'''simple docstring'''


from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

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





@dataclass
class       _a    (		__a      ):


  """simple docstring"""

  A_    							=						42
  A_    							=						42
  A_    							=						None






class       _a    (		__a ,				__a      ):


  """simple docstring"""

  A_    							=						2




  @register_to_config
  def __init__(		self      :       Optional[Any]   ,				lowercase_      :       float = 0.0_2   ,				lowercase_      :       float = 100   ,				lowercase_      :       float = 1.0_0_7   ,				lowercase_      :       float = 80   ,				lowercase_      :       float = 0.0_5   ,				lowercase_      :       float = 50   ,				):







    '''simple docstring'''


    lowercase_     =       sigma_max

    # setable values
    lowercase_     =       None
    lowercase_     =       None
    lowercase_     =       None  # sigma(t_i)




  def 		lowerCamelCase__  (		self      :       int   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       Optional[int] = None      ):







    '''simple docstring'''


    return sample




  def 		lowerCamelCase__  (		self      :       Dict   ,				lowercase_      :       int   ,				lowercase_      :       Union[str, torch.device] = None      ):







    '''simple docstring'''


    lowercase_     =       num_inference_steps
    lowercase_     =       np.arange(0   ,				self.num_inference_steps      )[::-1].copy()
    lowercase_     =       torch.from_numpy(lowercase_      ).to(lowercase_      )
    lowercase_     =       [
        (
            self.config.sigma_max**2
            * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
        )
        for i in self.timesteps
    ]
    lowercase_     =       torch.tensor(lowercase_   ,				dtype=torch.floataa   ,				device=lowercase_      )




  def 		lowerCamelCase__  (		self      :       List[Any]   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       float   ,				lowercase_      :       Optional[torch.Generator] = None      ):







    '''simple docstring'''


    if self.config.s_min <= sigma <= self.config.s_max:
      lowercase_     =       min(self.config.s_churn / self.num_inference_steps   ,				2**0.5 - 1      )
    else:
      lowercase_     =       0

    # sample eps ~ N(0, S_noise^2 * I)
    lowercase_     =       self.config.s_noise * randn_tensor(sample.shape   ,				generator=lowercase_      ).to(sample.device      )
    lowercase_     =       sigma + gamma * sigma
    lowercase_     =       sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

    return sample_hat, sigma_hat




  def 		lowerCamelCase__  (		self      :       Union[str, Any]   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       float   ,				lowercase_      :       float   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       bool = True   ,				):







    '''simple docstring'''


    lowercase_     =       sample_hat + sigma_hat * model_output
    lowercase_     =       (sample_hat - pred_original_sample) / sigma_hat
    lowercase_     =       sample_hat + (sigma_prev - sigma_hat) * derivative

    if not return_dict:
      return (sample_prev, derivative)

    return KarrasVeOutput(
        prev_sample=lowercase_   ,				derivative=lowercase_   ,				pred_original_sample=lowercase_      )




  def 		lowerCamelCase__  (		self      :       int   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       float   ,				lowercase_      :       float   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       torch.FloatTensor   ,				lowercase_      :       bool = True   ,				):







    '''simple docstring'''


    lowercase_     =       sample_prev + sigma_prev * model_output
    lowercase_     =       (sample_prev - pred_original_sample) / sigma_prev
    lowercase_     =       sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

    if not return_dict:
      return (sample_prev, derivative)

    return KarrasVeOutput(
        prev_sample=lowercase_   ,				derivative=lowercase_   ,				pred_original_sample=lowercase_      )





  def 		lowerCamelCase__  (		self      :       Dict   ,				lowercase_      :       Tuple   ,				lowercase_      :       Tuple   ,				lowercase_      :       Optional[Any]      ):







    '''simple docstring'''


    raise NotImplementedError()


'''simple docstring'''


import math

def   A_      (       SCREAMING_SNAKE_CASE_						)			->int:

  if not isinstance(SCREAMING_SNAKE_CASE_ ,	SCREAMING_SNAKE_CASE_						):
    lowercase_     =       f"""Input value of [number={number}] must be an integer"""
    raise TypeError(SCREAMING_SNAKE_CASE_						)

  if number < 1:
    lowercase_     =       f"""Input value of [number={number}] must be > 0"""
    raise ValueError(SCREAMING_SNAKE_CASE_						)
  elif number == 1:
    return 3
  elif number == 2:
    return 5
  else:
    lowercase_     =       int(math.log(number // 3 ,	2						)						) + 2

    lowercase_     =       [3, 5]
    lowercase_     =       2
    lowercase_     =       3
    for block in range(1 ,	SCREAMING_SNAKE_CASE_						):
      for _ in range(SCREAMING_SNAKE_CASE_						):
        proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]						)
        proth_index += 1
      increment *= 2

  return proth_list[number - 1]


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       for number in range(11):
              __snake_case						  =		0
              try:
                     __snake_case						  =		proth(number)
              except ValueError:
                     print(f'''ValueError: there is no {number}th Proth number''')
                     continue

              print(f'''The {number}th Proth number: {value}''')

