Adds sinusoids of diff frequencies to a Tensor, with timing position given.

  Args:
    x: a Tensor with shape [batch, length, channels]
    position: a Tensor with shape [batch, length]
    min_timescale: a float
    max_timescale: a float

  Returns:
    a Tensor the same shape as x.

def add_timing_signal_1d_given_position(x,
                                        position,
                                        min_timescale=1.0,
                                        max_timescale=1.0e4):
  """Adds sinusoids of diff frequencies to a Tensor, with timing position given.

  Args:
    x: a Tensor with shape [batch, length, channels]
    position: a Tensor with shape [batch, length]
    min_timescale: a float
    max_timescale: a float

  Returns:
    a Tensor the same shape as x.
  """
  channels = common_layers.shape_list(x)[2]
  num_timescales = channels // 2
  log_timescale_increment = (
      math.log(float(max_timescale) / float(min_timescale)) /
      (tf.to_float(num_timescales) - 1))
  inv_timescales = min_timescale * tf.exp(
      tf.to_float(tf.range(num_timescales)) * -log_timescale_increment)
  scaled_time = (
      tf.expand_dims(tf.to_float(position), 2) * tf.expand_dims(
          tf.expand_dims(inv_timescales, 0), 0))
  signal = tf.concat([tf.sin(scaled_time), tf.cos(scaled_time)], axis=2)
  signal = tf.pad(signal, [[0, 0], [0, 0], [0, tf.mod(channels, 2)]])
  signal = common_layers.cast_like(signal, x)
  return x + signal