cross_device_ops.py

# Copyright 2018 The TensorFlow 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.
# ==============================================================================
"""Classes for different algorithms of reduction and broadcasting."""

import collections
import copy
import multiprocessing.dummy
import multiprocessing.pool
import threading

import six

from tensorflow.python.client import device_lib
from tensorflow.python.distribute import collective_util
from tensorflow.python.distribute import cross_device_utils
from tensorflow.python.distribute import device_util
from tensorflow.python.distribute import distribute_utils
from tensorflow.python.distribute import ps_values
from tensorflow.python.distribute import reduce_util
from tensorflow.python.distribute import tpu_values
from tensorflow.python.distribute import values as value_lib
from tensorflow.python.distribute import values_util
from tensorflow.python.eager import context
from tensorflow.python.eager import def_function
from tensorflow.python.framework import indexed_slices
from tensorflow.python.framework import kernels
from tensorflow.python.framework import ops
from tensorflow.python.framework import tensor_util
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import resource_variable_ops
from tensorflow.python.platform import tf_logging as logging
from tensorflow.python.util import nest
from tensorflow.python.util.tf_export import tf_export
from tensorflow.tools.docs import doc_controls


def check_destinations(destinations):
  """Checks whether `destinations` is not empty.

  Args:
    destinations: a `DistributedValues`, variable, or string object.

  Returns:
    Boolean which is True if `destinations` is not empty.
  """
  # Calling bool() on a ResourceVariable is not allowed.
  if isinstance(destinations,
                (resource_variable_ops.BaseResourceVariable, ops.Tensor)):
    return bool(destinations.device)
  return bool(destinations)


def validate_destinations(destinations):
  """Validates the `destination` is one of expected types."""
  if not isinstance(
      destinations,
      (value_lib.DistributedValues, ops.Tensor, indexed_slices.IndexedSlices,
       ps_values.AggregatingVariable, six.string_types,
       tpu_values.TPUMirroredVariable
      )) and not resource_variable_ops.is_resource_variable(destinations):
    raise ValueError("destinations must be one of a `DistributedValues` object,"
                     " a tf.Variable object, or a device string.")

  if not check_destinations(destinations):
    raise ValueError("destinations can not be empty")


def reduce_non_distributed_value(reduce_op,
                                 value,
                                 destinations,
                                 num_replicas_in_graph,
                                 canonicalize_devices=True):
  """Reduce a non-DistributedValue `value` to `destinations`."""
  if isinstance(value, value_lib.DistributedValues):
    raise ValueError("You are passing a `DistributedValues` to "
                     "`reduce_non_distributed_value`, which is not allowed.")

  # If the same value is present on all replicas then the PerReplica value will
  # be a single value. We also handle the case when `value` is a single value
  # and equal to 0.
  # TODO:(b/138823479): handle the tensor value properly.
  if not tensor_util.is_tf_type(value) and value == 0:
    return 0
  # If there is only a single value and the reduce op is MEAN,
  # that value should be on all destinations.
  if reduce_op == reduce_util.ReduceOp.MEAN:
    return value
  elif num_replicas_in_graph != 1:
    # We do not support a reduce op of SUM if the value is the same across
    # all replicas. We call this as part of assign functions for
    # MirroredVariables and summing up identical values across replicas is not
    # clearly defined.
    raise ValueError("A non-DistributedValues value %s cannot be reduced with "
                     "the given reduce op %s." % (value, reduce_op))
  else:
    validate_destinations(destinations)
    return simple_broadcast(
        value, destinations, canonicalize_devices=canonicalize_devices)


def _make_tensor_into_per_replica(input_tensor):
  """Converts a single tensor into a PerReplica object."""
  if isinstance(input_tensor, (tuple, list)):
    raise ValueError("Cannot convert `input_tensor` to a `PerReplica` object, "
                     "got %r but expected a object that is not a tuple or list."
                     % (input_tensor,))
  if isinstance(input_tensor, value_lib.PerReplica):
    return input_tensor
  elif hasattr(input_tensor, "device"):
    return value_lib.PerReplica((input_tensor,))
  else:
    raise ValueError("Cannot convert `input_tensor` to a `PerReplica` object "
                     "because it doesn't have device set.")


def _normalize_value_destination_pairs(value_destination_pairs):
  """Converts each tensor into a PerReplica object in the input list."""
  result = []

  value_destination_pairs = list(value_destination_pairs)

  if not isinstance(value_destination_pairs, (list, tuple)):
    raise ValueError("`value_destination_pairs` should be a list or tuple")
  for pair in value_destination_pairs:
    if not isinstance(pair, tuple):
      raise ValueError(
          "Each element of `value_destination_pairs` should be a tuple.")
    if len(pair) != 2:
      raise ValueError("Each element of `value_destination_pairs` should be a "
                       "tuple of size 2.")

    per_replica = _make_tensor_into_per_replica(pair[0])
    result.append((per_replica, pair[1]))
  return result


def _validate_value_destination_pairs(value_destination_pairs):
  """Validates value_destination_pairs are valid."""
  # TODO(yuefengz): raise exceptions instead of returning False.
  if not value_destination_pairs: return False
  if not isinstance(value_destination_pairs, (list, tuple)): return False
  if not all(isinstance(pair, tuple) for pair in value_destination_pairs):
    return False
  if not all(isinstance(v[0], value_lib.PerReplica)
             for v in value_destination_pairs):
    return False
  return True


# TODO(yuefengz): consider calling this function in the caller of
# CrossDeviceOps.
def get_devices_from(destinations, canonicalize_devices=True):
  if isinstance(destinations, value_lib.DistributedValues):
    return destinations._devices  # pylint: disable=protected-access
  if canonicalize_devices:
    if isinstance(destinations, six.string_types):
      return (device_util.resolve(destinations),)
    return (device_util.resolve(destinations.device),)

  # Let placer canonicalize and resolve destination devices.
  if isinstance(destinations, six.string_types):
    return (device_util.canonicalize_without_job_and_task(destinations),)
  return (device_util.canonicalize_without_job_and_task(destinations.device),)


def _devices_match(left, right, canonicalize_devices=True):
  return left is right or set(get_devices_from(
      left, canonicalize_devices)) == set(
          get_devices_from(right, canonicalize_devices))


def _all_devices_match(value_destination_pairs, canonicalize_devices=True):
  if not all(
      _devices_match(v, d, canonicalize_devices)
      for v, d in value_destination_pairs):
    return False
  if not all(
      _devices_match(v, value_destination_pairs[0][0], canonicalize_devices)
      for v, _ in value_destination_pairs[1:]):
    return False
  return True


def simple_broadcast(value,
                     destinations,
                     always_mirrored=False,
                     canonicalize_devices=True):
  """Broadcast `value` to `destinations` using simple copies."""
  devices = get_devices_from(destinations, canonicalize_devices)
  if len(devices) == 1 and not always_mirrored:
    return cross_device_utils.copy_tensor_or_indexed_slices_to_device(
        value, devices[0])
  else:
    value_updates = []
    for d in devices:
      value_updates.append(
          cross_device_utils.copy_tensor_or_indexed_slices_to_device(value, d))
    return distribute_utils.regroup(value_updates,
                                    wrap_class=value_lib.Mirrored)


def _simple_reduce(per_replica_value, reduce_to_device, accumulation_fn,
                   reduce_op):
  """Reduces the value by accumulation_fn and reduce_op."""
  all_values = per_replica_value.values
  if not all_values:
    raise ValueError("`per_replica_value` must be non-empty")
  count = len(all_values)

  with ops.device(reduce_to_device):
    with context.device_policy(context.DEVICE_PLACEMENT_SILENT):
      reduced = cross_device_utils.aggregate_tensors_or_indexed_slices(
          all_values, accumulation_fn)
      if reduce_op == reduce_util.ReduceOp.MEAN:
        reduced = cross_device_utils.divide_by_n_tensors_or_indexed_slices(
            reduced, count)
      elif reduce_op != reduce_util.ReduceOp.SUM:
        raise ValueError("`reduce_op` must be Reduce.SUM or Reduce.MEAN.")
  return reduced


def _simple_gather(per_replica_value, reduce_to_device, axis):
  """Concatenate all values in the DistributedValues input and return."""
  all_values = per_replica_value.values
  if not all_values:
    raise ValueError("`per_replica_value` must be non-empty")

  with ops.device(reduce_to_device):
    with context.device_policy(context.DEVICE_PLACEMENT_SILENT):
      gathered = array_ops.concat(all_values, axis)
  return gathered


@tf_export("distribute.CrossDeviceOps")
class CrossDeviceOps(object):
  """Base class for cross-device reduction and broadcasting algorithms.

  The main purpose of this class is to be passed to
  `tf.distribute.MirroredStrategy` in order to choose among different cross
  device communication implementations. Prefer using the methods of
  `tf.distribute.Strategy` instead of the ones of this class.

  Implementations:
  * `tf.distribute.ReductionToOneDevice`
  * `tf.distribute.NcclAllReduce`
  * `tf.distribute.HierarchicalCopyAllReduce`
  """

  def __init__(self):
    self._canonicalize_devices = True
    pass

  @property
  def _num_between_graph_workers(self):
    # Returns 1 by default, the value may be overridden by sub classes.
    return 1

  def reduce(self, reduce_op, per_replica_value, destinations, options=None):
    """Reduce `per_replica_value` to `destinations`.

    See `tf.distribute.StrategyExtended.reduce_to`. This can only be called in
    the cross-replica context.

    Args:
      reduce_op: a `tf.distribute.ReduceOp` specifying how values should be
        combined.
      per_replica_value: a `tf.distribute.DistributedValues`, or a `tf.Tensor`
        like object.
      destinations: a `tf.distribute.DistributedValues`, a `tf.Variable`, a
        `tf.Tensor` alike object, or a device string. It specifies the devices
        to reduce to. To perform an all-reduce, pass the same to `value` and
        `destinations`. Note that if it's a `tf.Variable`, the value is reduced
        to the devices of that variable, and this method doesn't update the
        variable.
      options: a `tf.distribute.experimental.CommunicationOptions`. See
        `tf.distribute.experimental.CommunicationOptions` for details.

    Returns:
      A `tf.Tensor` or `tf.distribute.DistributedValues`.

    Raises:
      ValueError: if per_replica_value can't be converted to a
        `tf.distribute.DistributedValues` or if destinations is not a string,
        `tf.Variable` or `tf.distribute.DistributedValues`.
    """
    if options is None:
      options = collective_util.Options()
    if not isinstance(per_replica_value, value_lib.DistributedValues):
      per_replica_value = _make_tensor_into_per_replica(per_replica_value)

    validate_destinations(destinations)

    # Shortcut if `per_replica_value` only contains one value.
    if self._num_between_graph_workers == 1 and len(
        per_replica_value.values) == 1 and _devices_match(
            per_replica_value, destinations, self._canonicalize_devices):
      with ops.device(per_replica_value.values[0].device):
        v = array_ops.identity(per_replica_value.values[0])
      return distribute_utils.regroup((v,), wrap_class=value_lib.Mirrored)

    if options is None:
      options = collective_util.Options()
    return self.reduce_implementation(reduce_op, per_replica_value,
                                      destinations, options)

  def _gather(self, per_replica_value, destinations, axis, options=None):
    """Gather `per_replica_value` to `destinations`.

    Args:
      per_replica_value: a `tf.distribute.DistributedValues`, or a `tf.Tensor`
        like object.
      destinations: a `tf.distribute.DistributedValues`, a `tf.Variable`, a
        `tf.Tensor` alike object, or a device string. It specifies the devices
        to gather to. To perform an all-gather, pass the same to `value` and
        `destinations`. Note that if it's a `tf.Variable`, the value is gathered
        to the devices of that variable, and this method doesn't update the
        variable.
      axis: specifies the dimension to gather along within each replica's
        tensor.
      options: a `tf.distribute.experimental.CommunicationOptions`. See
        `tf.distribute.experimental.CommunicationOptions` for details.

    Returns:
      A `tf.Tensor` or `tf.distribute.DistributedValues`

    Raises:
      ValueError: if per_replica_value can't be converted to a
        `tf.distribute.DistributedValues` or if destinations is not a string,
        `tf.Variable` or `tf.distribute.DistributedValues`.
    """
    if isinstance(per_replica_value, indexed_slices.IndexedSlices):
      raise NotImplementedError("gather/all_gather does not support "
                                "IndexedSlices")
    if options is None:
      options = collective_util.Options()

    if not isinstance(per_replica_value, value_lib.DistributedValues):
      per_replica_value = _make_tensor_into_per_replica(per_replica_value)

    validate_destinations(destinations)

    # Shortcut if `per_replica_value` only contains one value.
    if self._num_between_graph_workers == 1 and len(
        per_replica_value.values) == 1 and _devices_match(
            per_replica_value, destinations, self._canonicalize_devices):
      with ops.device(per_replica_value.values[0].device):
        v = array_ops.identity(per_replica_value.values[0])
      return distribute_utils.regroup((v,), wrap_class=value_lib.Mirrored)

    return self._gather_implementation(per_replica_value, destinations, axis,
                                       options)

  def _gather_implementation(self, per_replica_value, destinations, axis,
                             options):
    """Implementation of `gather` method of `tf.distribute.CrossDeviceOps`.

    Overriding this method is useful for subclass implementers.

    Args:
      per_replica_value: a `tf.distribute.DistributedValues`, or a `tf.Tensor`
        like object.
      destinations: a `tf.distribute.DistributedValues`, a `tf.Variable`, a
        `tf.Tensor` alike object, or a device string. It specifies the devices
        to gather to. To perform an all-gather, pass the same to `value` and
        `destinations`. Note that if it's a `tf.Variable`, the value is gathered
        to the devices of that variable, this method doesn't update the
        variable.
      axis: specifies the dimension to gather along within each replica's
        tensor.
      options: a `tf.distribute.experimental.CommunicationOptions`. See
        `tf.distribute.experimental.CommunicationOptions` for details.

    Returns:
      A `tf.Tensor` or `tf.distribute.DistributedValues`.

    Raises:
      ValueError: if per_replica_value can't be converted to a
        `tf.distribute.DistributedValues` or if destinations is not a string,
        `tf.Variable` or `tf.distribute.DistributedValues`.
    """
    raise NotImplementedError(
        "_gather method must be implemented in descendants.")

  def batch_reduce(self, reduce_op, value_destination_pairs, options=None):
    """Reduce values to destinations in batches.

    See `tf.distribute.StrategyExtended.batch_reduce_to`. This can only be
    called in the cross-replica context.

    Args:
      reduce_op: a `tf.distribute.ReduceOp` specifying how values should be
        combined.
      value_destination_pairs: a sequence of (value, destinations) pairs. See
        `tf.distribute.CrossDeviceOps.reduce` for descriptions.
      options: a `tf.distribute.experimental.CommunicationOptions`. See
        `tf.distribute.experimental.CommunicationOptions` for details.

    Returns:
      A list of `tf.Tensor` or `tf.distribute.DistributedValues`, one per pair
      in `value_destination_pairs`.

    Raises:
      ValueError: if `value_destination_pairs` is not an iterable of
        tuples of `tf.distribute.DistributedValues` and destinations.
    """
    if options is None:
      options = collective_util.Options()
    # TODO(yuefengz): if destinations are different, split into several
    # `_batch_reduce` invocations.
    if not _validate_value_destination_pairs(value_destination_pairs):
      # If the first element of each pair is a tensor, we try to turn it into a
      # PerReplica object.
      value_destination_pairs = _normalize_value_destination_pairs(
          value_destination_pairs)

    for _, d in value_destination_pairs:
      validate_destinations(d)

    # Shortcut all PerReplica objects only contain one value.
    if self._num_between_graph_workers == 1 and _all_devices_match(
        value_destination_pairs, self._canonicalize_devices) and len(
            value_destination_pairs[0][0].values) == 1:
      return [
          distribute_utils.regroup(v.values, wrap_class=value_lib.Mirrored)
          for v, _ in value_destination_pairs
      ]

    if options is None:
      options = collective_util.Options()
    return self.batch_reduce_implementation(reduce_op, value_destination_pairs,
                                            options)

  def broadcast(self, tensor, destinations):
    """Broadcast `tensor` to `destinations`.

    This can only be called in the cross-replica context.

    Args:
      tensor: a `tf.Tensor` like object. The value to broadcast.
      destinations: a `tf.distribute.DistributedValues`, a `tf.Variable`, a
        `tf.Tensor` alike object, or a device string. It specifies the devices
        to broadcast to. Note that if it's a `tf.Variable`, the value is
        broadcasted to the devices of that variable, this method doesn't update
        the variable.

    Returns:
      A `tf.Tensor` or `tf.distribute.DistributedValues`.
    """
    validate_destinations(destinations)
    return self.broadcast_implementation(tensor, destinations)

  @doc_controls.for_subclass_implementers
  def reduce_implementation(self, reduce_op, per_replica_value, destinations,
                            options):
    """Implementation of `reduce`.

    Overriding this method is useful for subclass implementers.

    Args:
      reduce_op: a `tf.distribute.ReduceOp` specifying how values should be
        combined.
      per_replica_value: a `tf.distribute.DistributedValues`, or a `tf.Tensor`
        like object.
      destinations: a `tf.distribute.DistributedValues`, a `tf.Variable`, a
        `tf.Tensor` alike object, or a device string. It specifies the devices
        to reduce to. To perform an all-reduce, pass the same to `value` and
        `destinations`. Note that if it's a `tf.Variable`, the value is reduced
        to the devices of that variable, this method doesn't update the
        variable.
      options: a `tf.distribute.experimental.CommunicationOptions`. See
        `tf.distribute.experimental.CommunicationOptions` for details.

    Returns:
      A `tf.Tensor` or `tf.distribute.DistributedValues`.

    Raises:
      ValueError: if per_replica_value can't be converted to a
        `tf.distribute.DistributedValues` or if destinations is not a string,
        `tf.Variable` or `tf.distribute.DistributedValues`.
    """
    raise NotImplementedError(
        "_reduce method must be implemented in descendants.")

  @doc_controls.for_subclass_implementers
  def batch_reduce_implementation(self, reduce_op, value_destination_pairs,
                                  options):
    """Implementation of `batch_reduce`.

    Overriding this method is useful for subclass implementers.

    Args:
      reduce_op: a `tf.distribute.ReduceOp` specifying how values should be
        combined.
      value_destination_pairs: a sequence of (value, destinations) pairs. See
        `reduce` for descriptions.
      options: a `tf.distribute.experimental.CommunicationOptions`. See
        `tf.distribute.experimental.CommunicationOptions` for details.

    Returns:
      A list of `tf.Tensor` or `tf.distribute.DistributedValues`, one per pair
      in `value_destination_pairs`.

    Raises:
      ValueError: if `value_destination_pairs` is not an iterable of
        tuples of `tf.distribute.DistributedValues` and destinations.
    """
    raise NotImplementedError(
        "batch_reduce_implementation method must be implemented in descendants."
    )

  @doc_controls.for_subclass_implementers
  def broadcast_implementation(self, tensor, destinations):
    """Implementation of `broadcast`.

    Args:
      tensor: a `tf.Tensor` like object. The value to broadcast.
      destinations: a `tf.distribute.DistributedValues`, a `tf.Variable`, a
        `tf.Tensor` alike object, or a device string. It specifies the devices
        to broadcast to.
        `destinations`. Note that if it's a `tf.Variable`, the value is
        broadcasted to the devices of that variable, this method doesn't update
        the variable.

    Returns:
      A `tf.Tensor` or `tf.distribute.DistributedValues`.
    """
    return simple_broadcast(
        tensor,
        destinations,
        always_mirrored=True,
        canonicalize_devices=self._canonicalize_devices)

  # ========================== Collective APIs ================================
  #
  # Different than `reduce`, `batch_reduce` and `broadcast` which must be called
  # in cross-replcia context, collective APIs are to be called in replica
  # context.

  def _all_reduce(self, reduce_op, value, replica_id, options):
    """All-reduce the `value` across all replicas so that all get the result.

    `value` can be a nested structure of tensors or `IndexedSlices`. The
    implementation should generally batch the all-reduces when possible.
    `options` can be set to hint the batching behavior.

    This API must be called in a replica context.

    Args:
      reduce_op: A `tf.distribute.ReduceOp` value specifying how values should
        be combined.
      value: Value to be reduced. A tensor or a nested structure of tensors or
        `IndexedSlices`.
      replica_id: An interger indicating the id of the replica where this
        all_reduce is called under. This is the local replica id that ranges
        from 0 to len(local_devices) - 1.
      options: A `tf.distribute.experimental.CommunicationOptions`.

    Returns:
      A tensor/IndexedSlices or a nested strucutre of tensors/IndexedSlices with
      the reduced values. The structure is the same as `value`.
    """
    raise NotImplementedError("_all_reduce must be implemented in descendants.")


@tf_export("distribute.ReductionToOneDevice")
class ReductionToOneDevice(CrossDeviceOps):
  """A CrossDeviceOps implementation that copies values to one device to reduce.

  This implementation always copies values to one device to reduce them, then
  broadcast reduced values to the destinations. It doesn't support efficient
  batching.

  Here is how you can use `ReductionToOneDevice` in
  `tf.distribute.MirroredStrategy`:

  ```
    strategy = tf.distribute.MirroredStrategy(
      cross_device_ops=tf.distribute.ReductionToOneDevice())
  ```
  """

  def __init__(self, reduce_to_device=None, accumulation_fn=None):
    """Initializes with a device to reduce to and a way to accumulate.

    Args:
      reduce_to_device: the intermediate device to reduce to. If None, reduce
        to the first device in `destinations` of the `reduce` method.
      accumulation_fn: a function that does accumulation.  If None,
        `tf.math.add_n` is used.
    """
    self.reduce_to_device = reduce_to_device
    self.accumulation_fn = accumulation_fn or math_ops.add_n
    super(ReductionToOneDevice, self).__init__()

  def reduce_implementation(self, reduce_op, per_replica_value, destinations,
                            options):
    del options  # Unused.
    if check_destinations(destinations):
      devices = get_devices_from(destinations, self._canonicalize_devices)
    else:
      devices = get_devices_from(per_replica_value, self._canonicalize_devices)
    reduce_to_device = self.reduce_to_device or devices[0]
    logging.log_first_n(
        logging.INFO,
        "Reduce to %s then broadcast to %r." % (reduce_to_device, devices), 10)
    reduced = _simple_reduce(per_replica_value, reduce_to_device,
                             self.accumulation_fn, reduce_op)
    return self.broadcast(reduced, destinations)

  def _gather_implementation(self, per_replica_value, destinations, axis,
                             options):
    del options  # Unused.
    if check_destinations(destinations):
      devices = get_devices_from(destinations, self._canonicalize_devices)
    else:
      devices = get_devices_from(per_replica_value, self._canonicalize_devices)
    reduce_to_device = self.reduce_to_device or devices[0]
    logging.log_first_n(
        logging.INFO,
        "Gather to %s then broadcast to %r." % (reduce_to_device, devices), 10)
    gathered = _simple_gather(per_replica_value, reduce_to_device, axis)
    return self.broadcast(gathered, destinations)

  def batch_reduce_implementation(self, reduce_op, value_destination_pairs,
                                  options):
    return [
        self.reduce_implementation(
            reduce_op, t, destinations=v, options=options)
        for t, v in value_destination_pairs
    ]


def _group_value_by_device(per_replica_values):
  """Group values into sublists by their devices.

  This grouping is needed to call the all-reduce library because it expects a
  list of the following form:
    [[(grad0_gpu0, v0_gpu0), (grad1_gpu0, v1_gpu0), (grad2_gpu0, v2_gpu0) ...],
     [(grad0_gpu1, v0_gpu1), (grad1_gpu1, v1_gpu1), (grad2_gpu1, v2_gpu1) ...],
     [(grad0_gpu2, v0_gpu2), (grad1_gpu0, v1_gpu2), (grad2_gpu0, v2_gpu2) ...],
     ...
    ]

  Args:
    per_replica_values: a list of PerReplica objects.

  Returns:
    a list of lists, each sublist has components for its corresponding device of
      PerReplica objects, paired with a None.
  """
  destinations = per_replica_values[0]._devices  # pylint: disable=protected-access
  grouped = [[] for _ in range(len(destinations))]
  for per_replica_value in per_replica_values:
    # pylint: disable=protected-access
    for i, v in enumerate(per_replica_value.values):
      assert per_replica_value._devices == destinations
      grouped[i].append((v, None))
  return grouped


def _ungroup_and_make_mirrored(grouped_reduced,
                               destinations,
                               reduce_op,
                               num_between_graph_workers=1):
  """Ungroup results from all-reduce and make Mirrored objects.

  Each all-reduce result will be divided by the number of destinations before
  Mirrored objects are created if reduce_op is "mean".

  Args:
    grouped_reduced: a list of lists, each sublist has components for each
      device, paired with a None. It is the result from
      cross_device_utils.aggregate_gradients_using*.
    destinations: a value to colocate the result with.
    reduce_op: Indicates how values will be aggregated. Accepted values
      are `tf.distribute.ReduceOp.SUM`, `tf.distribute.ReduceOp.MEAN`.
    num_between_graph_workers: number of workers in the between-graph
      replication.

  Returns:
    a list of Mirrored objects.
  """
  num_replicas = len(get_devices_from(destinations)) * num_between_graph_workers
  index = [[] for _ in range(len(grouped_reduced[0]))]
  for per_replica_reduced in grouped_reduced:
    for i, (v, _) in enumerate(per_replica_reduced):
      if reduce_op == reduce_util.ReduceOp.MEAN:
        with ops.device(v.device):
          index[i].append(v / num_replicas)
      else:
        index[i].append(v)
  return [distribute_utils.regroup(
      v, wrap_class=value_lib.Mirrored) for v in index]


class _ConcatAndSplitPacker(object):
  """Concatenate and split tensors for reduction."""

  def __init__(self, num_packs=1):
    """Initialize the _ConcatAndSplitPacker object.

    Args:
      num_packs: specifies the number of split packs that will be
        formed.

    Raises:
      ValueError: if num_packs is not greater than 0.
    """
    if num_packs <= 0:
      raise ValueError("num_packs must be greater than zero.")
    self.num_packs = num_packs

  def pack(self, grouped_grads_and_vars):
    """Pack tensors."""
    self.grouped_grads_and_vars = grouped_grads_and_vars
    self.all_device_shapes = []
    self.all_device_sizes = []

    device_grad_packs = []
    for device_grads_and_vars in grouped_grads_and_vars:
      with ops.colocate_with(device_grads_and_vars[0][0]):
        # Flatten all the grads.
        flat_grads = [
            array_ops.reshape(g, [-1]) for g, _ in device_grads_and_vars
        ]
        # Remember the original shape of all the grads.
        device_shapes = [array_ops.shape(g) for g, _ in device_grads_and_vars]
        # Remember the original sizes of all the grads.
        device_sizes = [array_ops.size(g) for g, _ in device_grads_and_vars]
        # Concat all the flat grads into a big flat tensor.
        concat_grads = array_ops.concat(flat_grads, 0)

        # Split the big tensor into num_splits packs. In cases where the
        # total size is not divisible num_splits, the last pack gets
        # more elements.
        # TODO(zhengxq): it is also possible to optimize away all the concat
        # as well.
        num_splits = self.num_packs

        # The array_ops.size function will sometimes remove static shapes. So if
        # all gradient shapes are defined, we use another method to get the
        # total size.
        # TODO(yuefengz): move this logic to array_ops.size.
        if all(g.shape.is_fully_defined() for g, _ in device_grads_and_vars):
          total_grad_size = sum(
              [g.shape.num_elements() for g, _ in device_grads_and_vars])
        else:
          total_grad_size = array_ops.size(concat_grads)

        split_size = total_grad_size // num_splits
        split_size_last = total_grad_size - split_size * (num_splits - 1)
        split_sizes = [split_size] * (num_splits - 1) + [split_size_last]
        grad_packs = array_ops.split(concat_grads, split_sizes)

        # Ready to aggregate the repacked gradients, with fake variables.
        # TODO(zhengxq): It is hacky to have to use fake variables.
        # We should remove the need for variables in
        # aggregate_gradients_using*.
        device_grad_packs.append(zip(grad_packs, [None] * num_splits))
        self.all_device_shapes.append(device_shapes)
        self.all_device_sizes.append(device_sizes)

    return device_grad_packs

  def unpack(self, summed_device_grad_packs):
    """Reverse the pack."""
    aggregated_device_grads = []
    for (summed_device_grad_packs,
         device_grads_and_vars, device_shapes, device_sizes) in zip(
             summed_device_grad_packs, self.grouped_grads_and_vars,
             self.all_device_shapes, self.all_device_sizes):
      # pylint: enable=line-too-long
      # Reverse the packing operations in the previous steps. Form the
      # summed gradients back into their original shapes.
      with ops.colocate_with(summed_device_grad_packs[0][0]):
        # Form a list of the summed grad packs.
        device_grad_packs = [g for g, _ in summed_device_grad_packs]

        # Concat them back into a big flat tensor.
        device_grads_concat = array_ops.concat(device_grad_packs, 0)

        # Split the tensors back into their original sizes.
        grads_with_sizes = array_ops.split(device_grads_concat, device_sizes)

        # Reshape the tensors back into their original shapes.
        grads_with_shapes = [
            array_ops.reshape(grad, shape)
            for shape, grad in zip(device_shapes, grads_with_sizes)
        ]

        # Form the list with the original list of variables.
        summed_device_grads = [
            (g, v) for g, (_, v) in zip(grads_with_shapes,
                                        device_grads_and_vars)
        ]
        aggregated_device_grads.append(summed_device_grads)
    return aggregated_device_grads


def _pack_tensors(device_grads, num_packs=0):
  """Pack tensors if specified."""
  if num_packs > 0:
    tensor_packer = _ConcatAndSplitPacker(num_packs)
    device_grad_packs = tensor_packer.pack(device_grads)
  else:
    tensor_packer = None
    device_grad_packs = device_grads
  return device_grad_packs, tensor_packer


def _unpack_tensors(reduced, tensor_packer=None):
  """Unpack tensors if they are packed before all-reduce."""
  if tensor_packer:
    return tensor_packer.unpack(reduced)
  return reduced


class AllReduceCrossDeviceOps(CrossDeviceOps):
  """All-reduce implementation of CrossDeviceOps.

  It performs all-reduce when applicable using NCCL or hierarchical copy. For
  the batch API, tensors will be repacked or aggregated for more efficient
  cross-device transportation.

  For reduces that are not all-reduce, it falls back to
  `tf.distribute.ReductionToOneDevice`.
  """

  def __init__(self, all_reduce_alg="nccl", num_packs=1):
    """Initializes the object.

    Args:
      all_reduce_alg: the all-reduce algorithm to use, currently only "nccl" or
        "hierarchical_copy" are supported.
      num_packs: a non-negative integer. The number of packs to split values
        into. If zero, no packing will be done.
    """
    self._all_reduce_alg = all_reduce_alg
    self._num_packs = num_packs
    self._simple_cross_replica_ops = ReductionToOneDevice()
    super(AllReduceCrossDeviceOps, self).__init__()

  def reduce_implementation(self, reduce_op, per_replica_value, destinations,
                            options):
    del options  # Unused.
    # To use NCCL or all-reduce, source and destination devices should match,
    # and none of the devices should be CPU.
    if (_devices_match(per_replica_value, destinations) and
        not any("cpu" in d.lower() for d in get_devices_from(destinations))):
      return self._batch_all_reduce(reduce_op, [per_replica_value])[0]
    else:
      return self._simple_cross_replica_ops.reduce(reduce_op, per_replica_value,
                                                   destinations)

  def batch_reduce_implementation(self, reduce_op, value_destination_pairs,
                                  options):
    if _all_devices_match(value_destination_pairs):
      return self._batch_all_reduce(reduce_op,
                                    [v[0] for v in value_destination_pairs])
    else:
      return [
          self.reduce_implementation(reduce_op, value, dest, options)
          for value, dest in value_destination_pairs
      ]

  def _batch_all_reduce(self, reduce_op, per_replica_values):
    """All-reduce algorithm in a batch."""
    dense_values, dense_indices, sparse_values, sparse_indices = (
        cross_device_utils.split_by_sparsity(per_replica_values))
    if dense_values:
      dense_results = self._do_batch_all_reduce(reduce_op, dense_values)
    else:
      dense_results = []
    if sparse_values:
      sparse_results = self._do_batch_all_reduce_sparse(reduce_op,
                                                        sparse_values)
    else:
      sparse_results = []
    return cross_device_utils.stitch_values(((dense_results, dense_indices),
                                             (sparse_results, sparse_indices)))

  def _do_batch_all_reduce(self, reduce_op, dense_values):
    """Run batch all-reduces."""
    logging.log_first_n(
        logging.INFO,
        "batch_all_reduce: %d all-reduces with algorithm = %s, num_packs = %d" %
        (len(dense_values), self._all_reduce_alg, self._num_packs), 10)

    destinations = dense_values[0]._devices  # pylint: disable=protected-access
    grouped = _group_value_by_device(dense_values)

    # device_grad_packs:
    # [[(t0_gpu0, None), (t1_gpu0, None)], [(t0_gpu1, None), (t1_gpu1, None)]]
    device_grad_packs, tensor_packer = _pack_tensors(grouped, self._num_packs)

    # The actual aggregation of the repacked gradients. Note that they are
    # sharded among different aggregation trees. So it is important to strike
    # the balance on num_splits.
    if self._all_reduce_alg == "nccl":
      # TODO(yuefengz): merge this into the all-reduce library.
      reduced = cross_device_utils.aggregate_gradients_using_nccl(
          device_grad_packs)
    else:
      # TODO(yuefengz): check that gpu ids in `destinations` are in ascending
      # order.
      reduced = (
          cross_device_utils.aggregate_gradients_using_hierarchical_copy(
              destinations, device_grad_packs))

    reduced = _unpack_tensors(reduced, tensor_packer)
    return _ungroup_and_make_mirrored(reduced, dense_values[0], reduce_op)

  def _do_batch_all_reduce_sparse(self, reduce_op, sparse_values):
    """Run batch all-reduce for sparse values."""
    logging.log_first_n(
        logging.WARN,
        "Efficient allreduce is not supported for %d IndexedSlices" %
        len(sparse_values), 10)
    # Use `sparse_values` as destinations to do all-reduces. It is effectively
    # an allgather under the hood but not an efficient one.
    return self._simple_cross_replica_ops.batch_reduce(
        reduce_op, zip(sparse_values, sparse_values))

  def _gather_implementation(self, per_replica_value, destinations, axis,
                             options):
    logging.warning("gather/all_gather with NCCL or HierarchicalCopy is not "
                    "supported. Falling back to gather on one device and "
                    "then broadcast. We're working on a more efficient "
                    "implementation.")
    return ReductionToOneDevice()._gather(per_replica_value, destinations, axis,  # pylint: disable=protected-access
                                          options)


# For compatibility with code using the old name of `AllReduceCrossDeviceOps`.
AllReduceCrossTowerOps = AllReduceCrossDeviceOps


AllReduceSpecTuple = collections.namedtuple("AllReduceSpecTuple",
                                            "alg shards limit")


@tf_export("distribute.NcclAllReduce")
class NcclAllReduce(AllReduceCrossDeviceOps):
  """NCCL all-reduce implementation of CrossDeviceOps.

  It uses Nvidia NCCL for all-reduce. For the batch API, tensors will be
  repacked or aggregated for more efficient cross-device transportation.

  For reduces that are not all-reduce, it falls back to
  `tf.distribute.ReductionToOneDevice`.

  Here is how you can use `NcclAllReduce` in `tf.distribute.MirroredStrategy`:


  ```
    strategy = tf.distribute.MirroredStrategy(
      cross_device_ops=tf.distribute.NcclAllReduce())
  ```
  """

  def __init__(self, num_packs=1):
    """Initializes the object.

    Args:
      num_packs: a non-negative integer. The number of packs to split values
        into. If zero, no packing will be done.

    Raises:
      ValueError: if `num_packs` is negative.
    """
    if num_packs < 0:
      raise ValueError(
          "NCCL all-reduce requires num_packs >= 0, but {} is specified".format(
              num_packs))
    super(NcclAllReduce, self).__init__(
        all_reduce_alg="nccl", num_packs=num_packs)


@tf_export("distribute.HierarchicalCopyAllReduce")
class HierarchicalCopyAllReduce(AllReduceCrossDeviceOps):
  """Hierarchical copy all-reduce implementation of CrossDeviceOps.

  It reduces to one GPU along edges in some hierarchy and broadcasts back to
  each GPU along the same path. For the batch API, tensors will be repacked or
  aggregated for more efficient cross-device transportation.

  This is a reduction created for Nvidia DGX-1 which assumes GPUs connects like
  that on DGX-1 machine. If you have different GPU inter-connections, it is
  likely that it would be slower than `tf.distribute.ReductionToOneDevice`.

  For reduces that are not all-reduce, it falls back to
  `tf.distribute.ReductionToOneDevice`.

  Here is how you can use `HierarchicalCopyAllReduce` in
  `tf.distribute.MirroredStrategy`:

  ```
    strategy = tf.distribute.MirroredStrategy(
      cross_device_ops=tf.distribute.HierarchicalCopyAllReduce())
  ```
  """

  def __init__(self, num_packs=1):
    """Initializes the object.

    Args:
      num_packs: a non-negative integer. The number of packs to split values
        into. If zero, no packing will be done.

    Raises:
      ValueError if `num_packs` is negative.
    """
    if num_packs < 0:
      raise ValueError(
          "HierarchicalCopy requires num_packs >= 0, but {} is specified"
          .format(num_packs))
    super(HierarchicalCopyAllReduce, self).__init__(
        all_reduce_alg="hierarchical_copy",
        num_packs=num_packs)


# TODO(crccw): remove after migrating all callers.
CollectiveCommunication = collective_util.CommunicationImplementation
CommunicationImplementation = collective_util.CommunicationImplementation


# TODO(yuefengz): support in-graph collective all-reduce.
class CollectiveAllReduce(CrossDeviceOps):
  """All-reduce cross device ops using collective ops.

  In the between-graph replicated training, it will still do all-reduces across
  all workers and then put results on the right destinations.
  """

  def __init__(self,
               devices,
               group_size,
               options,
               collective_keys=None,
               canonicalize_devices=True):
    """Initializes the object.

    Args:
      devices: a list of device strings to run collectives on.
      group_size: the global group size. For between-graph replicated training
        it's the total number of devices across all workers.
      options: a `tf.distribute.experimental.CommunicationOptions`.
      collective_keys: an optional CollectiveKey object.
      canonicalize_devices: Whether to canonicalize devices for workers or not.
    """
    if group_size % len(devices) > 0:
      raise ValueError("group_size must be divisible by the number of devices.")

    self._group_size = group_size
    self._options = options
    self._collective_keys = (collective_keys or
                             cross_device_utils.CollectiveKeys())
    # This lock guards all collective launches, i.e. calls to
    # cross_device_utils.build_collectve_*.
    #
    # In a multi threaded eager program we need to ensure different groups of
    # collectives don't interleave each other, otherwise there could be
    # deadlocks. E.g. if two user threads both are launching collectives:
    #   user-thread-0  device0                 device1
    #   user-thread-1          device0 device1
    # In eager mode, we use one thread per device to launch collective ops, so
    # the above launch sequences end up with the following queues:
    #   device-0  collective-0  collective-1
    #   device-1  collective-1  collective-0
    # This deadlocks since neither collective is able to finish.
    self._lock = threading.Lock()

    if canonicalize_devices:
      self._devices = tuple(device_util.canonicalize(d) for d in devices)
    else:
      self._devices = tuple(
          device_util.canonicalize_without_job_and_task(d) for d in devices)
    group_key = self._collective_keys.get_group_key(self._devices)
    self._launchers = []
    # Whether to only use NCCL for batched all-reduce when NCCL is requested.
    # This is because of the lack of mechanism to order NCCL operations
    # deterministically.
    self._limited_nccl = False
    for device in self._devices:
      launcher = cross_device_utils.CollectiveReplicaLauncher(
          group_key, group_size, self._collective_keys, device, options)
      self._launchers.append(launcher)
      if not launcher.can_order_nccl():
        self._limited_nccl = True

    self._pool = multiprocessing.pool.ThreadPool(len(self._devices))

    super(CollectiveAllReduce, self).__init__()
    self._canonicalize_devices = canonicalize_devices

  @property
  def _num_between_graph_workers(self):
    # Currently we only support equal number of devices on each worker.
    return self._group_size / len(self._devices)

  def _all_reduce(self, reduce_op, value, replica_id, options):
    """Implements CrossDeviceOps.all_reduce."""
    # TODO(b/122840926): reuse this method in _batch_all_reduce.
    flat_values = nest.flatten(value)

    # If NCCL launches can't be ordered (self._limited_nccl == True), we only
    # use NCCL when batch_size > 1, hoping that there's only one batched
    # all-reduce, which is the gradient aggregation in optimizer. For TF 2.x,
    # NCCL launches are always ordered.
    if (self._limited_nccl and options.implementation
        == collective_util.CommunicationImplementation.NCCL and
        len(flat_values) == 1):
      options = options.merge(
          collective_util.Options(
              implementation=collective_util.CommunicationImplementation.RING))

    launcher = self._launchers[replica_id]
    dense_values, dense_indices, sparse_values, sparse_indices = (
        cross_device_utils.split_by_sparsity(flat_values))
    dense_results = []
    sparse_results = []

    if dense_values:
      # Reverse the lists so that there's better chance that values follows
      # the order in which they are calculated (e.g. when they're gradients), so
      # as to overlap calculation with communication. However, this may not be
      # optimal for cases like gradients of complicated non-sequential models.
      #
      # Note that we reverse the list before packing so that the first pack
      # won't be too small, since it's more likely for first few packs to have
      # long queuing time due to concurrent intense computation.
      #
      # TODO(b/147393503): explore solutions for optimal ordering.
      dense_values.reverse()
      packs = cross_device_utils.group_by_size(dense_values,
                                               options.bytes_per_pack)

      if not context.executing_eagerly() and replica_id == 0:
        logging.info(
            "Collective all_reduce tensors: %d all_reduces, num_devices = %d, "
            "group_size = %d, implementation = %s, num_packs = %d",
            len(dense_values), len(self._launchers), self._group_size,
            options.implementation, len(packs))

      dense_results = launcher.batch_all_reduce(packs, options)
      if reduce_op == reduce_util.ReduceOp.MEAN:
        for i, v in enumerate(dense_results):
          with ops.device(self._devices[replica_id]):
            dense_results[i] = v / self._group_size
      dense_results.reverse()

    if sparse_values:
      if not context.executing_eagerly() and replica_id == 0:
        logging.info(
            "Collective all_reduce IndexedSlices: %d all_reduces, num_devices ="
            "%d, group_size = %d, implementation = %s", len(sparse_values),
            len(self._launchers), self._group_size, options.implementation)

      for indexed_slice in sparse_values:
        sparse_results.append(
            launcher.all_reduce_indexed_slices(indexed_slice, options))

      if reduce_op == reduce_util.ReduceOp.MEAN:
        for i, v in enumerate(sparse_results):
          with ops.device(self._devices[replica_id]):
            sparse_results[i] = indexed_slices.IndexedSlices(
                values=sparse_results[i].values / self._group_size,
                indices=sparse_results[i].indices,
                dense_shape=sparse_results[i].dense_shape)

    flat_results = cross_device_utils.stitch_values(
        ((dense_results, dense_indices), (sparse_results, sparse_indices)))
    return nest.pack_sequence_as(value, flat_results)

  def _all_reduce_per_replica_values(self, reduce_op, per_replica_values,
                                     options):
    """All reduce a list of per_replica_value."""
    values_by_device = [[] for _ in self._devices]
    num_devices = len(self._devices)
    for per_replica in per_replica_values:
      for i in range(num_devices):
        values_by_device[i].append(per_replica.values[i])

    if context.executing_eagerly():

      def thread_fn(device_id):
        with context.eager_mode():
          return self._all_reduce(reduce_op, values_by_device[device_id],
                                  device_id, options)

      with self._lock:
        outputs_by_device = self._pool.map(thread_fn, list(range(num_devices)))
    else:
      outputs_by_device = []
      with self._lock:
        for i in range(num_devices):
          outputs_by_device.append(
              self._all_reduce(reduce_op, values_by_device[i], i, options))

    result = []
    for values in zip(*outputs_by_device):
      result.append(
          distribute_utils.regroup(values, wrap_class=value_lib.Mirrored))
    return result

  def reduce_implementation(self, reduce_op, per_replica_value, destinations,
                            options):
    values_util.mark_as_unsaveable()
    all_reduced = self._all_reduce_per_replica_values(reduce_op,
                                                      [per_replica_value],
                                                      options)[0]
    devices = get_devices_from(destinations, self._canonicalize_devices)

    if _devices_match(per_replica_value, destinations,
                      self._canonicalize_devices):
      return all_reduced

    # Convert `all_reduced` to a `Mirrored` object, as a simple and uniform
    # utility to access component for a particular device.
    if not isinstance(all_reduced, value_lib.Mirrored):
      all_reduced = value_lib.Mirrored([all_reduced])

    # If we got this far, the destination devices do not match the all-reduce
    # devices, so we must map from one to the other.
    index = []
    # We must add these control dependencies, otherwise we can get deadlock.
    with ops.control_dependencies(all_reduced.values):
      for d in devices:
        with ops.device(d):
          for v in all_reduced.values:
            if v.device == d:
              index.append(array_ops.identity(v))
              break
          else:
            # TODO(josh11b): Once we add support for model parallelism, get the
            # copy from the corresponding replica instead of the primary.
            index.append(array_ops.identity(all_reduced._primary))  # pylint: disable=protected-access
    return distribute_utils.regroup(index, wrap_class=value_lib.Mirrored)

  def batch_reduce_implementation(self, reduce_op, value_destination_pairs,
                                  options):
    values_util.mark_as_unsaveable()
    all_devices_match = _all_devices_match(value_destination_pairs,
                                           self._canonicalize_devices)
    if all_devices_match:
      return self._all_reduce_per_replica_values(
          reduce_op, [v[0] for v in value_destination_pairs], options)
    else:
      if not all_devices_match:
        logging.log_first_n(
            logging.WARN, "Efficient batch_reduce is not supported if "
            "destinations are different.", 10)

      return [
          self.reduce_implementation(reduce_op, value, dest, options)
          for value, dest in value_destination_pairs
      ]

  def _gather_implementation(self, per_replica_value, destinations, axis,
                             options):
    all_gathered = self._batch_all_gather([per_replica_value], axis, options)[0]
    values_util.mark_as_unsaveable()
    devices = get_devices_from(destinations, self._canonicalize_devices)

    if _devices_match(per_replica_value, destinations,
                      self._canonicalize_devices):
      return all_gathered

    # Convert `all_gathered` to a `Mirrored` object, as a simple and uniform
    # utility to access component for a particular device.
    if not isinstance(all_gathered, value_lib.Mirrored):
      all_gathered = value_lib.Mirrored([all_gathered])

    # If we got this far, the destination devices do not match the all-gather
    # devices, so we must map from one to the other.
    index = []
    # We must add these control dependencies, otherwise we can get deadlock.
    with ops.control_dependencies(all_gathered.values):
      for d in devices:
        with ops.device(d):
          for v in all_gathered.values:
            if v.device == d:
              index.append(array_ops.identity(v))
              break
            else:
              index.append(array_ops.identity(all_gathered._primary))  # pylint: disable=protected-access
    return distribute_utils.regroup(index, wrap_class=value_lib.Mirrored)

  def _batch_all_gather(self, per_replica_values, axis, options):
    """all gather multiple per-replica-values."""
    batch_size = len(per_replica_values)
    # For now, we use NCCL only when batch_size > 1.
    # TODO(b/132575814): switch to NCCL for all collectives when implementation
    # is NCCL.
    if (self._limited_nccl and options.implementation
        == collective_util.CommunicationImplementation.NCCL and
        batch_size == 1):
      options = options.merge(
          collective_util.Options(
              implementation=collective_util.CommunicationImplementation.RING))

    logging.log_first_n(
        logging.INFO, "Collective batch_all_gather: %d all-gathers, "
        "num_devices = %d, group_size = %d, implementation = %s, " %
        (batch_size, len(
            self._devices), self._group_size, options.implementation), 10)

    def compute_gathered_values():
      gathered_values = []
      with self._lock, ops.name_scope("allgather"):
        for per_replica in per_replica_values:
          outputs = []
          for i in range(len(self._devices)):
            outputs.append(self._launchers[i].all_gather(
                per_replica.values[i], axis, options))
          gathered_values.append(outputs)
      return gathered_values

    if context.executing_eagerly():
      gathered_values = def_function.function(compute_gathered_values)()
    else:
      gathered_values = compute_gathered_values()

    mirrored = []
    for value in gathered_values:
      mirrored.append(
          distribute_utils.regroup(value, wrap_class=value_lib.Mirrored))
    return mirrored

  def __deepcopy__(self, memo):
    # distribute_coordinator deep-copies the strategy object, so
    # CollectiveAllReduce needs to support deep copy as well.
    collective_keys = copy.deepcopy(self._collective_keys, memo)
    return CollectiveAllReduce(self._devices, self._group_size, self._options,
                               collective_keys, self._canonicalize_devices)


def select_cross_device_ops(devices, session_config=None):
  """Find the best `CrossDeviceOps` locally given a `tf.compat.v1.ConfigProto`.

  Args:
    devices: a list of devices passed to `tf.distribute.Strategy`.
    session_config: a `tf.compat.v1.ConfigProto` or `None`. If `None`, it will
      make decision based on all logical devices.

  Returns:
    A subclass of `CrossDeviceOps`.
  """
  requested_devices = set(device_util.canonicalize(d) for d in devices)
  if ops.executing_eagerly_outside_functions():
    logical_gpus = context.context().list_logical_devices(device_type="GPU")
    physical_gpus = context.context().list_physical_devices(device_type="GPU")
    if len(logical_gpus) != len(physical_gpus):
      logging.warning("NCCL is not supported when using virtual GPUs, falling"
                      "back to reduction to one device")
      return ReductionToOneDevice()

    machine_devices = context.context().list_logical_devices()
  else:
    machine_devices = device_lib.list_local_devices(
        session_config=session_config)
  using_devices = set()
  for d in machine_devices:
    if device_util.canonicalize(d.name) in requested_devices:
      using_devices.add(d.name)

  if len(using_devices) != len(requested_devices):
    logging.warning(
        "Some requested devices in `tf.distribute.Strategy` are not visible "
        "to TensorFlow: %s", ",".join(list(requested_devices - using_devices)))

  if any("gpu" not in d.lower() for d in requested_devices):
    logging.warning("There are non-GPU devices in `tf.distribute.Strategy`, "
                    "not using nccl allreduce.")
    return ReductionToOneDevice()

  if kernels.get_registered_kernels_for_op("NcclAllReduce"):
    return NcclAllReduce(num_packs=1)
  else:
    logging.warning("Nccl kernel is not found, not using nccl allreduce.")
    return ReductionToOneDevice()