"""Positonal Encoding Module."""

import math
from typing import Tuple, Union

import torch
import torch.nn.functional as F


class PositionalEncoding(torch.nn.Module):
    """Positional encoding.

    :param int d_model: embedding dim
    :param float dropout_rate: dropout rate
    :param int max_len: maximum input length

    PE(pos, 2i)   = sin(pos/(10000^(2i/dmodel)))
    PE(pos, 2i+1) = cos(pos/(10000^(2i/dmodel)))
    """

    def __init__(
        self,
        d_model: int,
        dropout_rate: float,
        max_len: int = 5000,
        reverse: bool = False,
    ):
        """Construct an PositionalEncoding object."""
        super().__init__()
        self.d_model = d_model
        self.xscale = math.sqrt(self.d_model)
        self.dropout = torch.nn.Dropout(p=dropout_rate)
        self.max_len = max_len

        self.pe = torch.zeros(self.max_len, self.d_model)
        position = torch.arange(0, self.max_len, dtype=torch.float32).unsqueeze(1)
        div_term = torch.exp(
            torch.arange(0, self.d_model, 2, dtype=torch.float32)
            * -(math.log(10000.0) / self.d_model)
        )
        self.pe[:, 0::2] = torch.sin(position * div_term)
        self.pe[:, 1::2] = torch.cos(position * div_term)
        self.pe = self.pe.unsqueeze(0)

    def forward(
        self, x: torch.Tensor, offset: Union[int, torch.Tensor] = 0
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """Add positional encoding.

        Args:
            x (torch.Tensor): Input. Its shape is (batch, time, ...)
            offset (int, torch.tensor): position offset

        Returns:
            torch.Tensor: Encoded tensor. Its shape is (batch, time, ...)
            torch.Tensor: for compatibility to RelPositionalEncoding
        """

        self.pe = self.pe.to(x.device)
        pos_emb = self.position_encoding(offset, x.size(1), False)
        x = x * self.xscale + pos_emb
        return self.dropout(x), self.dropout(pos_emb)

    def position_encoding(
        self, offset: Union[int, torch.Tensor], size: int, apply_dropout: bool = True
    ) -> torch.Tensor:
        """For getting encoding in a streaming fashion

        Attention!!!!!
        we apply dropout only once at the whole utterance level in a none
        streaming way, but will call this function several times with
        increasing input size in a streaming scenario, so the dropout will
        be applied several times.

        Args:
            offset (int or torch.tensor): start offset
            size (int): required size of position encoding

        Returns:
            torch.Tensor: Corresponding encoding
        """
        # How to subscript a Union type:
        #   https://github.com/pytorch/pytorch/issues/69434
        if isinstance(offset, int):
            assert offset + size < self.max_len
            pos_emb = self.pe[:, offset : offset + size]
        elif isinstance(offset, torch.Tensor) and offset.dim() == 0:  # scalar
            assert offset + size < self.max_len
            pos_emb = self.pe[:, offset : offset + size]
        else:  # for batched streaming decoding on GPU
            assert torch.max(offset) + size < self.max_len
            index = offset.unsqueeze(1) + torch.arange(0, size).to(
                offset.device
            )  # B X T
            flag = index > 0
            # remove negative offset
            index = index * flag
            pos_emb = F.embedding(index, self.pe[0])  # B X T X d_model

        if apply_dropout:
            pos_emb = self.dropout(pos_emb)
        return pos_emb


class RelPositionalEncoding(PositionalEncoding):
    """Relative positional encoding module.
    See : Appendix B in https://arxiv.org/abs/1901.02860
    Args:
        d_model (int): Embedding dimension.
        dropout_rate (float): Dropout rate.
        max_len (int): Maximum input length.
    """

    def __init__(self, d_model: int, dropout_rate: float, max_len: int = 5000):
        """Initialize class."""
        super().__init__(d_model, dropout_rate, max_len, reverse=True)

    def forward(
        self, x: torch.Tensor, offset: Union[int, torch.Tensor] = 0
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """Compute positional encoding.
        Args:
            x (torch.Tensor): Input tensor (batch, time, `*`).
        Returns:
            torch.Tensor: Encoded tensor (batch, time, `*`).
            torch.Tensor: Positional embedding tensor (1, time, `*`).
        """
        self.pe = self.pe.to(x.device)
        x = x * self.xscale
        pos_emb = self.position_encoding(offset, x.size(1), False)
        return self.dropout(x), self.dropout(pos_emb)


class NoPositionalEncoding(torch.nn.Module):
    """No position encoding"""

    def __init__(self, d_model: int, dropout_rate: float):
        super().__init__()
        self.d_model = d_model
        self.dropout = torch.nn.Dropout(p=dropout_rate)

    def forward(
        self, x: torch.Tensor, offset: Union[int, torch.Tensor] = 0
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """Just return zero vector for interface compatibility"""
        pos_emb = torch.zeros(1, x.size(1), self.d_model).to(x.device)
        return self.dropout(x), pos_emb

    def position_encoding(
        self, offset: Union[int, torch.Tensor], size: int
    ) -> torch.Tensor:
        return torch.zeros(1, size, self.d_model)
