
import random

from .binary_exp_mod import bin_exp_mod



def        UpperCamelCase    (							lowerCAmelCase__ ,			lowerCAmelCase__=1000		):
					'''simple docstring'''
					if n < 2:
										return False

					if n % 2 == 0:
										return n == 2

					# this means n is odd
					lowercase							=						n - 1
					lowercase							=						0
					while d % 2 == 0:
										d /= 2
										exp += 1

					# n - 1=d*(2**exp)
					lowercase							=						0
					while count < prec:
										lowercase							=						random.randint(2 ,			n - 1		)
										lowercase							=						bin_exp_mod(lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__		)
										if b != 1:
															lowercase							=						True
															for _ in range(lowerCAmelCase__		):
																				if b == n - 1:
																									lowercase							=						False
																									break
																				lowercase							=						b * b
																				b %= n
															if flag:
																				return False
															count += 1
					return True


if __name__ == "__main__":
							lowercase__		:Tuple   =    abs(int(input("Enter bound : ").strip()))
							print("Here's the list of primes:")
							print(", ".join(str(i) for i in range(n + 1) if is_prime_big(i)))





'''simple docstring'''




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

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





class     __magic_name__						:







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

										lowercase_					:			Any										=       config

										self.set_stage_and_offload()







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Union[str, Any]    ):
										# 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.
										lowercase_					:			Tuple										=       self.get_value("""zero_optimization.stage"""				,			-1    )

										# offload
										lowercase_					:			str										=       False
										if self.is_zeroa() or self.is_zeroa():
																	lowercase_					:			Dict										=       set(["""cpu""", """nvme"""]    )
																	lowercase_					:			List[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:
																								lowercase_					:			Tuple										=       True







			def 	SCREAMING_SNAKE_CASE_     (	self				:  List[Any]				,			lowercase_				:  Any    ):
										lowercase_					:			Optional[Any]										=       self.config

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

										return config, ds_key







			def 	SCREAMING_SNAKE_CASE_     (	self				:  str				,			lowercase_				:  List[str]				,			lowercase_				:  List[str]=None    ):
										lowercase_						,						lowercase_					:			List[Any]										=       self.find_config_node(lowercase_    )
										if config is None:
																	return default
										return config.get(lowercase_				,			lowercase_    )







			def 	SCREAMING_SNAKE_CASE_     (	self				:  List[str]				,			lowercase_				:  Optional[int]				,			lowercase_				:  int=False    ):
										lowercase_					:			int										=       self.config

										# find the config node of interest if it exists
										lowercase_					:			Dict										=       ds_key_long.split("""."""    )
										for node in nodes:
																	lowercase_					:			List[Any]										=       config
																	lowercase_					:			Dict										=       config.get(lowercase_    )
																	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(lowercase_    )







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Optional[int]				,			lowercase_				:  Tuple    ):
										lowercase_					:			str										=       self.get_value(lowercase_    )
										return False if value is None else bool(lowercase_    )







			def 	SCREAMING_SNAKE_CASE_     (	self				:  List[str]				,			lowercase_				:  Union[str, Any]    ):
										lowercase_					:			Union[str, Any]										=       self.get_value(lowercase_    )
										return False if value is None else not bool(lowercase_    )







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Dict    ):
										return self._stage == 2







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Any    ):
										return self._stage == 3







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Union[str, Any]    ):
										return self._offload





class     __magic_name__						:







			def __init__(	self				:  Any				,			lowercase_				:  Union[str, Any]    ):
										lowercase_					:			Any										=       engine







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Tuple				,			lowercase_				:  int				,			**lowercase_				:  str    ):
										# runs backpropagation and handles mixed precision
										self.engine.backward(lowercase_				,			**lowercase_    )

										# 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     __magic_name__						(    _UpperCAmelCase):







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







			def 	SCREAMING_SNAKE_CASE_     (	self				:  int				,			lowercase_				:  Tuple=None    ):
										pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed







			def 	SCREAMING_SNAKE_CASE_     (	self				:  Tuple    ):
										pass  # `accelerator.backward(loss)` is doing that automatically. Therefore, its implementation is not needed







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





class     __magic_name__						(    _UpperCAmelCase):







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







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





class     __magic_name__						:







			def __init__(	self				:  Any				,			lowercase_				:  Union[str, Any]				,			lowercase_				:  List[str]=0.0_01				,			lowercase_				:  List[str]=0				,			**lowercase_				:  List[Any]    ):
										lowercase_					:			str										=       params
										lowercase_					:			List[Any]										=       lr
										lowercase_					:			int										=       weight_decay
										lowercase_					:			Union[str, Any]										=       kwargs





class     __magic_name__						:







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





