content: r"""Functional interface"""
  import warnings
  import math
  
  import torch
  from torch import _VF
  from torch._jit_internal import Optional, Tuple
  from torch.overrides import has_torch_function, handle_torch_function
  
  from torch.nn.functional import _pad, linear, softmax, dropout
  
  Tensor = torch.Tensor
  pad = _pad
  
  
  def multi_head_attention_forward(query: Tensor,
                                   key: Tensor,
                                   value: Tensor,
                                   embed_dim_to_check: int,
                                   num_heads: int,
                                   in_proj_weight: Tensor,
                                   in_proj_bias: Tensor,
                                   bias_k: Optional[Tensor],
                                   bias_v: Optional[Tensor],
                                   add_zero_attn: bool,
                                   dropout_p: float,
                                   out_proj_weight: Tensor,
                                   out_proj_bias: Tensor,
                                   training: bool = True,
                                   key_padding_mask: Optional[Tensor] = None,
                                   need_weights: bool = True,
                                   attn_mask: Optional[Tensor] = None,
                                   use_separate_proj_weight: bool = False,
                                   q_proj_weight: Optional[Tensor] = None,
                                   k_proj_weight: Optional[Tensor] = None,
                                   v_proj_weight: Optional[Tensor] = None,
                                   static_k: Optional[Tensor] = None,
                                   static_v: Optional[Tensor] = None,
                                   return_qk: bool = False
                                   ) -> Tuple[Tensor, Optional[Tensor]]:
      r"""
      Args:
          query, key, value: map a query and a set of key-value pairs to an output.
              See "Attention Is All You Need" for more details.
          embed_dim_to_check: total dimension of the model.
          num_heads: parallel attention heads.
          in_proj_weight, in_proj_bias: input projection weight and bias.
          bias_k, bias_v: bias of the key and value sequences to be added at dim=0.
          add_zero_attn: add a new batch of zeros to the key and
                         value sequences at dim=1.
          dropout_p: probability of an element to be zeroed.
          out_proj_weight, out_proj_bias: the output projection weight and bias.
          training: apply dropout if is ``True``.
          key_padding_mask: if provided, specified padding elements in the key will
              be ignored by the attention. This is an binary mask. When the value is True,
              the corresponding value on the attention layer will be filled with -inf.
          need_weights: output attn_output_weights.
          attn_mask: 2D or 3D mask that prevents attention to certain positions. A 2D mask will be broadcasted for all
              the batches while a 3D mask allows to specify a different mask for the entries of each batch.
          use_separate_proj_weight: the function accept the proj. weights for query, key,
              and value in different forms. If false, in_proj_weight will be used, which is
              a combination of q_proj_weight, k_proj_weight, v_proj_weight.
          q_proj_weight, k_proj_weight, v_proj_weight, in_proj_bias: input projection weight and bias.
          static_k, static_v: static key and value used for attention operators.
  
  
      Shape:
          Inputs:
          - query: :math:`(L, N, E)` where L is the target sequence length, N is the batch size, E is
            the embedding dimension.
          - key: :math:`(S, N, E)`, where S is the source sequence length, N is the batch size, E is
            the embedding dimension.
          - value: :math:`(S, N, E)` where S is the source sequence length, N is the batch size, E is
            the embedding dimension.
          - key_padding_mask: :math:`(N, S)` where N is the batch size, S is the source sequence length.
            If a ByteTensor is provided, the non-zero positions will be ignored while the zero positions
            will be unchanged. If a BoolTensor is provided, the positions with the
            value of ``True`` will be ignored while the position with the value of ``False`` will be unchanged.
          - attn_mask: 2D mask :math:`(L, S)` where L is the target sequence length, S is the source sequence length.
            3D mask :math:`(N*num_heads, L, S)` where N is the batch size, L is the target sequence length,
            S is the source sequence length. attn_mask ensures that position i is allowed to attend the unmasked
            positions. If a ByteTensor is provided, the non-zero positions are not allowed to attend
            while the zero positions will be unchanged. If a BoolTensor is provided, positions with ``True``
            are not allowed to attend while ``False`` values will be unchanged. If a FloatTensor
            is provided, it will be added to the attention weight.
          - static_k: :math:`(N*num_heads, S, E/num_heads)`, where S is the source sequence length,
            N is the batch size, E is the embedding dimension. E/num_heads is the head dimension.
          - static_v: :math:`(N*num_heads, S, E/num_heads)`, where S is the source sequence length,
            N is the batch size, E is the embedding dimension. E/num_heads is the head dimension.
          - return_qk: whether return Q and K.
  
          Outputs:
          - attn_output: :math:`(L, N, E)` where L is the target sequence length, N is the batch size,
            E is the embedding dimension.
          - attn_output_weights: :math:`(N, L, S)` where N is the batch size,
            L is the target sequence length, S is the source sequence length.
      """
      if not torch.jit.is_scripting():
          tens_ops = (query, key, value, in_proj_weight, in_proj_bias, bias_k, bias_v,
                      out_proj_weight, out_proj_bias)
          if any([type(t) is not Tensor for t in tens_ops]) and has_torch_function(tens_ops):
              return handle_torch_function(
                  multi_head_attention_forward, tens_ops, query, key, value,
                  embed_dim_to_check, num_heads, in_proj_weight, in_proj_bias,
                  bias_k, bias_v, add_zero_attn, dropout_p, out_proj_weight,
                  out_proj_bias, training=training, key_padding_mask=key_padding_mask,
                  need_weights=need_weights, attn_mask=attn_mask,
                  use_separate_proj_weight=use_separate_proj_weight,
                  q_proj_weight=q_proj_weight, k_proj_weight=k_proj_weight,
                  v_proj_weight=v_proj_weight, static_k=static_k, static_v=static_v)
      tgt_len, bsz, embed_dim = query.size()
      assert embed_dim == embed_dim_to_check
      # allow MHA to have different sizes for the feature dimension
      assert key.size(0) == value.size(0) and key.size(1) == value.size(1)
  
      head_dim = embed_dim // num_heads
      assert head_dim * num_heads == embed_dim, "embed_dim must be divisible by num_heads"
      scaling = float(head_dim) ** -0.5
  
      if not use_separate_proj_weight:
          if torch.equal(query, key) and torch.equal(key, value):
              # self-attention
              q, k, v = linear(query, in_proj_weight, in_proj_bias).chunk(3, dim=-1)
  
          elif torch.equal(key, value):
              # encoder-decoder attention
              # This is inline in_proj function with in_proj_weight and in_proj_bias
              _b = in_proj_bias
              _start = 0
              _end = embed_dim
              _w = in_proj_weight[_start:_end, :]
              if _b is not None:
                  _b = _b[_start:_end]
              q = linear(query, _w, _b)
  
              if key is None:
                  assert value is None
                  k = None
                  v = None
              else:
  
                  # This is inline in_proj function with in_proj_weight and in_proj_bias
                  _b = in_proj_bias
                  _start = embed_dim
                  _end = None
                  _w = in_proj_weight[_start:, :]
                  if _b is not None:
                      _b = _b[_start:]
                  k, v = linear(key, _w, _b).chunk(2, dim=-1)
  
          else:
              # This is inline in_proj function with in_proj_weight and in_proj_bias
              _b = in_proj_bias
              _start = 0
              _end = embed_dim
              _w = in_proj_weight[_start:_end, :]
              if _b is not None:
                  _b = _b[_start:_end]
              q = linear(query, _w, _b)
  
              # This is inline in_proj function with in_proj_weight and in_proj_bias
              _b = in_proj_bias
              _start = embed_dim
              _end = embed_dim * 2
              _w = in_proj_weight[_start:_end, :]
              if _b is not None:
                  _b = _b[_start:_end]
              k = linear(key, _w, _b)
  
              # This is inline in_proj function with in_proj_weight and in_proj_bias
              _b = in_proj_bias
              _start = embed_dim * 2
              _end = None
              _w = in_proj_weight[_start:, :]
              if _b is not None:
                  _b = _b[_start:]
              v = linear(value, _w, _b)
      else:
          q_proj_weight_non_opt = torch.jit._unwrap_optional(q_proj_weight)
          len1, len2 = q_proj_weight_non_opt.size()
          assert len1 == embed_dim and len2 == query.size(-1)
  
          k_proj_weight_non_opt = torch.jit._unwrap_optional(k_proj_weight)
          len1, len2 = k_proj_weight_non_opt.size()
          assert len1 == embed_dim and len2 == key.size(-1)
  
          v_proj_weight_non_opt = torch.jit._unwrap_optional(v_proj_weight)
          len1, len2 = v_proj_weight_non_opt.size()
          assert len1 == embed_dim and len2 == value.size(-1)
  
          if in_proj_bias is not None:
              q = linear(query, q_proj_weight_non_opt, in_proj_bias[0:embed_dim])
              k = linear(key, k_proj_weight_non_opt, in_proj_bias[embed_dim:(embed_dim * 2)])
              v = linear(value, v_proj_weight_non_opt, in_proj_bias[(embed_dim * 2):])
          else:
              q = linear(query, q_proj_weight_non_opt, in_proj_bias)
              k = linear(key, k_proj_weight_non_opt, in_proj_bias)
              v = linear(value, v_proj_weight_non_opt, in_proj_bias)
      q = q * scaling
  
      if attn_mask is not None:
          assert attn_mask.dtype == torch.float32 or attn_mask.dtype == torch.float64 or \
              attn_mask.dtype == torch.float16 or attn_mask.dtype == torch.uint8 or attn_mask.dtype == torch.bool, \
              'Only float, byte, and bool types are supported for attn_mask, not {}'.format(attn_mask.dtype)
          if attn_mask.dtype == torch.uint8:
              warnings.warn("Byte tensor for attn_mask in nn.MultiheadAttention is deprecated. Use bool tensor instead.")
              attn_mask = attn_mask.to(torch.bool)
  
          if attn_mask.dim() == 2:
              attn_mask = attn_mask.unsqueeze(0)
              if list(attn_mask.size()) != [1, query.size(0), key.size(0)]:
                  raise RuntimeError('The size of the 2D attn_mask is not correct.')
          elif attn_mask.dim() == 3:
              if list(attn_mask.size()) != [bsz * num_heads, query.size(0), key.size(0)]:
                  raise RuntimeError('The size of the 3D attn_mask is not correct.')
          else:
              raise RuntimeError("attn_mask's dimension {} is not supported".format(attn_mask.dim()))
          # attn_mask's dim is 3 now.
  
      # convert ByteTensor key_padding_mask to bool
      if key_padding_mask is not None and key_padding_mask.dtype == torch.uint8:
          warnings.warn("Byte tensor for key_padding_mask in nn.MultiheadAttention is deprecated. Use bool tensor instead.")
          key_padding_mask = key_padding_mask.to(torch.bool)
  
      if bias_k is not None and bias_v is not None:
          if static_k is None and static_v is None:
              k = torch.cat([k, bias_k.repeat(1, bsz, 1)])
              v = torch.cat([v, bias_v.repeat(1, bsz, 1)])
              if attn_mask is not None:
                  attn_mask = pad(attn_mask, (0, 1))
              if key_padding_mask is not None:
                  key_padding_mask = pad(key_padding_mask, (0, 1))
          else:
              assert static_k is None, "bias cannot be added to static key."
              assert static_v is None, "bias cannot be added to static value."
      else:
          assert bias_k is None
          assert bias_v is None
  
      # L, N, E
      if return_qk:
          return_q = q.clone() / scaling
          return_k = k.clone()
  
      q = q.contiguous().view(tgt_len, bsz * num_heads, head_dim).transpose(0, 1)
      if k is not None:
          k = k.contiguous().view(-1, bsz * num_heads, head_dim).transpose(0, 1)
      if v is not None:
          v = v.contiguous().view(-1, bsz * num_heads, head_dim).transpose(0, 1)
  
      if static_k is not None:
          assert static_k.size(0) == bsz * num_heads
          assert static_k.size(2) == head_dim
          k = static_k
  
      if static_v is not None:
          assert static_v.size(0) == bsz * num_heads
          assert static_v.size(2) == head_dim
          v = static_v
  
      src_len = k.size(1)
  
      if key_padding_mask is not None:
          assert key_padding_mask.size(0) == bsz
          assert key_padding_mask.size(1) == src_len
  
      if add_zero_attn:
          src_len += 1
          k = torch.cat([k, torch.zeros((k.size(0), 1) + k.size()[2:], dtype=k.dtype, device=k.device)], dim=1)
          v = torch.cat([v, torch.zeros((v.size(0), 1) + v.size()[2:], dtype=v.dtype, device=v.device)], dim=1)
          if attn_mask is not None:
              attn_mask = pad(attn_mask, (0, 1))
          if key_padding_mask is not None:
              key_padding_mask = pad(key_padding_mask, (0, 1))
  
      attn_output_weights = torch.bmm(q, k.transpose(1, 2))
      assert list(attn_output_weights.size()) == [bsz * num_heads, tgt_len, src_len]
  
      if attn_mask is not None:
          if attn_mask.dtype == torch.bool:
              attn_output_weights.masked_fill_(attn_mask, float('-inf'))
          else:
              attn_output_weights += attn_mask
  
  
      if key_padding_mask is not None:
          attn_output_weights = attn_output_weights.view(bsz, num_heads, tgt_len, src_len)
          attn_output_weights = attn_output_weights.masked_fill(
              key_padding_mask.unsqueeze(1).unsqueeze(2),
              float('-inf'),
          )
          attn_output_weights = attn_output_weights.view(bsz * num_heads, tgt_len, src_len)
  
      attn_output_weights = softmax(
          attn_output_weights, dim=-1)
      attn_output_weights = dropout(attn_output_weights, p=dropout_p, training=training)
  
      attn_output = torch.bmm(attn_output_weights, v)
      assert list(attn_output.size()) == [bsz * num_heads, tgt_len, head_dim]
      attn_output = attn_output.transpose(0, 1).contiguous().view(tgt_len, bsz, embed_dim)
      attn_output = linear(attn_output, out_proj_weight, out_proj_bias)
  
      if return_qk:
          if need_weights:
              # average attention weights over heads
              attn_output_weights = attn_output_weights.view(bsz, num_heads, tgt_len, src_len)
              return return_q, return_k, attn_output, attn_output_weights.sum(dim=1) / num_heads
          else:
              return return_q, return_k, attn_output, None
      else:
          if need_weights:
              # average attention weights over heads
              attn_output_weights = attn_output_weights.view(bsz, num_heads, tgt_len, src_len)
              return attn_output, attn_output_weights.sum(dim=1) / num_heads
          else:
              return attn_output, None
  