Implements the frequency-based positional encoding described
    in `Attention is all you Need
    <https://www.semanticscholar.org/paper/Attention-Is-All-You-Need-Vaswani-Shazeer/0737da0767d77606169cbf4187b83e1ab62f6077>`_ .

    Adds sinusoids of different frequencies to a ``Tensor``. A sinusoid of a
    different frequency and phase is added to each dimension of the input ``Tensor``.
    This allows the attention heads to use absolute and relative positions.

    The number of timescales is equal to hidden_dim / 2 within the range
    (min_timescale, max_timescale). For each timescale, the two sinusoidal
    signals sin(timestep / timescale) and cos(timestep / timescale) are
    generated and concatenated along the hidden_dim dimension.

    Parameters
    ----------
    tensor : ``torch.Tensor``
        a Tensor with shape (batch_size, timesteps, hidden_dim).
    min_timescale : ``float``, optional (default = 1.0)
        The smallest timescale to use.
    max_timescale : ``float``, optional (default = 1.0e4)
        The largest timescale to use.

    Returns
    -------
    The input tensor augmented with the sinusoidal frequencies.

def add_positional_features(tensor: torch.Tensor,
                            min_timescale: float = 1.0,
                            max_timescale: float = 1.0e4):
    # pylint: disable=line-too-long
    """
    Implements the frequency-based positional encoding described
    in `Attention is all you Need
    <https://www.semanticscholar.org/paper/Attention-Is-All-You-Need-Vaswani-Shazeer/0737da0767d77606169cbf4187b83e1ab62f6077>`_ .

    Adds sinusoids of different frequencies to a ``Tensor``. A sinusoid of a
    different frequency and phase is added to each dimension of the input ``Tensor``.
    This allows the attention heads to use absolute and relative positions.

    The number of timescales is equal to hidden_dim / 2 within the range
    (min_timescale, max_timescale). For each timescale, the two sinusoidal
    signals sin(timestep / timescale) and cos(timestep / timescale) are
    generated and concatenated along the hidden_dim dimension.

    Parameters
    ----------
    tensor : ``torch.Tensor``
        a Tensor with shape (batch_size, timesteps, hidden_dim).
    min_timescale : ``float``, optional (default = 1.0)
        The smallest timescale to use.
    max_timescale : ``float``, optional (default = 1.0e4)
        The largest timescale to use.

    Returns
    -------
    The input tensor augmented with the sinusoidal frequencies.
    """
    _, timesteps, hidden_dim = tensor.size()

    timestep_range = get_range_vector(timesteps, get_device_of(tensor)).data.float()
    # We're generating both cos and sin frequencies,
    # so half for each.
    num_timescales = hidden_dim // 2
    timescale_range = get_range_vector(num_timescales, get_device_of(tensor)).data.float()

    log_timescale_increments = math.log(float(max_timescale) / float(min_timescale)) / float(num_timescales - 1)
    inverse_timescales = min_timescale * torch.exp(timescale_range * -log_timescale_increments)

    # Broadcasted multiplication - shape (timesteps, num_timescales)
    scaled_time = timestep_range.unsqueeze(1) * inverse_timescales.unsqueeze(0)
    # shape (timesteps, 2 * num_timescales)
    sinusoids = torch.cat([torch.sin(scaled_time), torch.cos(scaled_time)], 1)
    if hidden_dim % 2 != 0:
        # if the number of dimensions is odd, the cos and sin
        # timescales had size (hidden_dim - 1) / 2, so we need
        # to add a row of zeros to make up the difference.
        sinusoids = torch.cat([sinusoids, sinusoids.new_zeros(timesteps, 1)], 1)
    return tensor + sinusoids.unsqueeze(0)