


from __future__ import annotations

import math
import random
def     UpperCAmelCase__		(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_       ):



     """simple docstring"""






     snake_case					=       d * e - 1
     snake_case					=       0
     snake_case					=       0
     while p == 0:
          snake_case					=       random.randint(2							,n - 1       )
          snake_case					=       k
          while True:
               if t % 2 == 0:
                    snake_case					=       t // 2
                    snake_case					=       (g**t) % n
                    snake_case					=       math.gcd(x - 1							,UpperCamelCase_       )
                    if x > 1 and y > 1:
                         snake_case					=       y
                         snake_case					=       n // y
                         break  # find the correct factors
               else:
                    break  # t is not divisible by 2, break and choose another g
     return sorted([p, q]       )


if __name__ == "__main__":
 import doctest

 doctest.testmod()







import torch

from accelerate import Accelerator, DistributedType

class 						A__      :







    """simple docstring"""

    def __enter__( self					):
         if self.enabled:
              snake_case					=       self.model.no_sync()
              self.model_sync_obj.__enter__()

         return self
    def __exit__( self    ,      __snake_case    ,      __snake_case    ,      __snake_case					):
         if self.enabled:
              # Average all models on exit
              self._sync_and_avg_model_params()
              self.model_sync_obj.__exit__(__snake_case    ,      __snake_case    ,      __snake_case					)
    def __init__( self    ,      __snake_case    ,      __snake_case    ,      __snake_case    ,      __snake_case = True					):
         if accelerator.distributed_type not in [
             DistributedType.NO,
             DistributedType.MULTI_CPU,
             DistributedType.MULTI_GPU,
         ]:
              raise NotImplementedError('''LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)'''					)
         snake_case					=       enabled and accelerator.distributed_type != DistributedType.NO
         snake_case					=       0
         if self.enabled:
              snake_case					=       accelerator
              snake_case					=       model
              snake_case					=       local_sgd_steps
    def 	a_    ( self					):
         self.num_steps += 1
         if not self.enabled:
              return

         if self.num_steps % self.local_sgd_steps == 0:
              self._sync_and_avg_model_params()




    def 	a_    ( self					):
         self.accelerator.wait_for_everyone()
         with self.accelerator.autocast():
              for param in self.model.parameters():
                   snake_case					=       self.accelerator.reduce(param.data    ,      reduction='''mean'''					)




