
"""simple docstring"""


import baseaa
import io
import json
import os
from copy import deepcopy

from ..optimizer import AcceleratedOptimizer
from ..scheduler import AcceleratedScheduler







class 				lowerCAmelCase_				:



						'''simple docstring'''


						def __init__( self     :      List[Any]  ,A_     :      Union[str, Any]      )     ->   Dict:
							if isinstance(A_  ,A_      ):
								# Don't modify user's data should they want to reuse it (e.g. in tests), because once we
								# modified it, it will not be accepted here again, since `auto` values would have been overridden
								A						   =   deepcopy(A_      )
							elif os.path.exists(A_      ):
								with io.open(A_  ,'r'  ,encoding='utf-8'      ) as f:
									A						   =   json.load(A_      )
							else:
								try:
									A						   =   baseaa.urlsafe_baadecode(A_      ).decode('utf-8'      )
									A						   =   json.loads(A_      )
								except (UnicodeDecodeError, AttributeError, ValueError):
									raise ValueError(
									    F'Expected a string path to an existing deepspeed config, or a dictionary, or a base64 encoded string. Received: {config_file_or_dict}'      )

							A						   =   config

							self.set_stage_and_offload()


						def 						_SCREAMING_SNAKE_CASE      ( self     :      List[Any]      )     ->   Dict:
							# zero stage - this is done as early as possible, before model is created, to allow
							# ``is_deepspeed_zero3_enabled`` query and getting to the early deepspeed config object
							# during ``zero.Init()`` which needs to know the dtype, and some other hparams.
							A						   =   self.get_value('zero_optimization.stage'  ,-1      )

							# offload
							A						   =   False
							if self.is_zeroa() or self.is_zeroa():
								A						   =   set(['cpu', 'nvme']      )
								A						   =   set(
								    [
								        self.get_value('zero_optimization.offload_optimizer.device'      ),
								        self.get_value('zero_optimization.offload_param.device'      ),
								    ]      )
								if len(offload_devices & offload_devices_valid      ) > 0:
									A						   =   True


						def 						_SCREAMING_SNAKE_CASE      ( self     :      Dict  ,A_     :      List[Any]      )     ->   List[str]:
							A						   =   self.config

							# find the config node of interest if it exists
							A						   =   ds_key_long.split('.'      )
							A						   =   nodes.pop()
							for node in nodes:
								A						   =   config.get(A_      )
								if config is None:
									return None, ds_key

							return config, ds_key


						def 						_SCREAMING_SNAKE_CASE      ( self     :      Tuple  ,A_     :      Union[str, Any]  ,A_     :      List[str]=None      )     ->   Optional[int]:
							A   ,      A						   =   self.find_config_node(A_      )
							if config is None:
								return default
							return config.get(A_  ,A_      )


						def 						_SCREAMING_SNAKE_CASE      ( self     :      List[str]  ,A_     :      List[Any]  ,A_     :      Any=False      )     ->   Dict:
							A						   =   self.config

							# find the config node of interest if it exists
							A						   =   ds_key_long.split('.'      )
							for node in nodes:
								A						   =   config
								A						   =   config.get(A_      )
								if config is None:
									if must_exist:
										raise ValueError(F'Can\'t find {ds_key_long} entry in the config: {self.config}'      )
									else:
										return

        # if found remove it
							if parent_config is not None:
								parent_config.pop(A_      )


						def 						_SCREAMING_SNAKE_CASE      ( self     :      Union[str, Any]  ,A_     :      int      )     ->   Tuple:
							A						   =   self.get_value(A_      )
							return False if value is None else bool(A_      )


						def 						_SCREAMING_SNAKE_CASE      ( self     :      str  ,A_     :      int      )     ->   Union[str, Any]:
							A						   =   self.get_value(A_      )
							return False if value is None else not bool(A_      )


						def 						_SCREAMING_SNAKE_CASE      ( self     :      str      )     ->   str:
							return self._stage == 2


						def 						_SCREAMING_SNAKE_CASE      ( self     :      Optional[Any]      )     ->   Dict:
							return self._stage == 3




						def 						_SCREAMING_SNAKE_CASE      ( self     :      Union[str, Any]      )     ->   Optional[int]:
							return self._offload







class 				lowerCAmelCase_				:



						'''simple docstring'''


						def __init__( self     :      Dict  ,A_     :      str      )     ->   Union[str, Any]:
							A						   =   engine




						def 						_SCREAMING_SNAKE_CASE      ( self     :      Dict  ,A_     :      Union[str, Any]  ,**A_     :      int      )     ->   Tuple:
							# runs backpropagation and handles mixed precision
							self.engine.backward(A_  ,**A_      )

							# Deepspeed's `engine.step` performs the following operations:
							# - gradient accumulation check
							# - gradient clipping
							# - optimizer step
							# - zero grad
							# - checking overflow
							# - lr_scheduler step (only if engine.lr_scheduler is not None)
							self.engine.step()
							# and this plugin overrides the above calls with no-ops when Accelerate runs under
							# Deepspeed, but allows normal functionality for non-Deepspeed cases thus enabling a simple
							# training loop that works transparently under many training regimes.







class 				lowerCAmelCase_				(      _lowercase    ):



						'''simple docstring'''


						def __init__( self     :      List[Any]  ,A_     :      str      )     ->   List[Any]:
							super().__init__(A_  ,device_placement=A_  ,scaler=A_      )
							A						   =   hasattr(self.optimizer  ,'overflow'      )


						def 						_SCREAMING_SNAKE_CASE      ( self     :      Union[str, Any]  ,A_     :      Dict=None      )     ->   List[Any]:
							pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed


						def 						_SCREAMING_SNAKE_CASE      ( self     :      Optional[int]      )     ->   int:
							pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed




						@property
						def 						_SCREAMING_SNAKE_CASE      ( self     :      Union[str, Any]      )     ->   Optional[Any]:
							if self.__has_overflow__:
								return self.optimizer.overflow
							return False







class 				lowerCAmelCase_				(      _lowercase    ):



						'''simple docstring'''


						def __init__( self     :      List[str]  ,A_     :      int  ,A_     :      int      )     ->   Dict:
							super().__init__(A_  ,A_      )




						def 						_SCREAMING_SNAKE_CASE      ( self     :      Union[str, Any]      )     ->   Union[str, Any]:
							pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed







class 				lowerCAmelCase_				:



						'''simple docstring'''


						def __init__( self     :      str  ,A_     :      str  ,A_     :      List[str]=0.0_01  ,A_     :      Tuple=0  ,**A_     :      Tuple      )     ->   str:
							A						   =   params
							A						   =   lr
							A						   =   weight_decay
							A						   =   kwargs







class 				lowerCAmelCase_				:



						'''simple docstring'''


						def __init__( self     :      Optional[int]  ,A_     :      Dict  ,A_     :      int=None  ,A_     :      List[Any]=0  ,**A_     :      Optional[int]      )     ->   Any:
							A						   =   optimizer
							A						   =   total_num_steps
							A						   =   warmup_num_steps
							A						   =   kwargs

"""simple docstring"""


from math import pi, sqrt






def       _snake_case				(		snake_case__   :     float     ):
	if num <= 0:
		raise ValueError('math domain error'     )
	if num > 171.5:
		raise OverflowError('math range error'     )
	elif num - int(snake_case__     ) not in (0, 0.5):
		raise NotImplementedError('num must be an integer or a half-integer'     )
	elif num == 0.5:
		return sqrt(snake_case__     )
	else:
		return 1.0 if num == 1 else (num - 1) * gamma(num - 1     )






def       _snake_case				(		):
	assert gamma(0.5     ) == sqrt(snake_case__     )
	assert gamma(1     ) == 1.0
	assert gamma(2     ) == 1.0


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		_lowercase							   =				1.0
		while num:
				_lowercase							   =				float(input('''Gamma of: '''))
				print(F"""gamma({num}) = {gamma(num)}""")
				print('''\nEnter 0 to exit...''')