code: 
  
  
  
  
  
  
  import inspect
  import warnings
  
  import torch
  
  from .state import AcceleratorState, GradientState
  from .utils import DistributedType, honor_type, is_tpu_available
  
  
  if is_tpu_available(check_device=False):
  							import torch_xla.core.xla_model as xm
  
  
  
  def 		UpperCamelCase    (					_UpperCAmelCase     :      Tuple   , _UpperCAmelCase     :      Optional[int]     )      -> Union[str, Any]:
  
  
  
  
  
  
  						'''simple docstring'''
  
  						if isinstance(_UpperCAmelCase   , (list, tuple)     ):
  												return honor_type(_UpperCAmelCase   , (move_to_device(_UpperCAmelCase   , _UpperCAmelCase     ) for t in state)     )
  						elif isinstance(_UpperCAmelCase   , _UpperCAmelCase     ):
  												return type(_UpperCAmelCase     )({k: move_to_device(_UpperCAmelCase   , _UpperCAmelCase     ) for k, v in state.items()}     )
  						elif isinstance(_UpperCAmelCase   , torch.Tensor     ):
  												return state.to(_UpperCAmelCase     )
  						return state
  
  
  
  
  class      __lowercase	(	torch.optim.Optimizer					):
  
  
  
  
  
  
  	def __init__(self							:   int			,  snake_case							:   Dict			,  snake_case							:   Union[str, Any]=True			,  snake_case							:   str=None						)   -> Dict:
  							_lowercase					:  List[str]    			=      optimizer
  							_lowercase					:  str    			=      scaler
  							_lowercase					:  Dict    			=      AcceleratorState()
  							_lowercase					:  Optional[int]    			=      GradientState()
  							_lowercase					:  Optional[Any]    			=      device_placement
  							_lowercase					:  Optional[int]    			=      False
  							_lowercase					:  Any    			=      None
  
  							# Handle device placement
  							if device_placement:
  													_lowercase					:  int    			=      self.optimizer.state_dict()
  													if self.accelerator_state.distributed_type == DistributedType.TPU:
  																			xm.send_cpu_data_to_device(lowerCamelCase__			,  self.accelerator_state.device						)
  													else:
  																			_lowercase					:  List[str]    			=      move_to_device(lowerCamelCase__			,  self.accelerator_state.device						)
  													self.optimizer.load_state_dict(lowerCamelCase__						)
  
  
  
  
  
  
  	@property
  	def 			_a(self							:   Tuple						)   -> List[str]:
  							return self.optimizer.state
  
  
  
  
  
  
  	@state.setter
  	def 			_a(self							:   Optional[int]			,  snake_case							:   List[str]						)   -> List[str]:
  							_lowercase					:  Tuple    			=      state
  
  
  
  
  
  
  	@property
  	def 			_a(self							:   Union[str, Any]						)   -> int:
  							return self.optimizer.param_groups
  
  
  
  
  
  
  	@param_groups.setter
  	def 			_a(self							:   List[str]			,  snake_case							:   List[str]						)   -> Dict:
  							_lowercase					:  Tuple    			=      param_groups
  
  
  
  
  
  
  	@property
  	def 			_a(self							:   Optional[int]						)   -> Optional[int]:
  							return self.optimizer.defaults
  
  
  
  
  
  
  	@defaults.setter
  	def 			_a(self							:   int			,  snake_case							:   Tuple						)   -> Dict:
  							_lowercase					:  int    			=      defaults
  
  
  
  
  
  
  	def 			_a(self							:   Any			,  snake_case							:   Optional[int]						)   -> Optional[Any]:
  							self.optimizer.add_param_group(lowerCamelCase__						)
  
  
  
  
  
  
  	def 			_a(self							:   Tuple			,  snake_case							:   Optional[Any]						)   -> Union[str, Any]:
  							if self.accelerator_state.distributed_type == DistributedType.TPU and self.device_placement:
  													xm.send_cpu_data_to_device(lowerCamelCase__			,  self.accelerator_state.device						)
  							self.optimizer.load_state_dict(lowerCamelCase__						)
  
  
  
  
  
  
  	def 			_a(self							:   List[str]						)   -> Union[str, Any]:
  							return self.optimizer.state_dict()
  
  
  
  
  
  
  	def 			_a(self							:   Tuple			,  snake_case							:   Optional[Any]=None						)   -> Optional[int]:
  							if self.gradient_state.sync_gradients:
  													_lowercase					:  int    			=      "set_to_none" in inspect.signature(self.optimizer.zero_grad						).parameters
  													if accept_arg:
  																			if set_to_none is None:
  																									_lowercase					:  Dict    			=      False
  																			self.optimizer.zero_grad(set_to_none=lowerCamelCase__						)
  													else:
  																			if set_to_none is not None:
  																									raise ValueError("`set_to_none` for Optimizer.zero_grad` is not supported by this optimizer."						)
  																			self.optimizer.zero_grad()
  
  
  
  
  
  
  	def 			_a(self							:   Optional[int]			,  snake_case							:   int=None						)   -> int:
  							if self.gradient_state.sync_gradients:
  													if self.accelerator_state.distributed_type == DistributedType.TPU:
  																			_lowercase					:  Union[str, Any]    			=      {"closure": closure} if closure is not None else {}
  																			xm.optimizer_step(self.optimizer			,  optimizer_args=lowerCamelCase__						)
  													elif self.scaler is not None:
  																			_lowercase					:  Any    			=      False
  																			if self._last_scale is None:
  																									# `get_scale` is an async operation requiring full synchronization
  																									# on CPU and GPUs before finishing. As a result, we store away
  																									# the prior one to reduce the call overhead
  																									_lowercase					:  Optional[int]    			=      self.scaler.get_scale()
  																									_lowercase					:  Optional[Any]    			=      True
  																			self.scaler.step(self.optimizer			,  lowerCamelCase__						)
  																			self.scaler.update()
  																			_lowercase					:  Tuple    			=      self.scaler.get_scale()
  																			if not new_scale:
  																									# If we reduced the loss scale, it means the optimizer step was skipped because of gradient overflow.
  																									_lowercase					:  Optional[Any]    			=      scale_after < self._last_scale
  																			_lowercase					:  Dict    			=      scale_after
  
  													else:
  																			self.optimizer.step(lowerCamelCase__						)
  
  
  
  
  
  
  	def 			_a(self							:   List[str]			,  snake_case							:   str						)   -> Optional[Any]:
  							for param_group in self.optimizer.param_groups:
  													_lowercase					:  List[str]    			=      [parameters_map.get(lowerCamelCase__			,  lowerCamelCase__						) for p in param_group["params"]]
  
  
  
  
  
  
  	@property
  	def 			_a(self							:   List[str]						)   -> Any:
  							warnings.warn(
  							    "The `is_overflow` property is deprecated and will be removed in version 1.0 of Accelerate use "
  							    "`optimizer.step_was_skipped` instead."			,  lowerCamelCase__			,  )
  							return self._is_overflow
  
  
  
  
  
  
  	@property
  	def 			_a(self							:   List[str]						)   -> Optional[int]:
  							return self._is_overflow
  
  
  
  
  
  
  	def __getstate__(self							:   Any						)   -> Dict:
  							return self.__dict__.copy()
  
  
  
  
  
  
  	def __setstate__(self							:   str			,  snake_case							:   Optional[int]						)   -> Optional[int]:
  							self.__dict__.update(lowerCamelCase__						)
  
  
  
  
  
style_context: 
  import math
  
  
  
  def 		UpperCamelCase    (					_UpperCAmelCase     :      int     )      -> list:
  
  
  
  
  
  
  						'''simple docstring'''
  
  						if n <= 0:
  												raise ValueError("Only positive integers have prime factors"     )
  						_lowercase					:  Optional[int]    			=      []
  						while n % 2 == 0:
  												pf.append(2     )
  												_lowercase					:  Tuple    			=      int(n / 2     )
  						for i in range(3   , int(math.sqrt(_UpperCAmelCase     )     ) + 1   , 2     ):
  												while n % i == 0:
  																		pf.append(_UpperCAmelCase     )
  																		_lowercase					:  Optional[int]    			=      int(n / i     )
  						if n > 2:
  												pf.append(_UpperCAmelCase     )
  						return pf
  
  
  
  def 		UpperCamelCase    (					_UpperCAmelCase     :      int     )      -> int:
  
  
  
  
  
  
  						'''simple docstring'''
  
  						if n <= 0:
  												raise ValueError("Only positive numbers are accepted"     )
  						_lowercase					:  str    			=      1
  						_lowercase					:  Tuple    			=      1
  						while n % 2 == 0:
  												temp += 1
  												_lowercase					:  List[Any]    			=      int(n / 2     )
  						div *= temp
  						for i in range(3   , int(math.sqrt(_UpperCAmelCase     )     ) + 1   , 2     ):
  												_lowercase					:  Optional[Any]    			=      1
  												while n % i == 0:
  																		temp += 1
  																		_lowercase					:  Optional[Any]    			=      int(n / i     )
  												div *= temp
  						if n > 1:
  												div *= 2
  						return div
  
  
  
  def 		UpperCamelCase    (					_UpperCAmelCase     :      int     )      -> int:
  
  
  
  
  
  
  						'''simple docstring'''
  
  						if n <= 0:
  												raise ValueError("Only positive numbers are accepted"     )
  						_lowercase					:  int    			=      1
  						_lowercase					:  List[str]    			=      1
  						while n % 2 == 0:
  												temp += 1
  												_lowercase					:  str    			=      int(n / 2     )
  						if temp > 1:
  												s *= (2**temp - 1) / (2 - 1)
  						for i in range(3   , int(math.sqrt(_UpperCAmelCase     )     ) + 1   , 2     ):
  												_lowercase					:  int    			=      1
  												while n % i == 0:
  																		temp += 1
  																		_lowercase					:  List[Any]    			=      int(n / i     )
  												if temp > 1:
  																		s *= (i**temp - 1) / (i - 1)
  						return int(_UpperCAmelCase     )
  
  
  
  def 		UpperCamelCase    (					_UpperCAmelCase     :      int     )      -> int:
  
  
  
  
  
  
  						'''simple docstring'''
  
  						_lowercase					:  int    			=      n
  						for x in set(prime_factors(_UpperCAmelCase     )     ):
  												s *= (x - 1) / x
  						return int(_UpperCAmelCase     )
  
  
  if __name__ == "__main__":
  							import doctest
  
  							doctest.testmod()
  
  
  
  
  