# positional.py
import torch
import torch.nn as nn
from math import log

class PositionalEncoding(nn.Module):
    def __init__(self, d_model: int, dropout: float = 0.1, max_len: int = 500):
        super().__init__()
        self.dropout = nn.Dropout(p=dropout)

        position = torch.arange(max_len, dtype=torch.float).unsqueeze(1)  # (max_len, 1)
        div_term = torch.exp(
            torch.arange(0, d_model, 2, dtype=torch.float) * (-log(10000.0) / d_model)
        )  # (d_model/2,)

        pe = torch.zeros(max_len, d_model, dtype=torch.float)  # (max_len, d_model)
        pe[:, 0::2] = torch.sin(position * div_term)          # (max_len, d_model/2)
        pe[:, 1::2] = torch.cos(position * div_term)

        pe = pe.unsqueeze(0) 
        self.register_buffer("pe", pe, persistent=False)      # buffer, pas paramètre

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        # x: (B, S, D)
        s = x.size(1)
        x = x + self.pe[:, :s, :]  # (1,S,D) broadcast -> (B,S,D)
        return self.dropout(x)