



'''simple docstring'''





import math
from timeit import timeit

def 	a_					(							_lowerCAmelCase	)				->				int:
  __lowerCamelCase	:	int   	=			0
  __lowerCamelCase	:	Optional[int]   	=			abs(_lowerCAmelCase	)
  while True:
    __lowerCamelCase	:	List[str]   	=			n // 10
    digits += 1
    if n == 0:
      break
  return digits

def 	a_					(							_lowerCAmelCase	)				->				int:
  return 1 if n == 0 else math.floor(math.log(abs(_lowerCAmelCase	)	,10	) + 1	)

def 	a_					(							_lowerCAmelCase	)				->				int:
  return len(str(abs(_lowerCAmelCase	)	)	)

def 	a_					(							)				->				None:
  from collections.abc import Callable

  def benchmark_a_function(_lowerCAmelCase	,_lowerCAmelCase	) -> None:
    __lowerCamelCase	:	Any   	=			F'{func.__name__}({value})'
    __lowerCamelCase	:	int   	=			timeit(F'__main__.{call}'	,setup='import __main__'	)
    print(F'{call}: {func(_lowerCAmelCase	)} -- {timing} seconds'	)

  for value in (262144, 1125899906842624, 1267650600228229401496703205376):
    for func in (num_digits, num_digits_fast, num_digits_faster):
      benchmark_a_function(_lowerCAmelCase	,_lowerCAmelCase	)
    print()


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   benchmark()











'''simple docstring'''





import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class  lowerCamelCase_   (    SCREAMING_SNAKE_CASE_					):
  """simple docstring"""




  a_							 =42
  a_							 =None




def 	a_					(							_lowerCAmelCase	,_lowerCAmelCase=0.999	,_lowerCAmelCase="cosine"	,)				->				Union[str, Any]:
  if alpha_transform_type == "cosine":

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

  elif alpha_transform_type == "exp":

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

  else:
    raise ValueError(F'Unsupported alpha_tranform_type: {alpha_transform_type}'	)

  __lowerCamelCase	:	Union[str, Any]   	=			[]
  for i in range(_lowerCAmelCase	):
    __lowerCamelCase	:	Dict   	=			i / num_diffusion_timesteps
    __lowerCamelCase	:	Optional[int]   	=			(i + 1) / num_diffusion_timesteps
    betas.append(min(1 - alpha_bar_fn(_lowerCAmelCase	) / alpha_bar_fn(_lowerCAmelCase	)	,_lowerCAmelCase	)	)
  return torch.tensor(_lowerCAmelCase	,dtype=torch.floataa	)






class  lowerCamelCase_   (    SCREAMING_SNAKE_CASE_       ,       SCREAMING_SNAKE_CASE_					):
  """simple docstring"""




  a_							 =[e.name for e in KarrasDiffusionSchedulers]
  a_							 =1




  @register_to_config
  def __init__(			self				:     List[Any]      ,     _a				:     int = 1000      ,     _a				:     float = 0.0001      ,     _a				:     float = 0.02      ,     _a				:     str = "linear"      ,     _a				:     Optional[Union[np.ndarray, List[float]]] = None      ,     _a				:     Optional[bool] = False      ,     _a				:     str = "epsilon"      ,     _a				:     str = "linspace"      ,     _a				:     int = 0      ,     ) -> Tuple:
    if trained_betas is not None:
      __lowerCamelCase	:	Optional[int]   	=			torch.tensor(_a      ,     dtype=torch.floataa       )
    elif beta_schedule == "linear":
      __lowerCamelCase	:	List[str]   	=			torch.linspace(_a      ,     _a      ,     _a      ,     dtype=torch.floataa       )
    elif beta_schedule == "scaled_linear":
      # this schedule is very specific to the latent diffusion model.
      __lowerCamelCase	:	Optional[int]   	=			(
          torch.linspace(beta_start**0.5      ,     beta_end**0.5      ,     _a      ,     dtype=torch.floataa       ) ** 2
      )
    elif beta_schedule == "squaredcos_cap_v2":
      # Glide cosine schedule
      __lowerCamelCase	:	Any   	=			betas_for_alpha_bar(_a       )
    else:
      raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'       )

    __lowerCamelCase	:	Optional[Any]   	=			1.0 - self.betas
    __lowerCamelCase	:	Optional[int]   	=			torch.cumprod(self.alphas      ,     dim=0       )

    __lowerCamelCase	:	str   	=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
    __lowerCamelCase	:	Optional[Any]   	=			np.concatenate([sigmas[::-1], [0.0]]       ).astype(np.floataa       )
    __lowerCamelCase	:	Dict   	=			torch.from_numpy(_a       )

    # setable values
    __lowerCamelCase	:	List[str]   	=			None
    __lowerCamelCase	:	int   	=			use_karras_sigmas
    self.set_timesteps(_a      ,     _a       )
    __lowerCamelCase	:	int   	=			[]
    __lowerCamelCase	:	Dict   	=			False




  @property
  def 						_lowercase					(			self				:     Optional[Any]       ) -> Any:
    # standard deviation of the initial noise distribution
    if self.config.timestep_spacing in ["linspace", "trailing"]:
      return self.sigmas.max()

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




  def 						_lowercase					(			self				:     List[Any]      ,     _a				:     torch.FloatTensor      ,     _a				:     Union[float, torch.FloatTensor]       ) -> torch.FloatTensor:
    if isinstance(_a      ,     torch.Tensor       ):
      __lowerCamelCase	:	List[Any]   	=			timestep.to(self.timesteps.device       )
    __lowerCamelCase	:	int   	=			(self.timesteps == timestep).nonzero().item()
    __lowerCamelCase	:	Any   	=			self.sigmas[step_index]
    __lowerCamelCase	:	List[str]   	=			sample / ((sigma**2 + 1) ** 0.5)
    __lowerCamelCase	:	Any   	=			True
    return sample




  def 						_lowercase					(			self				:     Optional[int]      ,     _a				:     str      ,     _a				:     List[str]      ,     _a				:     Union[str, Any]       ) -> Optional[Any]:

    def lms_derivative(_a				:     List[str]       ):
      __lowerCamelCase	:	Any   	=			1.0
      for k in range(_a       ):
        if current_order == k:
          continue
        prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
      return prod

    __lowerCamelCase	:	Any   	=			integrate.quad(_a      ,     self.sigmas[t]      ,     self.sigmas[t + 1]      ,     epsrel=1e-4       )[0]

    return integrated_coeff




  def 						_lowercase					(			self				:     int      ,     _a				:     int      ,     _a				:     Union[str, torch.device] = None       ) -> str:
    __lowerCamelCase	:	Optional[Any]   	=			num_inference_steps

    # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
    if self.config.timestep_spacing == "linspace":
      __lowerCamelCase	:	Any   	=			np.linspace(0      ,     self.config.num_train_timesteps - 1      ,     _a      ,     dtype=_a       )[
          ::-1
      ].copy()
    elif self.config.timestep_spacing == "leading":
      __lowerCamelCase	:	Union[str, Any]   	=			self.config.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
      __lowerCamelCase	:	Union[str, Any]   	=			(np.arange(0      ,     _a       ) * step_ratio).round()[::-1].copy().astype(_a       )
      timesteps += self.config.steps_offset
    elif self.config.timestep_spacing == "trailing":
      __lowerCamelCase	:	int   	=			self.config.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
      __lowerCamelCase	:	str   	=			(np.arange(self.config.num_train_timesteps      ,     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\'.'       )

    __lowerCamelCase	:	Optional[Any]   	=			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
    __lowerCamelCase	:	List[Any]   	=			np.log(_a       )
    __lowerCamelCase	:	Optional[int]   	=			np.interp(_a      ,     np.arange(0      ,     len(_a       )       )      ,     _a       )

    if self.use_karras_sigmas:
      __lowerCamelCase	:	int   	=			self._convert_to_karras(in_sigmas=_a       )
      __lowerCamelCase	:	str   	=			np.array([self._sigma_to_t(_a      ,     _a       ) for sigma in sigmas]       )

    __lowerCamelCase	:	Optional[Any]   	=			np.concatenate([sigmas, [0.0]]       ).astype(np.floataa       )

    __lowerCamelCase	:	Dict   	=			torch.from_numpy(_a       ).to(device=_a       )
    if str(_a       ).startswith('mps'       ):
      # mps does not support float64
      __lowerCamelCase	:	List[str]   	=			torch.from_numpy(_a       ).to(_a      ,     dtype=torch.floataa       )
    else:
      __lowerCamelCase	:	str   	=			torch.from_numpy(_a       ).to(device=_a       )

    __lowerCamelCase	:	List[Any]   	=			[]




  def 						_lowercase					(			self				:     List[Any]      ,     _a				:     List[Any]      ,     _a				:     int       ) -> Tuple:
    # get log sigma
    __lowerCamelCase	:	Optional[int]   	=			np.log(_a       )

    # get distribution
    __lowerCamelCase	:	int   	=			log_sigma - log_sigmas[:, np.newaxis]

    # get sigmas range
    __lowerCamelCase	:	Dict   	=			np.cumsum((dists >= 0)      ,     axis=0       ).argmax(axis=0       ).clip(max=log_sigmas.shape[0] - 2       )
    __lowerCamelCase	:	List[Any]   	=			low_idx + 1

    __lowerCamelCase	:	Optional[Any]   	=			log_sigmas[low_idx]
    __lowerCamelCase	:	str   	=			log_sigmas[high_idx]

    # interpolate sigmas
    __lowerCamelCase	:	List[str]   	=			(low - log_sigma) / (low - high)
    __lowerCamelCase	:	List[str]   	=			np.clip(_a      ,     0      ,     1       )

    # transform interpolation to time range
    __lowerCamelCase	:	Dict   	=			(1 - w) * low_idx + w * high_idx
    __lowerCamelCase	:	List[str]   	=			t.reshape(sigma.shape       )
    return t




  def 						_lowercase					(			self				:     int      ,     _a				:     torch.FloatTensor       ) -> torch.FloatTensor:
    __lowerCamelCase	:	float   	=			in_sigmas[-1].item()
    __lowerCamelCase	:	float   	=			in_sigmas[0].item()

    __lowerCamelCase	:	Optional[Any]   	=			7.0  # 7.0 is the value used in the paper
    __lowerCamelCase	:	Any   	=			np.linspace(0      ,     1      ,     self.num_inference_steps       )
    __lowerCamelCase	:	Optional[Any]   	=			sigma_min ** (1 / rho)
    __lowerCamelCase	:	Tuple   	=			sigma_max ** (1 / rho)
    __lowerCamelCase	:	str   	=			(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
    return sigmas




  def 						_lowercase					(			self				:     Dict      ,     _a				:     torch.FloatTensor      ,     _a				:     Union[float, torch.FloatTensor]      ,     _a				:     torch.FloatTensor      ,     _a				:     int = 4      ,     _a				:     bool = True      ,     ) -> Union[LMSDiscreteSchedulerOutput, Tuple]:
    if not self.is_scale_input_called:
      warnings.warn(
          'The `scale_model_input` function should be called before `step` to ensure correct denoising. '
          'See `StableDiffusionPipeline` for a usage example.'       )

    if isinstance(_a      ,     torch.Tensor       ):
      __lowerCamelCase	:	Optional[int]   	=			timestep.to(self.timesteps.device       )
    __lowerCamelCase	:	List[str]   	=			(self.timesteps == timestep).nonzero().item()
    __lowerCamelCase	:	Optional[int]   	=			self.sigmas[step_index]

    # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
    if self.config.prediction_type == "epsilon":
      __lowerCamelCase	:	Optional[Any]   	=			sample - sigma * model_output
    elif self.config.prediction_type == "v_prediction":
      # * c_out + input * c_skip
      __lowerCamelCase	:	List[str]   	=			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
    elif self.config.prediction_type == "sample":
      __lowerCamelCase	:	Union[str, Any]   	=			model_output
    else:
      raise ValueError(
          f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'       )

    # 2. Convert to an ODE derivative
    __lowerCamelCase	:	str   	=			(sample - pred_original_sample) / sigma
    self.derivatives.append(_a       )
    if len(self.derivatives       ) > order:
      self.derivatives.pop(0       )

    # 3. Compute linear multistep coefficients
    __lowerCamelCase	:	List[str]   	=			min(step_index + 1      ,     _a       )
    __lowerCamelCase	:	int   	=			[self.get_lms_coefficient(_a      ,     _a      ,     _a       ) for curr_order in range(_a       )]

    # 4. Compute previous sample based on the derivatives path
    __lowerCamelCase	:	Optional[Any]   	=			sample + sum(
        coeff * derivative for coeff, derivative in zip(_a      ,     reversed(self.derivatives       )       )       )

    if not return_dict:
      return (prev_sample,)

    return LMSDiscreteSchedulerOutput(prev_sample=_a      ,     pred_original_sample=_a       )




  def 						_lowercase					(			self				:     List[str]      ,     _a				:     torch.FloatTensor      ,     _a				:     torch.FloatTensor      ,     _a				:     torch.FloatTensor      ,     ) -> torch.FloatTensor:
    # Make sure sigmas and timesteps have the same device and dtype as original_samples
    __lowerCamelCase	:	Any   	=			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
      __lowerCamelCase	:	Optional[int]   	=			self.timesteps.to(original_samples.device      ,     dtype=torch.floataa       )
      __lowerCamelCase	:	Optional[int]   	=			timesteps.to(original_samples.device      ,     dtype=torch.floataa       )
    else:
      __lowerCamelCase	:	int   	=			self.timesteps.to(original_samples.device       )
      __lowerCamelCase	:	Optional[Any]   	=			timesteps.to(original_samples.device       )

    __lowerCamelCase	:	List[str]   	=			[(schedule_timesteps == t).nonzero().item() for t in timesteps]

    __lowerCamelCase	:	Union[str, Any]   	=			sigmas[step_indices].flatten()
    while len(sigma.shape       ) < len(original_samples.shape       ):
      __lowerCamelCase	:	List[Any]   	=			sigma.unsqueeze(-1       )

    __lowerCamelCase	:	Optional[Any]   	=			original_samples + noise * sigma
    return noisy_samples




  def __len__(			self				:     Union[str, Any]       ) -> int:
    return self.config.num_train_timesteps






