Add n-dimensional embedding as the step (vertical) timing signal.

  Args:
    x: a tensor with shape [batch, length, depth]
    step: step
    hparams: model hyper parameters

  Returns:
    a Tensor with the same shape as x.

def add_step_timing_signal(x, step, hparams):
  """Add n-dimensional embedding as the step (vertical) timing signal.

  Args:
    x: a tensor with shape [batch, length, depth]
    step: step
    hparams: model hyper parameters

  Returns:
    a Tensor with the same shape as x.

  """
  if hparams.recurrence_type == "act":
    num_steps = hparams.act_max_steps
  else:
    num_steps = hparams.num_rec_steps
  channels = common_layers.shape_list(x)[-1]

  if hparams.step_timing_signal_type == "learned":
    signal = common_attention.get_layer_timing_signal_learned_1d(
        channels, step, num_steps)

  elif hparams.step_timing_signal_type == "sinusoid":
    signal = common_attention.get_layer_timing_signal_sinusoid_1d(
        channels, step, num_steps)

  if hparams.add_or_concat_timing_signal == "add":
    x_with_timing = x + common_layers.cast_like(signal, x)

  elif hparams.add_or_concat_timing_signal == "concat":
    batch_size = common_layers.shape_list(x)[0]
    length = common_layers.shape_list(x)[1]
    signal_tiled = tf.tile(signal, [batch_size, length, 1])
    x_with_timing = tf.concat((x, signal_tiled), axis=-1)

  return x_with_timing