

"""simple docstring"""

def 					__UpperCamelCase (     a__:			int      )					->      List[str]:




					"""simple docstring"""



					__lowercase        =      1
					__lowercase        =      0
					__lowercase        =      1
					__lowercase        =      1
					__lowercase        =      3
					__lowercase        =      3
					__lowercase        =      limit
					__lowercase        =      0

					__lowercase        =      ''''''
					while counter != decimal + 1:
										if 4 * q + r - t < n * t:
															result += str(lowercase_      )
															if counter == 0:
																				result += "."

															if decimal == counter:
																				break

															counter += 1
															__lowercase        =      10 * (r - n * t)
															__lowercase        =      ((10 * (3 * q + r)) // t) - 10 * n
															q *= 10
															__lowercase        =      nr
										else:
															__lowercase        =      (2 * q + r) * l
															__lowercase        =      (q * (7 * k) + 2 + (r * l)) // (t * l)
															q *= k
															t *= l
															l += 2
															k += 1
															__lowercase        =      nn
															__lowercase        =      nr
					return result





def 					__UpperCamelCase (     )					->      Any:




					"""simple docstring"""



					print(f'''{calculate_pi(50      ) = }'''      )
					import doctest

					doctest.testmod()


if __name__ == "__main__":
							main()







"""simple docstring"""


from typing import List, Optional, Tuple, Union

import torch

from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput







class  A_     (	SCREAMING_SNAKE_CASE_							):



						"""simple docstring"""






						def __init__(   self					:List[str]  ,    lowercase_					:List[str]  ,    lowercase_					:List[Any]   )							->     List[str]:
												super().__init__()
												self.register_modules(unet=lowercase_  ,    scheduler=lowercase_   )






						@torch.no_grad()
						def __call__(   self					:int  ,    lowercase_					:int = 1  ,    lowercase_					:Optional[Union[torch.Generator, List[torch.Generator]]] = None  ,    lowercase_					:int = 10_00  ,    lowercase_					:Optional[str] = "pil"  ,    lowercase_					:bool = True  ,    )							->     Union[ImagePipelineOutput, Tuple]:
												# Sample gaussian noise to begin loop
												if isinstance(self.unet.config.sample_size  ,    lowercase_   ):
																		UpperCAmelCase			 =					(
																		    batch_size,
																		    self.unet.config.in_channels,
																		    self.unet.config.sample_size,
																		    self.unet.config.sample_size,
																		)
												else:
																		UpperCAmelCase			 =					(batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

												if self.device.type == "mps":
																		# randn does not work reproducibly on mps
																		UpperCAmelCase			 =					randn_tensor(lowercase_  ,    generator=lowercase_   )
																		UpperCAmelCase			 =					image.to(self.device   )
												else:
																		UpperCAmelCase			 =					randn_tensor(lowercase_  ,    generator=lowercase_  ,    device=self.device   )

												# set step values
												self.scheduler.set_timesteps(lowercase_   )

												for t in self.progress_bar(self.scheduler.timesteps   ):
																		# 1. predict noise model_output
																		UpperCAmelCase			 =					self.unet(lowercase_  ,    lowercase_   ).sample

																		# 2. compute previous image: x_t -> x_t-1
																		UpperCAmelCase			 =					self.scheduler.step(lowercase_  ,    lowercase_  ,    lowercase_  ,    generator=lowercase_   ).prev_sample

												UpperCAmelCase			 =					(image / 2 + 0.5).clamp(0  ,    1   )
												UpperCAmelCase			 =					image.cpu().permute(0  ,    2  ,    3  ,    1   ).numpy()
												if output_type == "pil":
																		UpperCAmelCase			 =					self.numpy_to_pil(lowercase_   )

												if not return_dict:
																		return (image,)

												return ImagePipelineOutput(images=lowercase_   )





