# Copyright (c) 2017-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the LICENSE file in
# the root directory of this source tree. An additional grant of patent rights
# can be found in the PATENTS file in the same directory.

import math

import torch
from torch.autograd import Variable
import torch.nn as nn

from fairseq import utils


class SinusoidalPositionalEmbedding(nn.Module):
    """This module produces sinusoidal positional embeddings of any length.

    Padding symbols are ignored, but it is necessary to specify whether padding
    is added on the left side (left_pad=True) or right side (left_pad=False).
    """

    def __init__(self, embedding_dim, padding_idx, left_pad, init_size=1024):
        super().__init__()
        self.embedding_dim = embedding_dim
        self.padding_idx = padding_idx
        self.left_pad = left_pad
        self.weights = SinusoidalPositionalEmbedding.get_embedding(
            init_size,
            embedding_dim,
            padding_idx,
        )
        self.register_buffer('_float_tensor', torch.FloatTensor())

    @staticmethod
    def get_embedding(num_embeddings, embedding_dim, padding_idx=None):
        """Build sinusoidal embeddings.

        This matches the implementation in tensor2tensor, but differs slightly
        from the description in Section 3.5 of "Attention Is All You Need".
        """
        half_dim = embedding_dim // 2
        emb = math.log(10000) / (half_dim - 1)
        emb = torch.exp(torch.arange(half_dim) * -emb)
        emb = torch.arange(num_embeddings).unsqueeze(1) * emb.unsqueeze(0)
        emb = torch.cat([torch.sin(emb), torch.cos(emb)], dim=1).view(num_embeddings, -1)
        if embedding_dim % 2 == 1:
            # zero pad
            emb = torch.cat([emb, torch.zeros(num_embeddings, 1)], dim=1)
        if padding_idx is not None:
            emb[padding_idx, :] = 0
        return emb

    def forward(self, input, incremental_state=None):
        """Input is expected to be of size [bsz x seqlen]."""
        # recompute/expand embeddings if needed
        bsz, seq_len = input.size()
        max_pos = self.padding_idx + 1 + seq_len
        if max_pos > self.weights.size(0):
            self.weights = SinusoidalPositionalEmbedding.get_embedding(
                max_pos,
                self.embedding_dim,
                self.padding_idx,
            ).type_as(self.weights)
        self.weights = self.weights.type_as(self._float_tensor)
        weights = Variable(self.weights)

        if incremental_state is not None:
            # positions is the same for every token when decoding a single step
            return weights[self.padding_idx + seq_len, :].expand(bsz, 1, -1)

        positions = Variable(utils.make_positions(input.data, self.padding_idx, self.left_pad))
        return weights.index_select(0, positions.view(-1)).view(bsz, seq_len, -1)

    def max_positions(self):
        """Maximum number of supported positions."""
        return int(1e5)  # an arbitrary large number
