



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     UpperCAmelCase_       (			__a):
							lowerCamelCase__       =						42
							lowerCamelCase__       =						42
							lowerCamelCase__       =						None



class     UpperCAmelCase_       (			__a  ,   __a):
							lowerCamelCase__       =						2







							@register_to_config
							def __init__(  self,     __a = 0.02,     __a = 100,     __a = 1.007,     __a = 80,     __a = 0.05,     __a = 50,     ):

														'''simple docstring'''

														_lowerCAmelCase	:				Dict					  =       sigma_max

														# setable values
														_lowerCAmelCase	:				List[Any]					  =       None
														_lowerCAmelCase	:				int					  =       None
														_lowerCAmelCase	:				Any					  =       None  # sigma(t_i)







							def   snake_case__ (  self,     __a,     __a = None):

														'''simple docstring'''

														return sample







							def   snake_case__ (  self,     __a,     __a = None):

														'''simple docstring'''

														_lowerCAmelCase	:				Dict					  =       num_inference_steps
														_lowerCAmelCase	:				List[Any]					  =       np.arange(0,     self.num_inference_steps)[::-1].copy()
														_lowerCAmelCase	:				List[str]					  =       torch.from_numpy(lowercase_).to(lowercase_)
														_lowerCAmelCase	:				Optional[Any]					  =       [
														    (
														        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
														]
														_lowerCAmelCase	:				Dict					  =       torch.tensor(lowercase_,     dtype=torch.floataa,     device=lowercase_)







							def   snake_case__ (  self,     __a,     __a,     __a = None):

														'''simple docstring'''

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

														# sample eps ~ N(0, S_noise^2 * I)
														_lowerCAmelCase	:				Optional[int]					  =       self.config.s_noise * randn_tensor(sample.shape,     generator=lowercase_).to(sample.device)
														_lowerCAmelCase	:				List[str]					  =       sigma + gamma * sigma
														_lowerCAmelCase	:				str					  =       sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

														return sample_hat, sigma_hat







							def   snake_case__ (  self,     __a,     __a,     __a,     __a,     __a = True,     ):

														'''simple docstring'''

														_lowerCAmelCase	:				Any					  =       sample_hat + sigma_hat * model_output
														_lowerCAmelCase	:				Tuple					  =       (sample_hat - pred_original_sample) / sigma_hat
														_lowerCAmelCase	:				Union[str, Any]					  =       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   snake_case__ (  self,     __a,     __a,     __a,     __a,     __a,     __a,     __a = True,     ):

														'''simple docstring'''

														_lowerCAmelCase	:				Optional[Any]					  =       sample_prev + sigma_prev * model_output
														_lowerCAmelCase	:				Any					  =       (sample_prev - pred_original_sample) / sigma_prev
														_lowerCAmelCase	:				List[str]					  =       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   snake_case__ (  self,     __a,     __a,     __a):

														'''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}''')

