import math
import torch
import torch.nn as nn


class PositionalEncoding(nn.Module):
    def __init__(self, d_model, max_len=5000):
        super().__init__()

        pe = torch.zeros(max_len, d_model)
        position = torch.arange(0, max_len).unsqueeze(1)

        div_term = torch.exp(
            torch.arange(0, d_model, 2) *
            (-math.log(10000.0) / d_model)
        )

        pe[:, 0::2] = torch.sin(position * div_term)
        pe[:, 1::2] = torch.cos(position * div_term)

        pe = pe.unsqueeze(0)
        self.register_buffer("pe", pe)

    def forward(self, x):
        x = x + self.pe[:, :x.size(1)]
        return x