code: def allreduce_ring_single_shard(xs, devices, reduction_fn_string="SUM"):
    
    n = len(xs)
    binary_reduction = mtf.binary_reduction_fn(reduction_fn_string)
    assert len(devices) == n, "devices must be a list of length len(xs)"
    if n == 1:
      return xs
    result = [None] * n
    if n % 2 == 0:
      left_center = n // 2 - 1
      right_center = left_center + 1
    else:
      left_center = n // 2
      right_center = left_center
    left_sum = xs[0]
    for i in xrange(1, left_center + 1):
      with tf.device(devices[i]):
        left_sum = binary_reduction(left_sum, xs[i])
    right_sum = xs[n-1]
    for i in reversed(xrange(left_center + 1, n - 1)):
      with tf.device(devices[i]):
        right_sum = binary_reduction(xs[i], right_sum)
    with tf.device(devices[left_center]):
      result[left_center] = binary_reduction(left_sum, right_sum)
    if n % 2 == 0:
      with tf.device(devices[right_center]):
        result[right_center] = binary_reduction(left_sum, right_sum)
    for i in reversed(xrange(left_center)):
      with tf.device(devices[i]):
        result[i] = tf.identity(result[i + 1])
    for i in xrange(right_center + 1, n):
      with tf.device(devices[i]):
        result[i] = tf.identity(result[i - 1])
    return result
docs: Compute the reduction of all Tensors and put the result everywhere.
  
    Performance-optimized for a ring of devices.
  
    Args:
      xs: a list of n tf.Tensors
      devices: a list of strings
      reduction_fn_string: "SUM" or "MAX"
  
    Returns:
      a list of n Tensors
    Raises:
      ValueError: if devices is not a list of n strings