import math
import torch


def masked_sin_pos_encoding(x, mask, num_pos_feats, temperature=10000, scale=2 * math.pi):
    """ Masked Sinusoidal Positional Encoding

    Parameters:
        x: [PATCH] tokens
        mask: the padding mask for [PATCH] tokens
        num_pos_feats: the size of channel dimension
        temperature: the temperature value
        scale: the normalization scale

    Returns:
        pos: Sinusoidal positional encodings
    """

    num_pos_feats = num_pos_feats // 2
    not_mask = ~mask

    y_embed = not_mask.cumsum(1, dtype=torch.float32)
    x_embed = not_mask.cumsum(2, dtype=torch.float32)

    eps = 1e-6
    y_embed = y_embed / (y_embed[:, -1:, :] + eps) * scale
    x_embed = x_embed / (x_embed[:, :, -1:] + eps) * scale

    dim_t = torch.arange(num_pos_feats, dtype=torch.float32, device=x.device)
    dim_t = temperature ** (2 * (dim_t // 2) / num_pos_feats)

    pos_x = x_embed[:, :, :, None] / dim_t
    pos_y = y_embed[:, :, :, None] / dim_t

    pos_x = torch.stack((pos_x[:, :, :, 0::2].sin(), pos_x[:, :, :, 1::2].cos()), dim=4).flatten(3)
    pos_y = torch.stack((pos_y[:, :, :, 0::2].sin(), pos_y[:, :, :, 1::2].cos()), dim=4).flatten(3)
    pos = torch.cat((pos_y, pos_x), dim=3)

    return pos