code: from typing import List, Optional, Tuple, Union
  
  from . import logging
  from .import_utils import is_torch_available, is_torch_version
  
  
  if is_torch_available():
  	import torch
  
  lowercase__    :       Dict						=			logging.get_logger(__name__)  # pylint: disable=invalid-name
  
  try:
  	from torch._dynamo import allow_in_graph as maybe_allow_in_graph
  except (ImportError, ModuleNotFoundError):
  
  	def      SCREAMING_SNAKE_CASE_  (		cls							)  ->			List[Any]:
  								return cls
  
  def      SCREAMING_SNAKE_CASE_  (		snake_case__     ,						snake_case__ = None     ,						snake_case__ = None     ,						snake_case__ = None     ,						snake_case__ = None     ,						)  ->			Any:
  							lowerCAmelCase				=	device
  							lowerCAmelCase				=	shape[0]
  
  							lowerCAmelCase				=	layout or torch.strided
  							lowerCAmelCase				=	device or torch.device('''cpu'''							)
  
  							if generator is not None:
  														lowerCAmelCase				=	generator.device.type if not isinstance(snake_case__     ,						snake_case__							) else generator[0].device.type
  														if gen_device_type != device.type and gen_device_type == "cpu":
  																					lowerCAmelCase				=	'''cpu'''
  																					if device != "mps":
  																												logger.info(
  																												    f"The passed generator was created on 'cpu' even though a tensor on {device} was expected."
  																												    f" Tensors will be created on 'cpu' and then moved to {device}. Note that one can probably"
  																												    f" slighly speed up this function by passing a generator that was created on the {device} device."							)
  														elif gen_device_type != device.type and gen_device_type == "cuda":
  																					raise ValueError(f"Cannot generate a {device} tensor from a generator of type {gen_device_type}."							)
  
  							if isinstance(snake_case__     ,						snake_case__							):
  														lowerCAmelCase				=	(1,) + shape[1:]
  														lowerCAmelCase				=	[
  														    torch.randn(snake_case__     ,						generator=generator[i]     ,						device=snake_case__     ,						dtype=snake_case__     ,						layout=snake_case__							)
  														    for i in range(snake_case__							)
  														]
  														lowerCAmelCase				=	torch.cat(snake_case__     ,						dim=0							).to(snake_case__							)
  							else:
  														lowerCAmelCase				=	torch.randn(snake_case__     ,						generator=snake_case__     ,						device=snake_case__     ,						dtype=snake_case__     ,						layout=snake_case__							).to(snake_case__							)
  
  							return latents
  
  
  
  
  
  
  def      SCREAMING_SNAKE_CASE_  (		snake_case__							)  ->			int:
  							if is_torch_version('''<'''     ,						'''2.0.0'''							) or not hasattr(snake_case__     ,						'''_dynamo'''							):
  														return False
  							return isinstance(snake_case__     ,						torch._dynamo.eval_frame.OptimizedModule							)
  
  
  
  
style_context: import math
  
  def      SCREAMING_SNAKE_CASE_  (		snake_case__							)  ->			float:
  							lowerCAmelCase				=	math.log(2     ,						1_0							) * number
  							lowerCAmelCase				=	round((log_number - int(snake_case__							))     ,						1_5							)
  
  							return difference
  
  def      SCREAMING_SNAKE_CASE_  (		snake_case__ = 6_7_8_9_1_0							)  ->			int:
  							lowerCAmelCase				=	9_0
  							lowerCAmelCase				=	0
  
  							lowerCAmelCase				=	math.log(1.23     ,						1_0							)
  							lowerCAmelCase				=	math.log(1.24     ,						1_0							)
  							lowerCAmelCase				=	0
  
  							while position < number:
  														lowerCAmelCase				=	log_difference(snake_case__							)
  
  														if difference >= upper_limit:
  																					power_iterator += 9_3
  
  														elif difference < lower_limit:
  																					power_iterator += 1_9_6
  
  														else:
  																					lowerCAmelCase				=	power_iterator
  																					power_iterator += 1_9_6
  																					position += 1
  
  							return previous_power
  
  
  if __name__ == "__main__":
  	import doctest
  
  	doctest.testmod()
  
  	print(f'{solution() = }')
  
  
  
  