules[root_node.target] = observed_standalone_module
  
  def save_state(
      observed: GraphModule,
      qconfig_map: Dict[str, QConfigAny],
      node_name_to_scope: Dict[str, Tuple[str, type]],
      patterns: Dict[Pattern, QuantizeHandler],
      prepare_custom_config_dict: Dict[str, Any],
      equalization_qconfig_map: Dict[str, Any],
  ) -> None:
      observed._patterns = patterns  # type: ignore[assignment]
      observed._qconfig_map = qconfig_map  # type: ignore[assignment]
      observed._prepare_custom_config_dict = \
          prepare_custom_config_dict  # type: ignore[assignment]
      observed._node_name_to_scope = node_name_to_scope  # type: ignore[assignment]
      observed._equalization_qconfig_map = equalization_qconfig_map  # type: ignore[assignment]
  
  def prepare(
          model: GraphModule,
          qconfig_dict: Any,
          node_name_to_scope: Dict[str, Tuple[str, type]],
          prepare_custom_config_dict: Optional[Dict[str, Any]] = None,
          equalization_qconfig_dict: Optional[Dict[str, Any]] = None,
          backend_config_dict: Optional[Dict[str, Any]] = None,
          is_standalone_module: bool = False) -> ObservedGraphModule:
      """ standalone_module means it a submodule that is not inlined in
      parent module, and will be quantized separately as one unit.
  
      How the standalone module is observed is specified by `input_quantized_idxs` and
      `output_quantized_idxs` in the prepare_custom_config for the standalone module
      Args:
          node_name_to_scope: mapping from node name to the scope of the module which contains the node.
          The scope is a tuple of fully qualified path of the module and the type of the module
      Returns:
          model(GraphModule): prepared standalone module
          attributes:
              _standalone_module_input_quantized_idxs(List[Int]): a list of
                  indexes for the graph input that is expected to be quantized,
                  same as input_quantized_idxs configuration provided
                  for the standalone module
              _standalone_module_output_quantized_idxs(List[Int]): a list of
                  indexs for the graph output that is quantized
                  same as input_quantized_idxs configuration provided
                  for the standalone module
      """
      if prepare_custom_config_dict is None:
          prepare_custom_config_dict = {}
      if equalization_qconfig_dict is None:
          equalization_qconfig_dict = {}
      if backend_config_dict is None:
          backend_config_dict = get_fbgemm_backend_config_dict()
  
      validate_backend_config_dict(backend_config_dict)
  
      additional_quant_patterns = \
          prepare_custom_config_dict.get("additional_quant_pattern", {})
      # mapping from a tuple of nodes in reverse order to uninitialized
      #   QuantizeHandler subclass. For example,
      # {
      #   # match a single node
      #   (<class 'torch.nn.modules.conv.Conv3d'>:
      #     <class 'torch.quantization.fx.quantize.ConvRelu'>),
      #   # match multiple nodes in reverse order
      #   ((<function relu at 0x7f766a7360d0>, <built-in function add>):
      #     <class 'torch.quantization.fx.quantize.Add'>),
      # }
      quant_patterns = backend_config_dict["quant_patterns"]
      patterns: Dict[Pattern, QuantizeHandler] = get_combined_dict(
          quant_patterns, additional_quant_patterns)
  
      convert_dict_to_ordered_dict(qconfig_dict)
      convert_dict_to_ordered_dict(equalization_qconfig_dict)
      flattened_qconfig_dict = get_flattened_qconfig_dict(qconfig_dict)
      # TODO: support regex as well
      propagate_qconfig_(model, flattened_qconfig_dict)
  
      if model.training:
          additional_qat_module_mapping = prepare_custom_config_dict.get(
              "additional_qat_module_mapping", {})
          qat_swap_modules(model, additional_qat_module_mapping)
          qconfig_dict = update_qconfig_for_qat(qconfig_dict, additional_qat_module_mapping)
  
      qconfig_dict = update_qconfig_for_fusion(model, qconfig_dict)
      equalization_qconfig_dict = update_qconfig_for_fusion(model, equalization_qconfig_dict)
  
      # mapping from fully qualified module name to module instance
      # for example,
      # {
      #   '': Model(...),
      #   'linear': Linear(...),
      #   'linear.weight_fake_quant': PerChannelMinMaxObserver(...),
      # }
      modules = dict(model.named_modules())
  
      # fill qconfig_map, a map from node name to qconfig, used in find_matches
      equalization_qconfig_map = generate_qconfig_map(model, modules, model.graph, equalization_qconfig_dict, node_name_to_scope)
      qconfig_map = generate_qconfig_map(model, modules, model.graph, qconfig_dict, node_name_to_scope)
  
      # match the patterns that will get quantized
      standalone_module_name_configs = prepare_custom_config_dict.get(
          "standalone_module_name", [])
      standalone_module_class_configs = prepare_custom_config_dict.get(
          "standalone_module_class", [])
  
      standalone_module_names = [config[0] for config in standalone_module_name_configs]
      standalone_module_classes = [config[0] for config in standalone_module_class_configs]
      custom_module_classes = get_custom_module_class_keys(
          prepare_custom_config_dict, "float_to_observed_custom_module_class")
      matches = find_matches(
          model.graph, modules, patterns, qconfig_map, standalone_module_names,
          standalone_module_classes, custom_module_classes)
  
      input_quantized_idxs: List[int] = prepare_custom_config_dict.get(
          "input_quantized_idxs", [])
      output_quantized_idxs: List[int] = prepare_custom_config_dict.get(
          "output_quantized_idxs", [])
  
      run_prepare_fx_on_standalone_modules(
          model, modules, matches, prepare_custom_config_dict)
  
      result_node = insert_observers_for_model(
          model, modules, matches, qconfig_map,
          model.graph, prepare_custom_config_dict,
          equalization_qconfig_map,
          input_quantized_idxs, output_quantized_idxs)
  
      save_state(model, qconfig_map, node_name_to_scope, patterns,
                 prepare_custom_config_dict, equalization_qconfig_map)
      preserved_attributes = set(prepare_custom_config_dict.get("preserved_attributes", []))
      model = ObservedGraphModule(model, model.graph, preserved_attributes)
      if is_standalone_module:
          assert result_node is not None
          assert isinstance(result_node.args[0], Node), \
              "standalone module only supports returning simple value currently"\
              "(not tuple, dict etc.)"
          # these inputs are observed in parent
          # converting List[int] to Tensor since module attribute is
          # Union[Tensor, Module]
          model._standalone_module_input_quantized_idxs = \
              torch.tensor(input_quantized_idxs)
          model._standalone_module_output_quantized_idxs = torch.tensor(output_quantized_idxs)
      return model
  