


import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput







def   lowerCamelCase(				a__		,a__=0.999		,a__="cosine"		,):
				if alpha_transform_type == "cosine":

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

				elif alpha_transform_type == "exp":

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

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

				_SCREAMING_SNAKE_CASE     					=[]
				for i in range(a__):
								_SCREAMING_SNAKE_CASE     					=i / num_diffusion_timesteps
								_SCREAMING_SNAKE_CASE     					=(i + 1) / num_diffusion_timesteps
								betas.append(min(1 - alpha_bar_fn(a__) / alpha_bar_fn(a__)		,a__))
				return torch.tensor(a__		,dtype=torch.floataa)


class   A__							(						UpperCamelCase__				,       UpperCamelCase__					):
						UpperCAmelCase     =  [e.name for e in KarrasDiffusionSchedulers]
						UpperCAmelCase     =  2




						@register_to_config
						def __init__(    self   : str			,      _a   : int = 1000			,      _a   : float = 0.0_00_85			,      _a   : float = 0.0_12			,      _a   : str = "linear"			,      _a   : Optional[Union[np.ndarray, List[float]]] = None			,      _a   : str = "epsilon"			,      _a   : str = "linspace"			,      _a   : int = 0			,      )							->       Optional[int]:


										"""simple docstring"""





										if trained_betas is not None:
														_SCREAMING_SNAKE_CASE     					=torch.tensor(_a			,      dtype=torch.floataa					)
										elif beta_schedule == "linear":
														_SCREAMING_SNAKE_CASE     					=torch.linspace(_a			,      _a			,      _a			,      dtype=torch.floataa					)
										elif beta_schedule == "scaled_linear":
														# this schedule is very specific to the latent diffusion model.
														_SCREAMING_SNAKE_CASE     					=(
														    torch.linspace(beta_start**0.5			,      beta_end**0.5			,      _a			,      dtype=torch.floataa					) ** 2
														)
										elif beta_schedule == "squaredcos_cap_v2":
														# Glide cosine schedule
														_SCREAMING_SNAKE_CASE     					=betas_for_alpha_bar(_a					)
										else:
														raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"					)

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

										#  set all values
										self.set_timesteps(_a			,      _a			,      _a					)




						def 							__UpperCamelCase			(    self   : Union[str, Any]			,      _a   : List[str]			,      _a   : int=None					)							->       Optional[Any]:


										"""simple docstring"""





										if schedule_timesteps is None:
														_SCREAMING_SNAKE_CASE     					=self.timesteps

										_SCREAMING_SNAKE_CASE     					=(schedule_timesteps == timestep).nonzero()

										# The sigma index that is taken for the **very** first `step`
										# is always the second index (or the last index if there is only 1)
										# This way we can ensure we don't accidentally skip a sigma in
										# case we start in the middle of the denoising schedule (e.g. for image-to-image)
										if len(self._index_counter					) == 0:
														_SCREAMING_SNAKE_CASE     					=1 if len(_a					) > 1 else 0
										else:
														_SCREAMING_SNAKE_CASE     					=timestep.cpu().item() if torch.is_tensor(_a					) else timestep
														_SCREAMING_SNAKE_CASE     					=self._index_counter[timestep_int]

										return indices[pos].item()




						@property
						def 							__UpperCamelCase			(    self   : Tuple					)							->       Optional[Any]:


										"""simple docstring"""





										if self.config.timestep_spacing in ["linspace", "trailing"]:
														return self.sigmas.max()

										return (self.sigmas.max() ** 2 + 1) ** 0.5




						def 							__UpperCamelCase			(    self   : Tuple			,      _a   : torch.FloatTensor			,      _a   : Union[float, torch.FloatTensor]			,      )							->       torch.FloatTensor:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE     					=self.index_for_timestep(_a					)

										if self.state_in_first_order:
														_SCREAMING_SNAKE_CASE     					=self.sigmas[step_index]
										else:
														_SCREAMING_SNAKE_CASE     					=self.sigmas_interpol[step_index - 1]

										_SCREAMING_SNAKE_CASE     					=sample / ((sigma**2 + 1) ** 0.5)
										return sample




						def 							__UpperCamelCase			(    self   : Dict			,      _a   : int			,      _a   : Union[str, torch.device] = None			,      _a   : Optional[int] = None			,      )							->       List[Any]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE     					=num_inference_steps

										_SCREAMING_SNAKE_CASE     					=num_train_timesteps or self.config.num_train_timesteps

										# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
										if self.config.timestep_spacing == "linspace":
														_SCREAMING_SNAKE_CASE     					=np.linspace(0			,      num_train_timesteps - 1			,      _a			,      dtype=_a					)[::-1].copy()
										elif self.config.timestep_spacing == "leading":
														_SCREAMING_SNAKE_CASE     					=num_train_timesteps // self.num_inference_steps
														# creates integer timesteps by multiplying by ratio
														# casting to int to avoid issues when num_inference_step is power of 3
														_SCREAMING_SNAKE_CASE     					=(np.arange(0			,      _a					) * step_ratio).round()[::-1].copy().astype(_a					)
														timesteps += self.config.steps_offset
										elif self.config.timestep_spacing == "trailing":
														_SCREAMING_SNAKE_CASE     					=num_train_timesteps / self.num_inference_steps
														# creates integer timesteps by multiplying by ratio
														# casting to int to avoid issues when num_inference_step is power of 3
														_SCREAMING_SNAKE_CASE     					=(np.arange(_a			,      0			,      -step_ratio					)).round().copy().astype(_a					)
														timesteps -= 1
										else:
														raise ValueError(
														    f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."					)

										_SCREAMING_SNAKE_CASE     					=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
										_SCREAMING_SNAKE_CASE     					=torch.from_numpy(np.log(_a					)					).to(_a					)

										_SCREAMING_SNAKE_CASE     					=np.interp(_a			,      np.arange(0			,      len(_a					)					)			,      _a					)
										_SCREAMING_SNAKE_CASE     					=np.concatenate([sigmas, [0.0]]					).astype(np.floataa					)
										_SCREAMING_SNAKE_CASE     					=torch.from_numpy(_a					).to(device=_a					)

										# compute up and down sigmas
										_SCREAMING_SNAKE_CASE     					=sigmas.roll(-1					)
										_SCREAMING_SNAKE_CASE     					=0.0
										_SCREAMING_SNAKE_CASE     					=(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
										_SCREAMING_SNAKE_CASE     					=(sigmas_next**2 - sigmas_up**2) ** 0.5
										_SCREAMING_SNAKE_CASE     					=0.0

										# compute interpolated sigmas
										_SCREAMING_SNAKE_CASE     					=sigmas.log().lerp(sigmas_down.log()			,      0.5					).exp()
										_SCREAMING_SNAKE_CASE     					=0.0

										# set sigmas
										_SCREAMING_SNAKE_CASE     					=torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2					), sigmas[-1:]]					)
										_SCREAMING_SNAKE_CASE     					=torch.cat(
										    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2					), sigmas_interpol[-1:]]					)
										_SCREAMING_SNAKE_CASE     					=torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2					), sigmas_up[-1:]]					)
										_SCREAMING_SNAKE_CASE     					=torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2					), sigmas_down[-1:]]					)

										if str(_a					).startswith('''mps'''					):
														# mps does not support float64
														_SCREAMING_SNAKE_CASE     					=torch.from_numpy(_a					).to(_a			,      dtype=torch.floataa					)
										else:
														_SCREAMING_SNAKE_CASE     					=torch.from_numpy(_a					).to(_a					)

										_SCREAMING_SNAKE_CASE     					=self.sigma_to_t(_a					).to(_a			,      dtype=timesteps.dtype					)
										_SCREAMING_SNAKE_CASE     					=torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])			,      dim=-1					).flatten()

										_SCREAMING_SNAKE_CASE     					=torch.cat([timesteps[:1], interleaved_timesteps]					)

										_SCREAMING_SNAKE_CASE     					=None

										# for exp beta schedules, such as the one for `pipeline_shap_e.py`
										# we need an index counter
										_SCREAMING_SNAKE_CASE     					=defaultdict(_a					)




						def 							__UpperCamelCase			(    self   : str			,      _a   : Optional[Any]					)							->       Union[str, Any]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE     					=sigma.log()

										# get distribution
										_SCREAMING_SNAKE_CASE     					=log_sigma - self.log_sigmas[:, None]

										# get sigmas range
										_SCREAMING_SNAKE_CASE     					=dists.ge(0					).cumsum(dim=0					).argmax(dim=0					).clamp(max=self.log_sigmas.shape[0] - 2					)
										_SCREAMING_SNAKE_CASE     					=low_idx + 1

										_SCREAMING_SNAKE_CASE     					=self.log_sigmas[low_idx]
										_SCREAMING_SNAKE_CASE     					=self.log_sigmas[high_idx]

										# interpolate sigmas
										_SCREAMING_SNAKE_CASE     					=(low - log_sigma) / (low - high)
										_SCREAMING_SNAKE_CASE     					=w.clamp(0			,      1					)

										# transform interpolation to time range
										_SCREAMING_SNAKE_CASE     					=(1 - w) * low_idx + w * high_idx
										_SCREAMING_SNAKE_CASE     					=t.view(sigma.shape					)
										return t




						@property
						def 							__UpperCamelCase			(    self   : Any					)							->       Dict:


										"""simple docstring"""





										return self.sample is None




						def 							__UpperCamelCase			(    self   : Dict			,      _a   : Union[torch.FloatTensor, np.ndarray]			,      _a   : Union[float, torch.FloatTensor]			,      _a   : Union[torch.FloatTensor, np.ndarray]			,      _a   : Optional[torch.Generator] = None			,      _a   : bool = True			,      )							->       Union[SchedulerOutput, Tuple]:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE     					=self.index_for_timestep(_a					)

										# advance index counter by 1
										_SCREAMING_SNAKE_CASE     					=timestep.cpu().item() if torch.is_tensor(_a					) else timestep
										self._index_counter[timestep_int] += 1

										if self.state_in_first_order:
														_SCREAMING_SNAKE_CASE     					=self.sigmas[step_index]
														_SCREAMING_SNAKE_CASE     					=self.sigmas_interpol[step_index]
														_SCREAMING_SNAKE_CASE     					=self.sigmas_up[step_index]
														_SCREAMING_SNAKE_CASE     					=self.sigmas_down[step_index - 1]
										else:
														# 2nd order / KPDM2's method
														_SCREAMING_SNAKE_CASE     					=self.sigmas[step_index - 1]
														_SCREAMING_SNAKE_CASE     					=self.sigmas_interpol[step_index - 1]
														_SCREAMING_SNAKE_CASE     					=self.sigmas_up[step_index - 1]
														_SCREAMING_SNAKE_CASE     					=self.sigmas_down[step_index - 1]

										# currently only gamma=0 is supported. This usually works best anyways.
										# We can support gamma in the future but then need to scale the timestep before
										# passing it to the model which requires a change in API
										_SCREAMING_SNAKE_CASE     					=0
										_SCREAMING_SNAKE_CASE     					=sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

										_SCREAMING_SNAKE_CASE     					=model_output.device
										_SCREAMING_SNAKE_CASE     					=randn_tensor(model_output.shape			,      dtype=model_output.dtype			,      device=_a			,      generator=_a					)

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
														_SCREAMING_SNAKE_CASE     					=sigma_hat if self.state_in_first_order else sigma_interpol
														_SCREAMING_SNAKE_CASE     					=sample - sigma_input * model_output
										elif self.config.prediction_type == "v_prediction":
														_SCREAMING_SNAKE_CASE     					=sigma_hat if self.state_in_first_order else sigma_interpol
														_SCREAMING_SNAKE_CASE     					=model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
														    sample / (sigma_input**2 + 1)
														)
										elif self.config.prediction_type == "sample":
														raise NotImplementedError('''prediction_type not implemented yet: sample'''					)
										else:
														raise ValueError(
														    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"					)

										if self.state_in_first_order:
														# 2. Convert to an ODE derivative for 1st order
														_SCREAMING_SNAKE_CASE     					=(sample - pred_original_sample) / sigma_hat
														# 3. delta timestep
														_SCREAMING_SNAKE_CASE     					=sigma_interpol - sigma_hat

														# store for 2nd order step
														_SCREAMING_SNAKE_CASE     					=sample
														_SCREAMING_SNAKE_CASE     					=dt
														_SCREAMING_SNAKE_CASE     					=sample + derivative * dt
										else:
														# DPM-Solver-2
														# 2. Convert to an ODE derivative for 2nd order
														_SCREAMING_SNAKE_CASE     					=(sample - pred_original_sample) / sigma_interpol
														# 3. delta timestep
														_SCREAMING_SNAKE_CASE     					=sigma_down - sigma_hat

														_SCREAMING_SNAKE_CASE     					=self.sample
														_SCREAMING_SNAKE_CASE     					=None

														_SCREAMING_SNAKE_CASE     					=sample + derivative * dt
														_SCREAMING_SNAKE_CASE     					=prev_sample + noise * sigma_up

										if not return_dict:
														return (prev_sample,)

										return SchedulerOutput(prev_sample=_a					)




						def 							__UpperCamelCase			(    self   : Dict			,      _a   : torch.FloatTensor			,      _a   : torch.FloatTensor			,      _a   : torch.FloatTensor			,      )							->       torch.FloatTensor:


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE     					=self.sigmas.to(device=original_samples.device			,      dtype=original_samples.dtype					)
										if original_samples.device.type == "mps" and torch.is_floating_point(_a					):
														# mps does not support float64
														_SCREAMING_SNAKE_CASE     					=self.timesteps.to(original_samples.device			,      dtype=torch.floataa					)
														_SCREAMING_SNAKE_CASE     					=timesteps.to(original_samples.device			,      dtype=torch.floataa					)
										else:
														_SCREAMING_SNAKE_CASE     					=self.timesteps.to(original_samples.device					)
														_SCREAMING_SNAKE_CASE     					=timesteps.to(original_samples.device					)

										_SCREAMING_SNAKE_CASE     					=[self.index_for_timestep(_a			,      _a					) for t in timesteps]

										_SCREAMING_SNAKE_CASE     					=sigmas[step_indices].flatten()
										while len(sigma.shape					) < len(original_samples.shape					):
														_SCREAMING_SNAKE_CASE     					=sigma.unsqueeze(-1					)

										_SCREAMING_SNAKE_CASE     					=original_samples + noise * sigma
										return noisy_samples




						def __len__(    self   : Optional[int]					)							->       Union[str, Any]:


										"""simple docstring"""





										return self.config.num_train_timesteps



import math







def   lowerCamelCase(				a__):
				_SCREAMING_SNAKE_CASE     					=math.log(2		,10) * number
				_SCREAMING_SNAKE_CASE     					=round((log_number - int(a__))		,15)

				return difference







def   lowerCamelCase(				a__ = 67_8910):
				_SCREAMING_SNAKE_CASE     					=90
				_SCREAMING_SNAKE_CASE     					=0

				_SCREAMING_SNAKE_CASE     					=math.log(1.23		,10)
				_SCREAMING_SNAKE_CASE     					=math.log(1.24		,10)
				_SCREAMING_SNAKE_CASE     					=0

				while position < number:
								_SCREAMING_SNAKE_CASE     					=log_difference(a__)

								if difference >= upper_limit:
												power_iterator += 93

								elif difference < lower_limit:
												power_iterator += 196

								else:
												_SCREAMING_SNAKE_CASE     					=power_iterator
												power_iterator += 196
												position += 1

				return previous_power


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							print(f"""{solution() = }""")