import math
from dataclasses import dataclass
from typing import Literal

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from ..utils.torch_utils import randn_tensor
from .scheduling_utils import SchedulerMixin


# Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
def betas_for_alpha_bar(
    num_diffusion_timesteps: int,
    max_beta: float = 0.999,
    alpha_transform_type: Literal["cosine", "exp", "laplace"] = "cosine",
) -> torch.Tensor:
    """
    Create a beta schedule that discretizes the given alpha_t_bar function, which defines the cumulative product of
    (1-beta) over time from t = [0,1].

    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
    to that part of the diffusion process.

    Args:
        num_diffusion_timesteps (`int`):
            The number of betas to produce.
        max_beta (`float`, defaults to `0.999`):
            The maximum beta to use; use values lower than 1 to avoid numerical instability.
        alpha_transform_type (`str`, defaults to `"cosine"`):
            The type of noise schedule for `alpha_bar`. Choose from `cosine`, `exp`, or `laplace`.

    Returns:
        `torch.Tensor`:
            The betas used by the scheduler to step the model outputs.
    """
    if alpha_transform_type == "cosine":

        def alpha_bar_fn(t):
            return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2

    elif alpha_transform_type == "laplace":

        def alpha_bar_fn(t):
            lmb = -0.5 * math.copysign(1, 0.5 - t) * math.log(1 - 2 * math.fabs(0.5 - t) + 1e-6)
            snr = math.exp(lmb)
            return math.sqrt(snr / (1 + snr))

    elif alpha_transform_type == "exp":

        def alpha_bar_fn(t):
            return math.exp(t * -12.0)

    else:
        raise ValueError(f"Unsupported alpha_transform_type: {alpha_transform_type}")

    betas = []
    for i in range(num_diffusion_timesteps):
        t1 = i / num_diffusion_timesteps
        t2 = (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar_fn(t2) / alpha_bar_fn(t1), max_beta))
    return torch.tensor(betas, dtype=torch.float32)


@dataclass
class ConsistencyDecoderSchedulerOutput(BaseOutput):
    """
    Output class for the scheduler's `step` function.

    Args:
        prev_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images):
            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
            denoising loop.
    """

    prev_sample: torch.Tensor


class ConsistencyDecoderScheduler(SchedulerMixin, ConfigMixin):
    """
    A scheduler for the consistency decoder used in Stable Diffusion pipelines.

    This scheduler implements a two-step denoising process using consistency models for decoding latent representations
    into images.

    This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic
    methods the library implements for all schedulers such as loading and saving.

    Args:
        num_train_timesteps (`int`, *optional*, defaults to `1024`):
            The number of diffusion steps to train the model.
        sigma_data (`float`, *optional*, defaults to `0.5`):
            The standard deviation of the data distribution. Used for computing the skip and output scaling factors.
    """

    order = 1

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1024,
        sigma_data: float = 0.5,
    ) -> None:
        betas = betas_for_alpha_bar(num_train_timesteps)

        alphas = 1.0 - betas
        alphas_cumprod = torch.cumprod(alphas, dim=0)

        self.sqrt_alphas_cumprod = torch.sqrt(alphas_cumprod)
        self.sqrt_one_minus_alphas_cumprod = torch.sqrt(1.0 - alphas_cumprod)

        sigmas = torch.sqrt(1.0 / alphas_cumprod - 1)

        sqrt_recip_alphas_cumprod = torch.sqrt(1.0 / alphas_cumprod)

        self.c_skip = sqrt_recip_alphas_cumprod * sigma_data**2 / (sigmas**2 + sigma_data**2)
        self.c_out = sigmas * sigma_data / (sigmas**2 + sigma_data**2) ** 0.5
        self.c_in = sqrt_recip_alphas_cumprod / (sigmas**2 + sigma_data**2) ** 0.5

    def set_timesteps(
        self,
        num_inference_steps: int | None = None,
        device: str | torch.device = None,
    ):
        if num_inference_steps != 2:
            raise ValueError("Currently more than 2 inference steps are not supported.")

        self.timesteps = torch.tensor([1008, 512], dtype=torch.long, device=device)
        self.sqrt_alphas_cumprod = self.sqrt_alphas_cumprod.to(device)
        self.sqrt_one_minus_alphas_cumprod = self.sqrt_one_minus_alphas_cumprod.to(device)
        self.c_skip = self.c_skip.to(device)
        self.c_out = self.c_out.to(device)
        self.c_in = self.c_in.to(device)

    @property
    def init_noise_sigma(self) -> torch.Tensor:
        """
        Return the standard deviation of the initial noise distribution.

        Returns:
            `torch.Tensor`:
                The initial noise sigma value from the precomputed `sqrt_one_minus_alphas_cumprod` at the first
                timestep.
        """
        return self.sqrt_one_minus_alphas_cumprod[self.timesteps[0]]

    def scale_model_input(self, sample: torch.Tensor, timestep: int | None = None) -> torch.Tensor:
        """
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep.

        Args:
            sample (`torch.Tensor`):
                The input sample.
            timestep (`int`, *optional*):
                The current timestep in the diffusion chain.

        Returns:
            `torch.Tensor`:
                A scaled input sample.
        """
        return sample * self.c_in[timestep]

    def step(
        self,
        model_output: torch.Tensor,
        timestep: float | torch.Tensor,
        sample: torch.Tensor,
        generator: torch.Generator | None = None,
        return_dict: bool = True,
    ) -> ConsistencyDecoderSchedulerOutput | tuple:
        """
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`torch.Tensor`):
                The direct output from the learned diffusion model.
            timestep (`float` or `torch.Tensor`):
                The current timestep in the diffusion chain.
            sample (`torch.Tensor`):
                A current instance of a sample created by the diffusion process.
            generator (`torch.Generator`, *optional*):
                A random number generator for reproducibility.
            return_dict (`bool`, *optional*, defaults to `True`):
                Whether or not to return a
                [`~schedulers.scheduling_consistency_decoder.ConsistencyDecoderSchedulerOutput`] or `tuple`.

        Returns:
            [`~schedulers.scheduling_consistency_decoder.ConsistencyDecoderSchedulerOutput`] or `tuple`:
                If `return_dict` is `True`,
                [`~schedulers.scheduling_consistency_decoder.ConsistencyDecoderSchedulerOutput`] is returned, otherwise
                a tuple is returned where the first element is the sample tensor.
        """
        x_0 = self.c_out[timestep] * model_output + self.c_skip[timestep] * sample

        timestep_idx = torch.where(self.timesteps == timestep)[0]

        if timestep_idx == len(self.timesteps) - 1:
            prev_sample = x_0
        else:
            noise = randn_tensor(x_0.shape, generator=generator, dtype=x_0.dtype, device=x_0.device)
            prev_sample = (
                self.sqrt_alphas_cumprod[self.timesteps[timestep_idx + 1]].to(x_0.dtype) * x_0
                + self.sqrt_one_minus_alphas_cumprod[self.timesteps[timestep_idx + 1]].to(x_0.dtype) * noise
            )

        if not return_dict:
            return (prev_sample,)

        return ConsistencyDecoderSchedulerOutput(prev_sample=prev_sample)
