






'''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 				lowercase       (							__lowercase      ):


    '''simple docstring'''

    lowerCAmelCase__      				=							42
    lowerCAmelCase__      				=							42
    lowerCAmelCase__      				=							None
class 				lowercase       (							__lowercase ,       __lowercase      ):


    '''simple docstring'''

    lowerCAmelCase__      				=							2

    @register_to_config
    def __init__(					self     :     Any				,     __lowerCamelCase     :     float = 0.0_2				,     __lowerCamelCase     :     float = 100				,     __lowerCamelCase     :     float = 1.0_0_7				,     __lowerCamelCase     :     float = 80				,     __lowerCamelCase     :     float = 0.0_5				,     __lowerCamelCase     :     float = 50				,     )							->							Tuple:

     '''simple docstring'''




     lowerCamelCase__  =     sigma_max

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

    def    a__				(					self     :     Union[str, Any]				,     __lowerCamelCase     :     torch.FloatTensor				,     __lowerCamelCase     :     Optional[int] = None     )							->							Union[str, Any]:

     '''simple docstring'''




     return sample

    def    a__				(					self     :     Tuple				,     __lowerCamelCase     :     int				,     __lowerCamelCase     :     Union[str, torch.device] = None     )							->							Tuple:

     '''simple docstring'''




     lowerCamelCase__  =     num_inference_steps
     lowerCamelCase__  =     np.arange(0				,     self.num_inference_steps     )[::-1].copy()
     lowerCamelCase__  =     torch.from_numpy(_A     ).to(_A     )
     lowerCamelCase__  =     [
         (
             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__  =     torch.tensor(_A				,     dtype=torch.floataa				,     device=_A     )

    def    a__				(					self     :     Dict				,     __lowerCamelCase     :     torch.FloatTensor				,     __lowerCamelCase     :     float				,     __lowerCamelCase     :     Optional[torch.Generator] = None     )							->							int:

     '''simple docstring'''




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

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

     return sample_hat, sigma_hat

    def    a__				(					self     :     Optional[Any]				,     __lowerCamelCase     :     torch.FloatTensor				,     __lowerCamelCase     :     float				,     __lowerCamelCase     :     float				,     __lowerCamelCase     :     torch.FloatTensor				,     __lowerCamelCase     :     bool = True				,     )							->							str:

     '''simple docstring'''




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

     if not return_dict:
      return (sample_prev, derivative)

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

    def    a__				(					self     :     Union[str, Any]				,     __lowerCamelCase     :     torch.FloatTensor				,     __lowerCamelCase     :     float				,     __lowerCamelCase     :     float				,     __lowerCamelCase     :     torch.FloatTensor				,     __lowerCamelCase     :     torch.FloatTensor				,     __lowerCamelCase     :     torch.FloatTensor				,     __lowerCamelCase     :     bool = True				,     )							->							Dict:

     '''simple docstring'''




     lowerCamelCase__  =     sample_prev + sigma_prev * model_output
     lowerCamelCase__  =     (sample_prev - pred_original_sample) / sigma_prev
     lowerCamelCase__  =     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=_A				,     derivative=_A				,     pred_original_sample=_A     )




    def    a__				(					self     :     Dict				,     __lowerCamelCase     :     List[Any]				,     __lowerCamelCase     :     int				,     __lowerCamelCase     :     Tuple     )							->							List[Any]:

     '''simple docstring'''




     raise NotImplementedError()













'''simple docstring'''





from decimal import Decimal, getcontext
from math import ceil, factorial






def    lowerCamelCase_     (    lowercase__):

 if not isinstance(lowercase__				,     lowercase__):
  raise TypeError("Undefined for non-integers")
 elif precision < 1:
  raise ValueError("Undefined for non-natural numbers")

 lowerCamelCase__  =     precision
 lowerCamelCase__  =     ceil(precision / 14)
 lowerCamelCase__  =     426880 * Decimal(10005).sqrt()
 lowerCamelCase__  =     1
 lowerCamelCase__  =     13591409
 lowerCamelCase__  =     Decimal(lowercase__)
 for k in range(1				,     lowercase__):
  lowerCamelCase__  =     factorial(6 * k) // (factorial(3 * k) * factorial(lowercase__) ** 3)
  linear_term += 545140134
  exponential_term *= -262537412640768000
  partial_sum += Decimal(multinomial_term * linear_term) / exponential_term
 return str(constant_term / partial_sum)[:-1]


if __name__ == "__main__":
 __A							:							Dict  							=		50
 print(F"""The first {n} digits of pi is: {pi(n)}""")

