





'''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]	,			lowerCAmelCase__       :		Tuple					)   ->					Tuple:

            '''simple docstring'''




            if isinstance(lowerCAmelCase__	,			lowerCAmelCase__					):
                 # 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
                 _UpperCamelCase       =	deepcopy(lowerCAmelCase__					)
            elif os.path.exists(lowerCAmelCase__					):
                 with io.open(lowerCAmelCase__	,			'''r'''	,			encoding='''utf-8'''					) as f:
                      _UpperCamelCase       =	json.load(lowerCAmelCase__					)
            else:
                 try:
                      _UpperCamelCase       =	baseaa.urlsafe_baadecode(lowerCAmelCase__					).decode('''utf-8'''					)
                      _UpperCamelCase       =	json.loads(lowerCAmelCase__					)
                 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}"""					)

            _UpperCamelCase       =	config

            self.set_stage_and_offload()





       def snake_case__						(							self       :		Optional[int]					)   ->					Optional[int]:

            '''simple docstring'''




            _UpperCamelCase       =	self.get_value('''zero_optimization.stage'''	,			-1					)

            # offload
            _UpperCamelCase       =	False
            if self.is_zeroa() or self.is_zeroa():
                 _UpperCamelCase       =	set(['''cpu''', '''nvme''']					)
                 _UpperCamelCase       =	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:
                      _UpperCamelCase       =	True





       def snake_case__						(							self       :		Tuple	,			lowerCAmelCase__       :		int					)   ->					Dict:

            '''simple docstring'''




            _UpperCamelCase       =	self.config

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

            return config, ds_key





       def snake_case__						(							self       :		Dict	,			lowerCAmelCase__       :		str	,			lowerCAmelCase__       :		Tuple=None					)   ->					List[Any]:

            '''simple docstring'''




            _UpperCamelCase   ,    _UpperCamelCase       =	self.find_config_node(lowerCAmelCase__					)
            if config is None:
                 return default
            return config.get(lowerCAmelCase__	,			lowerCAmelCase__					)





       def snake_case__						(							self       :		Optional[Any]	,			lowerCAmelCase__       :		str	,			lowerCAmelCase__       :		int=False					)   ->					Any:

            '''simple docstring'''




            _UpperCamelCase       =	self.config

            # find the config node of interest if it exists
            _UpperCamelCase       =	ds_key_long.split('''.'''					)
            for node in nodes:
                 _UpperCamelCase       =	config
                 _UpperCamelCase       =	config.get(lowerCAmelCase__					)
                 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(lowerCAmelCase__					)





       def snake_case__						(							self       :		List[str]	,			lowerCAmelCase__       :		List[str]					)   ->					Any:

            '''simple docstring'''




            _UpperCamelCase       =	self.get_value(lowerCAmelCase__					)
            return False if value is None else bool(lowerCAmelCase__					)





       def snake_case__						(							self       :		Any	,			lowerCAmelCase__       :		Optional[Any]					)   ->					Dict:

            '''simple docstring'''




            _UpperCamelCase       =	self.get_value(lowerCAmelCase__					)
            return False if value is None else not bool(lowerCAmelCase__					)





       def snake_case__						(							self       :		Optional[int]					)   ->					str:

            '''simple docstring'''




            return self._stage == 2





       def snake_case__						(							self       :		Optional[Any]					)   ->					Dict:

            '''simple docstring'''




            return self._stage == 3







       def snake_case__						(							self       :		List[str]					)   ->					str:

            '''simple docstring'''




            return self._offload

class     __lowerCAmelCase					:






       """simple docstring"""





       def __init__(							self       :		str	,			lowerCAmelCase__       :		int					)   ->					Tuple:

            '''simple docstring'''




            _UpperCamelCase       =	engine







       def snake_case__						(							self       :		List[str]	,			lowerCAmelCase__       :		Tuple	,			**lowerCAmelCase__       :		Union[str, Any]					)   ->					List[str]:

            '''simple docstring'''




            self.engine.backward(lowerCAmelCase__	,			**lowerCAmelCase__					)

            # 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					(   __magic_name__			):






       """simple docstring"""





       def __init__(							self       :		Optional[Any]	,			lowerCAmelCase__       :		Any					)   ->					List[Any]:

            '''simple docstring'''




            super().__init__(lowerCAmelCase__	,			device_placement=lowerCAmelCase__	,			scaler=lowerCAmelCase__					)
            _UpperCamelCase       =	hasattr(self.optimizer	,			'''overflow'''					)





       def snake_case__						(							self       :		Optional[Any]	,			lowerCAmelCase__       :		Union[str, Any]=None					)   ->					Tuple:

            '''simple docstring'''




            pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed





       def snake_case__						(							self       :		List[Any]					)   ->					List[Any]:

            '''simple docstring'''




            pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed







       @property
       def snake_case__						(							self       :		Dict					)   ->					str:

            '''simple docstring'''




            if self.__has_overflow__:
                 return self.optimizer.overflow
            return False

class     __lowerCAmelCase					(   __magic_name__			):






       """simple docstring"""





       def __init__(							self       :		Optional[int]	,			lowerCAmelCase__       :		str	,			lowerCAmelCase__       :		Tuple					)   ->					Tuple:

            '''simple docstring'''




            super().__init__(lowerCAmelCase__	,			lowerCAmelCase__					)







       def snake_case__						(							self       :		Any					)   ->					List[Any]:

            '''simple docstring'''




            pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed

class     __lowerCAmelCase					:






       """simple docstring"""





       def __init__(							self       :		int	,			lowerCAmelCase__       :		List[str]	,			lowerCAmelCase__       :		Any=0.001	,			lowerCAmelCase__       :		str=0	,			**lowerCAmelCase__       :		Optional[int]					)   ->					List[str]:

            '''simple docstring'''




            _UpperCamelCase       =	params
            _UpperCamelCase       =	lr
            _UpperCamelCase       =	weight_decay
            _UpperCamelCase       =	kwargs

class     __lowerCAmelCase					:






       """simple docstring"""





       def __init__(							self       :		Any	,			lowerCAmelCase__       :		Optional[Any]	,			lowerCAmelCase__       :		List[str]=None	,			lowerCAmelCase__       :		Dict=0	,			**lowerCAmelCase__       :		List[str]					)   ->					Any:

            '''simple docstring'''




            _UpperCamelCase       =	optimizer
            _UpperCamelCase       =	total_num_steps
            _UpperCamelCase       =	warmup_num_steps
            _UpperCamelCase       =	kwargs










'''simple docstring'''

from math import isclose, sqrt







def  a__    (    lowercase :					float, lowercase :					float, lowercase :					float				)		->		tuple[float, float, float]:





     """simple docstring"""

     _UpperCamelCase       =	point_y / 4 / point_x
     _UpperCamelCase       =	2 * normal_gradient / (1 + normal_gradient * normal_gradient)
     _UpperCamelCase       =	(1 - normal_gradient * normal_gradient) / (
         1 + normal_gradient * normal_gradient
     )
     _UpperCamelCase       =	(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

     # to find the next point, solve the simultaeneous equations:
     # y^2 + 4x^2 = 100
     # y - b = m * (x - a)
     # ==> A x^2 + B x + C = 0
     _UpperCamelCase       =	outgoing_gradient**2 + 4
     _UpperCamelCase       =	2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
     _UpperCamelCase       =	(point_y - outgoing_gradient * point_x) ** 2 - 100

     _UpperCamelCase       =	(
         -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term				)
     ) / (2 * quadratic_term)
     _UpperCamelCase       =	(
         -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term				)
     ) / (2 * quadratic_term)

     # two solutions, one of which is our input point
     _UpperCamelCase       =	x_minus if isclose(lowercase, lowercase				) else x_plus
     _UpperCamelCase       =	point_y + outgoing_gradient * (next_x - point_x)

     return next_x, next_y, outgoing_gradient







def  a__    (    lowercase :					float = 1.4, lowercase :					float = -9.6				)		->		int:





     """simple docstring"""

     _UpperCamelCase       =	0
     _UpperCamelCase       =	first_x_coord
     _UpperCamelCase       =	first_y_coord
     _UpperCamelCase       =	(1_0.1 - point_y) / (0.0 - point_x)

     while not (-0.0_1 <= point_x <= 0.0_1 and point_y > 0):
          _UpperCamelCase   ,    _UpperCamelCase   ,    _UpperCamelCase       =	next_point(lowercase, lowercase, lowercase				)
          num_reflections += 1

     return num_reflections


if __name__ == "__main__":
   print(F"""{solution() = }""")



