'''simple docstring'''

import math



def lowerCamelCase__    (							A_							):





 if 1 < number < 4:
  # 2 and 3 are primes
  return True
 elif number < 2 or number % 2 == 0 or number % 3 == 0:
  # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
  return False

 # All primes number are in format of 6k +/- 1
 for i in range(5							,      int(math.sqrt(a__							) + 1							)							,      6							):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True



def lowerCamelCase__    (							A_ = 0.1							):
 UpperCAmelCase_												=       3
 UpperCAmelCase_												=       3

 while primes / (2 * j - 1) >= ratio:
  for i in range(j * j + j + 1							,      (j + 2) * (j + 2)							,      j + 1							):
   primes += is_prime(a__							)
  j += 2
 return j


if __name__ == "__main__":
      import doctest

      doctest.testmod()







# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings("ignore", category=UserWarning, module="torch.optim.lr_scheduler")

class 							__SCREAMING_SNAKE_CASE       :






							def __init__(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase = True	,			__lowerCAmelCase = False	):
														UpperCamelCase__					  =      scheduler
														UpperCamelCase__					  =      optimizers if isinstance(__lowerCAmelCase	,			(list, tuple)	) else [optimizers]
														UpperCamelCase__					  =      split_batches
														UpperCamelCase__					  =      step_with_optimizer
														UpperCamelCase__					  =      GradientState()






							def 					_lowerCamelCase		(    self	,			*__lowerCAmelCase	,			**__lowerCAmelCase	):
														if not self.step_with_optimizer:
																					# No link between scheduler and optimizer -> just step
																					self.scheduler.step(*__lowerCAmelCase	,			**__lowerCAmelCase	)
																					return

														# Otherwise, first make sure the optimizer was stepped.
														if not self.gradient_state.sync_gradients:
																					if self.gradient_state.adjust_scheduler:
																												self.scheduler._step_count += 1
																					return

														for opt in self.optimizers:
																					if opt.step_was_skipped:
																												return
														if self.split_batches:
																					# Split batches -> the training dataloader batch size is not changed so one step per training step
																					self.scheduler.step(*__lowerCAmelCase	,			**__lowerCAmelCase	)
														else:
																					# Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
																					# num_processes steps per training step
																					UpperCamelCase__					  =      AcceleratorState().num_processes
																					for _ in range(__lowerCAmelCase	):
																												# Special case when using OneCycle and `drop_last` was not used
																												if hasattr(self.scheduler	,			"""total_steps"""	):
																																			if self.scheduler._step_count <= self.scheduler.total_steps:
																																										self.scheduler.step(*__lowerCAmelCase	,			**__lowerCAmelCase	)
																												else:
																																			self.scheduler.step(*__lowerCAmelCase	,			**__lowerCAmelCase	)






							def 					_lowerCamelCase		(    self	):
														return self.scheduler.get_last_lr()






							def 					_lowerCamelCase		(    self	):
														return self.scheduler.state_dict()






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	):
														self.scheduler.load_state_dict(__lowerCAmelCase	)






							def 					_lowerCamelCase		(    self	):
														return self.scheduler.get_lr()







							def 					_lowerCamelCase		(    self	,			*__lowerCAmelCase	,			**__lowerCAmelCase	):
														return self.scheduler.print_lr(*__lowerCAmelCase	,			**__lowerCAmelCase	)




