


'''simple docstring'''




from typing import List, Optional, Tuple, Union

from . import logging
from .import_utils import is_torch_available, is_torch_version


if is_torch_available():
				import torch

_lowerCAmelCase	:		int		  =						logging.get_logger(__name__)  # pylint: disable=invalid-name

try:
				from torch._dynamo import allow_in_graph as maybe_allow_in_graph
except (ImportError, ModuleNotFoundError):

				def       __UpperCamelCase     (     cls     :					int					)     ->   List[Any]:




					"""simple docstring"""





					return cls

def       __UpperCamelCase     (     _A     :					Union[Tuple, List]       , _A     :					Optional[Union[List["torch.Generator"], "torch.Generator"]] = None       , _A     :					Optional["torch.device"] = None       , _A     :					Optional["torch.dtype"] = None       , _A     :					Optional["torch.layout"] = None       , )     ->   str:




	"""simple docstring"""





	lowerCAmelCase       :     Dict   				=			device
	lowerCAmelCase       :     Optional[int]   				=			shape[0]

	lowerCAmelCase       :     List[str]   				=			layout or torch.strided
	lowerCAmelCase       :     Optional[Any]   				=			device or torch.device('cpu'					)

	if generator is not None:
		lowerCAmelCase       :     List[Any]   				=			generator.device.type if not isinstance(_A       , _A					) else generator[0].device.type
		if gen_device_type != device.type and gen_device_type == "cpu":
			lowerCAmelCase       :     Optional[int]   				=			'cpu'
			if device != "mps":
				logger.info(
				    F"The passed generator was created on 'cpu' even though a tensor on {device} was expected."
				    F" Tensors will be created on 'cpu' and then moved to {device}. Note that one can probably"
				    F" slighly speed up this function by passing a generator that was created on the {device} device."					)
		elif gen_device_type != device.type and gen_device_type == "cuda":
			raise ValueError(F"Cannot generate a {device} tensor from a generator of type {gen_device_type}."					)

	if isinstance(_A       , _A					):
		lowerCAmelCase       :     Optional[int]   				=			(1,) + shape[1:]
		lowerCAmelCase       :     Tuple   				=			[
		    torch.randn(_A       , generator=generator[i]       , device=_A       , dtype=_A       , layout=_A					)
		    for i in range(_A					)
		]
		lowerCAmelCase       :     Optional[int]   				=			torch.cat(_A       , dim=0					).to(_A					)
	else:
		lowerCAmelCase       :     Union[str, Any]   				=			torch.randn(_A       , generator=_A       , device=_A       , dtype=_A       , layout=_A					).to(_A					)

	return latents






def       __UpperCamelCase     (     _A     :					Optional[int]					)     ->   Optional[int]:




	"""simple docstring"""





	if is_torch_version('<'       , '2.0.0'					) or not hasattr(_A       , '_dynamo'					):
		return False
	return isinstance(_A       , torch._dynamo.eval_frame.OptimizedModule					)




'''simple docstring'''




import math
from collections.abc import Generator

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""simple docstring"""





	lowerCAmelCase       :     Generator   				=			(i for i in range(1       , (max_n + 1)					))
	for i in (n for n in numbers if n > 1):
		for j in range(2       , _A					):
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""simple docstring"""





	lowerCAmelCase       :     Generator   				=			(i for i in range(1       , (max_n + 1)					))
	for i in (n for n in numbers if n > 1):
		# only need to check for factors up to sqrt(i)
		lowerCAmelCase       :     List[str]   				=			int(math.sqrt(_A					)					) + 1
		for j in range(2       , _A					):
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""simple docstring"""





	lowerCAmelCase       :     Generator   				=			(i for i in range(1       , (max_n + 1)       , 2					))
	# It's useless to test even numbers as they will not be prime
	if max_n > 2:
		yield 2  # Because 2 will not be tested, it's necessary to yield it now
	for i in (n for n in numbers if n > 1):
		lowerCAmelCase       :     int   				=			int(math.sqrt(_A					)					) + 1
		for j in range(3       , _A       , 2					):
			# As we removed the even numbers, we don't need them now
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     )     ->   Dict:




	"""simple docstring"""





	from timeit import timeit

	lowerCAmelCase       :     Tuple   				=			'from __main__ import slow_primes, primes, fast_primes'
	print(timeit('slow_primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)
	print(timeit('primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)
	print(timeit('fast_primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)


if __name__ == "__main__":
				_lowerCAmelCase	:		Optional[Any]		  =						int(input('Calculate primes up to:\n>> ').strip())
				for ret in primes(number):
								print(ret)
				benchmark()
