code: def all_reduce_ring(
      x, parallelism, maybe_reduce=True, use_bfloat16=True
  ):
      """Compute the sum of all Tensors and put the result everywhere.
  
      Assumes that the devices are connected in a ring.
  
      Args:
        x: a list of Tensors with length parallelism.n
        parallelism: a expert_utils.Parallelism object.
        maybe_reduce: a boolean - first reduce per device.
        use_bfloat16: a boolean - saves bandwidth but loses precision
  
      Returns:
        a list of Tensors with length parallelism.n
      """
      if parallelism.n == 1:
          return x
  
      if maybe_reduce:
          original_parallelism = parallelism
          parallelism, x = reduce_by_device(parallelism, x, tf.add_n)
  
      if parallelism.n == 1:
          y = x
      else:
          # first shard the input:
          x_flat = parallelism(tf.reshape, x, [[-1]] * parallelism.n)
          # [device, shard]
          x_split = parallelism(
              common_layers.approximate_split, x_flat, parallelism.n, 0
          )
  
          def _step(
              source_replica, target_replica, x_split, op="plus_eq"
          ):
              """Helper function - one step of summing or copying.
  
              If op == "plus_eq", then adds source_replica into target_replica
              If op == "copy", then copies source_replica onto target_replica
  
              These operations happen for all shards.  The replica numbers are offset
              by the shard numbers to keep all physical links busy.
  
              Args:
                source_replica: an integer
                target_replica: an integer
                x_split: a list of lists of tensors
                op: a string
              """
              for shard in range(parallelism.n):
                  source_device = (
                      shard + source_replica
                  ) % parallelism.n
                  target_device = (
                      shard + target_replica
                  ) % parallelism.n
                  source = x_split[source_device][shard]
                  if use_bfloat16:
                      with tf.device(
                          parallelism.devices[source_device]
                      ):
                          source = tf.to_bfloat16(source)
                  with tf.device(parallelism.devices[target_device]):
                      source = tf.to_float(source)
                      if op == "plus_eq":
                          x_split[target_device][shard] += source
                      else:
                          assert op == "copy"
                          x_split[target_device][shard] = tf.identity(
                              source
                          )
  
          center = parallelism.n // 2
  
          # accumulate everything towards the center.
          for i in reversed(range(center, parallelism.n - 1)):
              _step(i + 1, i, x_split, op="plus_eq")
          for i in range(center):
              _step(i, i + 1, x_split, op="plus_eq")
          # copy everything away from the center.
          for i in range(center, parallelism.n - 1):
              _step(i, i + 1, x_split, op="copy")
          for i in reversed(range(center)):
              _step(i + 1, i, x_split, op="copy")
          x_concat = parallelism(tf.concat, x_split, 0)
          y = parallelism(
              common_layers.reshape_like_all_dims, x_concat, x
          )
      if maybe_reduce:
          y = expand_by_device(original_parallelism, parallelism, y)
      return y
  
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  import functools
  import math
  import six
  from six.moves import range
  from six.moves import zip
  from tensor2tensor.layers import common_layers
  from tensor2tensor.layers.vq_discrete import DiscreteBottleneck
  import tensorflow.compat.v1
label_desc: Use image node_id 22 for calling a global function with example usage: all_reduce_ring(x, parallelism, maybe_reduce, use_bfloat16) and returns: y, x