



"""simple docstring"""







import os
import socket
from contextlib import contextmanager

import torch

from ..commands.config.default import write_basic_config  # noqa: F401
from ..state import PartialState
from .dataclasses import DistributedType
from .imports import is_deepspeed_available, is_tpu_available
from .transformer_engine import convert_model
from .versions import is_torch_version


if is_deepspeed_available():
							from deepspeed import DeepSpeedEngine

if is_tpu_available(check_device=False):
							import torch_xla.core.xla_model as xm



def      __UpperCAmelCase      (    __lowerCamelCase	)							->      Any:
		if is_torch_version('''<'''						,     '''2.0.0'''	) or not hasattr(__lowerCamelCase						,     '''_dynamo'''	):
				return False
		return isinstance(__lowerCamelCase						,     torch._dynamo.eval_frame.OptimizedModule	)



def      __UpperCAmelCase      (    __lowerCamelCase						,     __lowerCamelCase = True	)							->      Dict:
		lowercase__   :    Optional[Any]				=			(torch.nn.parallel.DistributedDataParallel, torch.nn.DataParallel)

		lowercase__   :    Any				=			is_compiled_module(__lowerCamelCase	)
		if is_compiled:
				lowercase__   :    Dict				=			model
				lowercase__   :    Tuple				=			model._orig_mod

		if is_deepspeed_available():
				options += (DeepSpeedEngine,)

		while isinstance(__lowerCamelCase						,     __lowerCamelCase	):
				lowercase__   :    int				=			model.module

		if not keep_fpaa_wrapper:
				lowercase__   :    str				=			getattr(__lowerCamelCase						,     '''forward'''	)
				lowercase__   :    List[str]				=			model.__dict__.pop('''_original_forward'''						,     __lowerCamelCase	)
				if original_forward is not None:
						while hasattr(__lowerCamelCase						,     '''__wrapped__'''	):
								lowercase__   :    List[Any]				=			forward.__wrapped__
								if forward == original_forward:
										break
						lowercase__   :    Optional[Any]				=			forward
				if getattr(__lowerCamelCase						,     '''_converted_to_transformer_engine'''						,     __lowerCamelCase	):
						convert_model(__lowerCamelCase						,     to_transformer_engine=__lowerCamelCase	)

		if is_compiled:
				lowercase__   :    Optional[Any]				=			model
				lowercase__   :    Tuple				=			compiled_model

		return model



def      __UpperCAmelCase      (    )							->      str:
		PartialState().wait_for_everyone()



def      __UpperCAmelCase      (    __lowerCamelCase						,     __lowerCamelCase	)							->      Union[str, Any]:
		if PartialState().distributed_type == DistributedType.TPU:
				xm.save(__lowerCamelCase						,     __lowerCamelCase	)
		elif PartialState().local_process_index == 0:
				torch.save(__lowerCamelCase						,     __lowerCamelCase	)



@contextmanager
def      __UpperCAmelCase      (    **__lowerCamelCase	)							->      Optional[Any]:
		for key, value in kwargs.items():
				lowercase__   :    Tuple				=			str(__lowerCamelCase	)

		yield

		for key in kwargs:
				if key.upper() in os.environ:
						del os.environ[key.upper()]



def      __UpperCAmelCase      (    __lowerCamelCase	)							->      List[Any]:
		if not hasattr(__lowerCamelCase						,     '''__qualname__'''	) and not hasattr(__lowerCamelCase						,     '''__name__'''	):
				lowercase__   :    Tuple				=			getattr(__lowerCamelCase						,     '''__class__'''						,     __lowerCamelCase	)
		if hasattr(__lowerCamelCase						,     '''__qualname__'''	):
				return obj.__qualname__
		if hasattr(__lowerCamelCase						,     '''__name__'''	):
				return obj.__name__
		return str(__lowerCamelCase	)



def      __UpperCAmelCase      (    __lowerCamelCase						,     __lowerCamelCase	)							->      str:
		for key, value in source.items():
				if isinstance(__lowerCamelCase						,     __lowerCamelCase	):
						lowercase__   :    List[str]				=			destination.setdefault(__lowerCamelCase						,     {}	)
						merge_dicts(__lowerCamelCase						,     __lowerCamelCase	)
				else:
						lowercase__   :    Any				=			value

		return destination





def      __UpperCAmelCase      (    __lowerCamelCase = None	)							->      bool:
		if port is None:
				lowercase__   :    Optional[Any]				=			2_95_00
		with socket.socket(socket.AF_INET						,     socket.SOCK_STREAM	) as s:
				return s.connect_ex(('''localhost''', port)	) == 0





"""simple docstring"""
from math import factorial
class 				lowerCamelCase  :






					'''simple docstring'''





					def __init__(       self:							Optional[int]						,     snake_case:							Dict						,     snake_case:							int						)   ->	Tuple:
											snake_case_ :List[Any]						=			real
											if isinstance(snake_case						,     snake_case						):
																	snake_case_ :Tuple						=			[1] * rank
											else:
																	snake_case_ :Optional[Any]						=			rank






					def __repr__(       self:							List[str]						)   ->	Tuple:
											return (
											    f"""{self.real}+"""
											    f"""{'+'.join(str(snake_case						)+'E'+str(n+1						)for n,dual in enumerate(self.duals						)						)}"""
											)






					def    lowerCAmelCase_				(       self:							Optional[int]						)   ->	Optional[int]:
											snake_case_ :Any						=			self.duals.copy()
											while cur[-1] == 0:
																	cur.pop(-1						)
											return Dual(self.real						,     snake_case						)






					def __add__(       self:							Optional[int]						,     snake_case:							Dict						)   ->	List[str]:
											if not isinstance(snake_case						,     snake_case						):
																	return Dual(self.real + other						,     self.duals						)
											snake_case_ :List[Any]						=			self.duals.copy()
											snake_case_ :Tuple						=			other.duals.copy()
											if len(snake_case						) > len(snake_case						):
																	o_dual.extend([1] * (len(snake_case						) - len(snake_case						))						)
											elif len(snake_case						) < len(snake_case						):
																	s_dual.extend([1] * (len(snake_case						) - len(snake_case						))						)
											snake_case_ :Dict						=			[]
											for i in range(len(snake_case						)						):
																	new_duals.append(s_dual[i] + o_dual[i]						)
											return Dual(self.real + other.real						,     snake_case						)

					_A		:			str						=     __add__






					def __sub__(       self:							Tuple						,     snake_case:							Union[str, Any]						)   ->	Tuple:
											return self + other * -1






					def __mul__(       self:							str						,     snake_case:							Tuple						)   ->	Optional[Any]:
											if not isinstance(snake_case						,     snake_case						):
																	snake_case_ :Dict						=			[]
																	for i in self.duals:
																							new_duals.append(i * other						)
																	return Dual(self.real * other						,     snake_case						)
											snake_case_ :int						=			[0] * (len(self.duals						) + len(other.duals						) + 1)
											for i, item in enumerate(self.duals						):
																	for j, jtem in enumerate(other.duals						):
																							new_duals[i + j + 1] += item * jtem
											for k in range(len(self.duals						)						):
																	new_duals[k] += self.duals[k] * other.real
											for index in range(len(other.duals						)						):
																	new_duals[index] += other.duals[index] * self.real
											return Dual(self.real * other.real						,     snake_case						)

					_A		:			int						=     __mul__






					def __truediv__(       self:							List[str]						,     snake_case:							List[str]						)   ->	List[str]:
											if not isinstance(snake_case						,     snake_case						):
																	snake_case_ :Optional[Any]						=			[]
																	for i in self.duals:
																							new_duals.append(i / other						)
																	return Dual(self.real / other						,     snake_case						)
											raise ValueError






					def __floordiv__(       self:							int						,     snake_case:							List[Any]						)   ->	Any:
											if not isinstance(snake_case						,     snake_case						):
																	snake_case_ :Optional[int]						=			[]
																	for i in self.duals:
																							new_duals.append(i // other						)
																	return Dual(self.real // other						,     snake_case						)
											raise ValueError






					def __pow__(       self:							Optional[Any]						,     snake_case:							Optional[int]						)   ->	List[Any]:
											if n < 0 or isinstance(snake_case						,     snake_case						):
																	raise ValueError("""power must be a positive integer"""						)
											if n == 0:
																	return 1
											if n == 1:
																	return self
											snake_case_ :str						=			self
											for _ in range(n - 1						):
																	x *= self
											return x

def    A_  (			_lowercase,					_lowercase,					_lowercase	):







						'''simple docstring'''


						if not callable(_lowercase	):
												raise ValueError("""differentiate() requires a function as input for func"""	)
						if not isinstance(_lowercase,					(float, int)	):
												raise ValueError("""differentiate() requires a float as input for position"""	)
						if not isinstance(_lowercase,					_lowercase	):
												raise ValueError("""differentiate() requires an int as input for order"""	)
						snake_case_ :Optional[Any]						=			Dual(_lowercase,					1	)
						snake_case_ :List[Any]						=			func(_lowercase	)
						if order == 0:
												return result.real
						return result.duals[order - 1] * factorial(_lowercase	)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						def    A_  (			_lowercase	):







												'''simple docstring'''


												return y**2 * y**4

						print(differentiate(f, 9, 2))
