


"""simple docstring"""






from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean







def        lowerCamelCase_(		_lowerCamelCase       )    ->     Tuple:
   '''simple docstring'''





   def is_in_circle(_lowerCamelCase			,		_lowerCamelCase       ) -> bool:
      _lowerCamelCase   :				int							=     sqrt((x**2) + (y**2)       )
      # Our circle has a radius of 1, so a distance
      # greater than 1 would land outside the circle.
      return distance_from_centre <= 1

   # The proportion of guesses that landed in the circle
   _lowerCamelCase   :				Tuple							=     mean(
       int(is_in_circle(uniform(-1.0			,		1.0       )			,		uniform(-1.0			,		1.0       )       )       )
       for _ in range(_lowerCamelCase       )       )
   # The ratio of the area for circle to square is pi/4.
   _lowerCamelCase   :				List[Any]							=     proportion * 4
   print(F"""The estimated value of pi is {pi_estimate}"""       )
   print(F"""The numpy value of pi is {pi}"""       )
   print(F"""The total error is {abs(pi - pi_estimate       )}"""       )







def        lowerCamelCase_(		_lowerCamelCase			,		_lowerCamelCase			,		_lowerCamelCase = 0.0			,		_lowerCamelCase = 1.0			,		)    ->     float:
   '''simple docstring'''





   return mean(
       function_to_integrate(uniform(_lowerCamelCase			,		_lowerCamelCase       )       ) for _ in range(_lowerCamelCase       )       ) * (max_value - min_value)







def        lowerCamelCase_(		_lowerCamelCase			,		_lowerCamelCase = 0.0			,		_lowerCamelCase = 1.0       )    ->     None:
   '''simple docstring'''





   def identity_function(_lowerCamelCase       ) -> float:
      return x

   _lowerCamelCase   :				Union[str, Any]							=     area_under_curve_estimator(
       _lowerCamelCase			,		_lowerCamelCase			,		_lowerCamelCase			,		_lowerCamelCase       )
   _lowerCamelCase   :				Tuple							=     (max_value * max_value - min_value * min_value) / 2

   print("******************"       )
   print(F"""Estimating area under y=x where x varies from {min_value} to {max_value}"""       )
   print(F"""Estimated value is {estimated_value}"""       )
   print(F"""Expected value is {expected_value}"""       )
   print(F"""Total error is {abs(estimated_value - expected_value       )}"""       )
   print("******************"       )







def        lowerCamelCase_(		_lowerCamelCase       )    ->     None:
   '''simple docstring'''





   def function_to_integrate(_lowerCamelCase       ) -> float:
      return sqrt(4.0 - x * x       )

   _lowerCamelCase   :				int							=     area_under_curve_estimator(
       _lowerCamelCase			,		_lowerCamelCase			,		0.0			,		2.0       )

   print("******************"       )
   print("Estimating pi using area_under_curve_estimator"       )
   print(F"""Estimated value is {estimated_value}"""       )
   print(F"""Expected value is {pi}"""       )
   print(F"""Total error is {abs(estimated_value - pi       )}"""       )
   print("******************"       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()




'''simple docstring'''





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

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







class        UpperCAmelCase_			:
    """simple docstring"""







    def __init__(       self   :	Tuple					,	snake_case_   :	List[str]		):
          if isinstance(snake_case_					,	snake_case_		):
                # 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
                snake_case__    :       Optional[Any]       		= deepcopy(snake_case_		)
          elif os.path.exists(snake_case_		):
                with io.open(snake_case_					,	"""r"""					,	encoding="""utf-8"""		) as f:
                      snake_case__    :       Union[str, Any]       		= json.load(snake_case_		)
          else:
                try:
                      snake_case__    :       List[Any]       		= baseaa.urlsafe_baadecode(snake_case_		).decode("""utf-8"""		)
                      snake_case__    :       Optional[int]       		= json.loads(snake_case_		)
                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}"		)

          snake_case__    :       str       		= config

          self.set_stage_and_offload()




    def lowerCamelCase			(       self   :	int		):
          # 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.
          snake_case__    :       Union[str, Any]       		= self.get_value("""zero_optimization.stage"""					,	-1		)

          # offload
          snake_case__    :       Optional[Any]       		= False
          if self.is_zeroa() or self.is_zeroa():
                snake_case__    :       int       		= set(["""cpu""", """nvme"""]		)
                snake_case__    :       Any       		= 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:
                      snake_case__    :       List[Any]       		= True




    def lowerCamelCase			(       self   :	Any					,	snake_case_   :	Optional[Any]		):
          snake_case__    :       Optional[Any]       		= self.config

          # find the config node of interest if it exists
          snake_case__    :       List[Any]       		= ds_key_long.split("""."""		)
          snake_case__    :       Tuple       		= nodes.pop()
          for node in nodes:
                snake_case__    :       Optional[Any]       		= config.get(snake_case_		)
                if config is None:
                      return None, ds_key

          return config, ds_key




    def lowerCamelCase			(       self   :	List[Any]					,	snake_case_   :	int					,	snake_case_   :	List[str]=None		):
          snake_case__		,							snake_case__    :       Dict       		= self.find_config_node(snake_case_		)
          if config is None:
                return default
          return config.get(snake_case_					,	snake_case_		)




    def lowerCamelCase			(       self   :	Dict					,	snake_case_   :	Optional[int]					,	snake_case_   :	int=False		):
          snake_case__    :       Dict       		= self.config

          # find the config node of interest if it exists
          snake_case__    :       str       		= ds_key_long.split("""."""		)
          for node in nodes:
                snake_case__    :       Union[str, Any]       		= config
                snake_case__    :       List[Any]       		= config.get(snake_case_		)
                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(snake_case_		)




    def lowerCamelCase			(       self   :	str					,	snake_case_   :	Optional[Any]		):
          snake_case__    :       Dict       		= self.get_value(snake_case_		)
          return False if value is None else bool(snake_case_		)




    def lowerCamelCase			(       self   :	List[str]					,	snake_case_   :	Union[str, Any]		):
          snake_case__    :       Optional[int]       		= self.get_value(snake_case_		)
          return False if value is None else not bool(snake_case_		)




    def lowerCamelCase			(       self   :	Optional[Any]		):
          return self._stage == 2




    def lowerCamelCase			(       self   :	Dict		):
          return self._stage == 3




    def lowerCamelCase			(       self   :	List[Any]		):
          return self._offload







class        UpperCAmelCase_			:
    """simple docstring"""







    def __init__(       self   :	Any					,	snake_case_   :	List[Any]		):
          snake_case__    :       Tuple       		= engine




    def lowerCamelCase			(       self   :	Dict					,	snake_case_   :	Optional[Any]					,	**snake_case_   :	int		):
          # runs backpropagation and handles mixed precision
          self.engine.backward(snake_case_					,	**snake_case_		)

          # 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        UpperCAmelCase_			(			_a      ):
    """simple docstring"""







    def __init__(       self   :	Tuple					,	snake_case_   :	Any		):
          super().__init__(snake_case_					,	device_placement=snake_case_					,	scaler=snake_case_		)
          snake_case__    :       Optional[int]       		= hasattr(self.optimizer					,	"""overflow"""		)




    def lowerCamelCase			(       self   :	int					,	snake_case_   :	Optional[Any]=None		):
          pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed




    def lowerCamelCase			(       self   :	List[Any]		):
          pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed




    @property
    def lowerCamelCase			(       self   :	List[str]		):
          if self.__has_overflow__:
                return self.optimizer.overflow
          return False







class        UpperCAmelCase_			(			_a      ):
    """simple docstring"""







    def __init__(       self   :	Tuple					,	snake_case_   :	Optional[Any]					,	snake_case_   :	Tuple		):
          super().__init__(snake_case_					,	snake_case_		)




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







class        UpperCAmelCase_			:
    """simple docstring"""







    def __init__(       self   :	Optional[int]					,	snake_case_   :	Dict					,	snake_case_   :	int=0.001					,	snake_case_   :	Optional[Any]=0					,	**snake_case_   :	List[Any]		):
          snake_case__    :       int       		= params
          snake_case__    :       Optional[Any]       		= lr
          snake_case__    :       Any       		= weight_decay
          snake_case__    :       Optional[Any]       		= kwargs







class        UpperCAmelCase_			:
    """simple docstring"""







    def __init__(       self   :	Dict					,	snake_case_   :	str					,	snake_case_   :	Optional[int]=None					,	snake_case_   :	Any=0					,	**snake_case_   :	List[str]		):
          snake_case__    :       List[Any]       		= optimizer
          snake_case__    :       List[Any]       		= total_num_steps
          snake_case__    :       List[Any]       		= warmup_num_steps
          snake_case__    :       Optional[Any]       		= kwargs
