text: import torch.nn as nn
  import torch
  import math
  
  
  class PositionalEmbedding(nn.Module):
      "Implement the PE function."
  
      def __init__(self, d_model, dropout, max_len=512):
          super().__init__()
          self.dropout = nn.Dropout(p=dropout)
  
          # Compute the positional encodings once in log space.
          pe = torch.zeros(max_len, d_model).float()
          pe.require_grad = False
  
          position = torch.arange(0, max_len).float().unsqueeze(1)
          div_term = (torch.arange(0, d_model, 2) * -(math.log(10000.0) / d_model)).float().exp()
  
          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 self.dropout(x)
  5