text: import torch
  import torch.nn as nn
  
  
  class FixedPositionalEncoding(nn.Module):
      def __init__(self, embedding_dim, max_length=5000):
          super(FixedPositionalEncoding, self).__init__()
  
          pe = torch.zeros(max_length, embedding_dim)
          position = torch.arange(0, max_length, dtype=torch.float).unsqueeze(1)
          div_term = torch.exp(
              torch.arange(0, embedding_dim, 2).float()
              * (-torch.log(torch.tensor(10000.0)) / embedding_dim)
          )
          pe[:, 0::2] = torch.sin(position * div_term)
          pe[:, 1::2] = torch.cos(position * div_term)
          pe = pe.unsqueeze(0).transpose(0, 1)
          self.register_buffer('pe', pe)
  
      def forward(self, x):
          x = x + self.pe[: x.size(0), :]
          return x
  
  
  class LearnedPositionalEncoding(nn.Module):
      def __init__(self, max_position_embeddings, embedding_dim, seq_length):
          super(LearnedPositionalEncoding, self).__init__()
          self.pe = nn.Embedding(max_position_embeddings, embedding_dim)
          self.seq_length = seq_length
  
          self.register_buffer(
              "position_ids",
              torch.arange(max_position_embeddings).expand((1, -1)),
          )
  
      def forward(self, x, position_ids=None):
          if position_ids is None:
              position_ids = self.position_ids[:, : self.seq_length]
  
          position_embeddings = self.pe(position_ids)
          return x + position_embeddings
  