import math
import torch
from torch import nn

def get_timestep_embedding(
        timesteps: torch.Tensor,
        embedding_dim: int,
        flip_sin_to_cos: bool = False,
        downscale_freq_shift: float = 1,
        scale: float = 1,
        max_period: int = 10000,
) -> torch.Tensor:
    """
    This matches the implementation in Denoising Diffusion Probabilistic Models: Create sinusoidal timestep embeddings.

    :param timesteps: a 1-D Tensor of N indices, one per batch element.
                      These may be fractional.
    :param embedding_dim: the dimension of the output. :param max_period: controls the minimum frequency of the
    embeddings. :return: an [N x dim] Tensor of positional embeddings.
    """
    assert len(timesteps.shape) == 1, "Timesteps should be a 1d-array"

    half_dim = embedding_dim // 2
    exponent = -math.log(max_period) * torch.arange(
            start = 0,
            end = half_dim,
            dtype = torch.float32,
            device = timesteps.device
    )
    exponent = exponent / (half_dim - downscale_freq_shift)

    emb = torch.exp(exponent)
    emb = timesteps[:, None].float() * emb[None, :]

    # scale embeddings
    emb = scale * emb

    # concat sine and cosine embeddings
    emb = torch.cat([torch.sin(emb), torch.cos(emb)], dim = -1)

    # flip sine and cosine embeddings
    if flip_sin_to_cos:
        emb = torch.cat([emb[:, half_dim:], emb[:, :half_dim]], dim = -1)

    # zero pad
    if embedding_dim % 2 == 1:
        emb = torch.nn.functional.pad(emb, (0, 1, 0, 0))
    return emb


class TimestepEmbedding(nn.Module):
    def __init__(self, in_channels: int, time_embed_dim: int, act_fn: str = "silu", out_dim: int = None):
        super().__init__()

        self.linear_1 = nn.Linear(in_channels, time_embed_dim)
        self.act = None
        if act_fn == "silu":
            self.act = nn.SiLU()
        elif act_fn == "mish":
            self.act = nn.Mish()

        if out_dim is not None:
            time_embed_dim_out = out_dim
        else:
            time_embed_dim_out = time_embed_dim
        self.linear_2 = nn.Linear(time_embed_dim, time_embed_dim_out)

    def forward(self, sample):
        sample = self.linear_1(sample)

        if self.act is not None:
            sample = self.act(sample)

        sample = self.linear_2(sample)
        return sample


class Timesteps(nn.Module):
    def __init__(self, num_channels: int, flip_sin_to_cos: bool, downscale_freq_shift: float):
        super().__init__()
        self.num_channels = num_channels
        self.flip_sin_to_cos = flip_sin_to_cos
        self.downscale_freq_shift = downscale_freq_shift

    def forward(self, timesteps):
        t_emb = get_timestep_embedding(
            timesteps,
            self.num_channels,
            flip_sin_to_cos=self.flip_sin_to_cos,
            downscale_freq_shift=self.downscale_freq_shift,
        )
        return t_emb