def _left_doubling_increments(batch_shape, max_doublings, step_size, seed=None,
                              name=None):
  """
  """
  with tf.compat.v1.name_scope(name, 'left_doubling_increments',
                               [batch_shape, max_doublings, step_size]):

    step_size = tf.convert_to_tensor(value=step_size)
    dtype = step_size.dtype.base_dtype
    # Output shape of the left increments tensor.
    output_shape = tf.concat(([max_doublings + 1], batch_shape), axis=0)
    # A sample realization of X_k.
    expand_left = distributions.Bernoulli(0.5, dtype=dtype).sample(
        sample_shape=output_shape, seed=seed)

    # The widths of the successive intervals. Starts with 1.0 and ends with
    # 2^max_doublings.
    width_multipliers = tf.cast(2 ** tf.range(0, max_doublings+1), dtype=dtype)
    # Output shape of the `widths` tensor.
    widths_shape = tf.concat(([max_doublings + 1],
                              tf.ones_like(batch_shape)), axis=0)
    width_multipliers = tf.reshape(width_multipliers, shape=widths_shape)
    # Widths shape is [max_doublings + 1, 1, 1, 1...].
    widths = width_multipliers * step_size

    # Take the cumulative sum of the left side increments in slice width to give
    # the resulting distance from the inital lower bound.
    left_increments = tf.cumsum(widths * expand_left, exclusive=True, axis=0)
    return left_increments, widths