import math
from typing import Union

import torch

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




class  _snake_case		(    __snake_case   ,       __snake_case ):







				"""simple docstring"""






				a			=						1





				@register_to_config
				def __init__(      self							:							Union[str, Any]      ,    _A							:							Optional[int]=2_0_0_0      ,    _A							:							Any=0.1      ,    _A							:							Optional[Any]=2_0      ,    _A							:							Optional[Any]=1e-3):



											"""simple docstring"""







											_SCREAMING_SNAKE_CASE		:						Union[str, Any]			  =    None
											_SCREAMING_SNAKE_CASE		:						int			  =    None
											_SCREAMING_SNAKE_CASE		:						Any			  =    None





				def 		_lowerCAmelCase		(      self							:							Tuple      ,    _A							:							Optional[Any]      ,    _A							:							Union[str, torch.device] = None):



											"""simple docstring"""







											_SCREAMING_SNAKE_CASE		:						Dict			  =    torch.linspace(1      ,    self.config.sampling_eps      ,    _A      ,    device=_A)





				def 		_lowerCAmelCase		(      self							:							int      ,    _A							:							List[str]      ,    _A							:							List[Any]      ,    _A							:							Union[str, Any]      ,    _A							:							Any=None):



											"""simple docstring"""







											if self.timesteps is None:
																		raise ValueError(
																		    """`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler""")

											# TODO(Patrick) better comments + non-PyTorch
											# postprocess model score
											_SCREAMING_SNAKE_CASE		:						Optional[Any]			  =    (
											    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
											)
											_SCREAMING_SNAKE_CASE		:						List[Any]			  =    torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff))
											_SCREAMING_SNAKE_CASE		:						List[str]			  =    std.flatten()
											while len(std.shape) < len(score.shape):
																		_SCREAMING_SNAKE_CASE		:						Tuple			  =    std.unsqueeze(-1)
											_SCREAMING_SNAKE_CASE		:						int			  =    -score / std

											# compute
											_SCREAMING_SNAKE_CASE		:						Optional[int]			  =    -1.0 / len(self.timesteps)

											_SCREAMING_SNAKE_CASE		:						List[str]			  =    self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
											_SCREAMING_SNAKE_CASE		:						int			  =    beta_t.flatten()
											while len(beta_t.shape) < len(x.shape):
																		_SCREAMING_SNAKE_CASE		:						Union[str, Any]			  =    beta_t.unsqueeze(-1)
											_SCREAMING_SNAKE_CASE		:						List[Any]			  =    -0.5 * beta_t * x

											_SCREAMING_SNAKE_CASE		:						Union[str, Any]			  =    torch.sqrt(_A)
											_SCREAMING_SNAKE_CASE		:						int			  =    drift - diffusion**2 * score
											_SCREAMING_SNAKE_CASE		:						Any			  =    x + drift * dt

											# add noise
											_SCREAMING_SNAKE_CASE		:						List[str]			  =    randn_tensor(x.shape      ,    layout=x.layout      ,    generator=_A      ,    device=x.device      ,    dtype=x.dtype)
											_SCREAMING_SNAKE_CASE		:						Optional[Any]			  =    x_mean + diffusion * math.sqrt(-dt) * noise

											return x, x_mean





				def __len__(      self							:							int):



											"""simple docstring"""







											return self.config.num_train_timesteps



"""simple docstring"""





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



def      lowerCamelCase_(__SCREAMING_SNAKE_CASE  )->    str:

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

							_SCREAMING_SNAKE_CASE		:						int			  =    precision
							_SCREAMING_SNAKE_CASE		:						Dict			  =    ceil(precision / 14  )
							_SCREAMING_SNAKE_CASE		:						int			  =    426_880 * Decimal(10_005  ).sqrt()
							_SCREAMING_SNAKE_CASE		:						Union[str, Any]			  =    1
							_SCREAMING_SNAKE_CASE		:						str			  =    13_591_409
							_SCREAMING_SNAKE_CASE		:						Tuple			  =    Decimal(__SCREAMING_SNAKE_CASE  )
							for k in range(1     ,	__SCREAMING_SNAKE_CASE  ):
														_SCREAMING_SNAKE_CASE		:						Tuple			  =    factorial(6 * k  ) // (factorial(3 * k  ) * factorial(__SCREAMING_SNAKE_CASE  ) ** 3)
														linear_term += 545_140_134
														exponential_term *= -262_537_412_640_768_000
														partial_sum += Decimal(multinomial_term * linear_term  ) / exponential_term
							return str(constant_term / partial_sum  )[:-1]


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


