


"""simple docstring"""
from __future__ import annotations






def 						lowercase				(	_snake_case		: list[int | float]	,  _snake_case		: int	,  _snake_case		: int	)	->int | float:
	"""simple docstring"""





	if len(_snake_case	) == 0:
		raise ValueError('''find_min() arg is an empty sequence'''	)
	if (
	    left >= len(_snake_case	)
	    or left < -len(_snake_case	)
	    or right >= len(_snake_case	)
	    or right < -len(_snake_case	)
	):
		raise IndexError('''list index out of range'''	)
	if left == right:
		return nums[left]
	__snake_case      :		List[Any]         =							(left + right) >> 1  # the middle
	__snake_case      :		Dict         =							find_min(_snake_case	,  _snake_case	,  _snake_case	)  # find min in range[left, mid]
	__snake_case      :		Tuple         =							find_min(_snake_case	,  mid + 1	,  _snake_case	)  # find min in range[mid + 1, right]

	return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
			import doctest

			doctest.testmod(verbose=True)






import torch

from accelerate import Accelerator, DistributedType



class 			UpperCamelCase					:

     '''simple docstring'''

     def __enter__(       self    )			->					int:






           """simple docstring"""
           if self.enabled:
                 _lowerCamelCase           =					self.model.no_sync()
                 self.model_sync_obj.__enter__()

           return self



     def __exit__(       self					,					A_					,					A_					,					A_    )			->					Union[str, Any]:






           """simple docstring"""
           if self.enabled:
                 # Average all models on exit
                 self._sync_and_avg_model_params()
                 self.model_sync_obj.__exit__(A_					,					A_					,					A_    )



     def __init__(       self					,					A_					,					A_					,					A_					,					A_ = True    )			->					List[str]:






           """simple docstring"""
           if accelerator.distributed_type not in [
               DistributedType.NO,
               DistributedType.MULTI_CPU,
               DistributedType.MULTI_GPU,
           ]:
                 raise NotImplementedError('''LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)'''    )
           _lowerCamelCase           =					enabled and accelerator.distributed_type != DistributedType.NO
           _lowerCamelCase           =					0
           if self.enabled:
                 _lowerCamelCase           =					accelerator
                 _lowerCamelCase           =					model
                 _lowerCamelCase           =					local_sgd_steps



     def 		UpperCamelCase_    (       self    )			->					Optional[Any]:






           """simple docstring"""
           self.num_steps += 1
           if not self.enabled:
                 return

           if self.num_steps % self.local_sgd_steps == 0:
                 self._sync_and_avg_model_params()





     def 		UpperCamelCase_    (       self    )			->					Union[str, Any]:






           """simple docstring"""
           self.accelerator.wait_for_everyone()
           with self.accelerator.autocast():
                 for param in self.model.parameters():
                       _lowerCamelCase           =					self.accelerator.reduce(param.data					,					reduction='''mean'''    )