import torch
import torch.nn as nn
import torch.nn.functional as F
import math

class Embeddings(nn.Module):
    def __init__(self, d_model, vocab):
        super().__init__()
        self.lut = nn.Embedding(vocab, d_model)
        self.d_model = d_model
    def forward(self, x):
        return self.lut(x) * math.sqrt(self.d_model)

class PositionalEncoding(nn.Module):
    def __init__(self, d_model, dropout, max_len=4000):
        super().__init__()
        self.dropout = nn.Dropout(dropout)
        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)
        self.register_buffer("pe", pe.unsqueeze(0))
    def forward(self, x):
        x = x + self.pe[:, :x.size(1)].detach()
        return self.dropout(x)

class Generator(nn.Module):
    def __init__(self, d_model, vocab):
        super().__init__()
        self.proj = nn.Linear(d_model, vocab)
    def forward(self, x):
        return F.log_softmax(self.proj(x), dim=-1)