




"""simple docstring"""


from typing import Dict

from transformers import EvalPrediction, HfArgumentParser, TrainingArguments, is_torch_available
from transformers.testing_utils import (
    TestCasePlus,
    execute_subprocess_async,
    get_torch_dist_unique_port,
    require_torch_multi_gpu,
    require_torch_neuroncore,
)
from transformers.training_args import ParallelMode
from transformers.utils import logging


A_      =    logging.get_logger(__name__)


if is_torch_available():
     import torch
     from torch import nn
     from torch.utils.data import Dataset

     from transformers import Trainer






     class  lowercase(					__a			):







      '''simple docstring'''





      def __init__(    self:		Optional[int],				a_:		int = 101		):




        '''simple docstring'''



        _snake_case							:		List[Any]								=  length


      def __len__(    self:		List[str]		):




        '''simple docstring'''



        return self.length


      def __getitem__(    self:		List[str],				a_:		Optional[Any]		):




        '''simple docstring'''



        return i







     class  lowercase:







      '''simple docstring'''





      def __call__(    self:		Union[str, Any],				a_:		Optional[int]		):




        '''simple docstring'''



        return {"input_ids": torch.tensor(a_		), "labels": torch.tensor(a_		)}







     class  lowercase(					nn.Module			):







      '''simple docstring'''





      def __init__(    self:		Optional[int]		):




        '''simple docstring'''



        super().__init__()
        # Add some (unused) params otherwise DDP will complain.
        _snake_case							:		Any								=  nn.Linear(120,				80		)


      def 			UpperCamelCase_       (    self:		Dict,				a_:		Optional[Any],				a_:		Union[str, Any]=None		):




        '''simple docstring'''



        if labels is not None:
          return torch.tensor(0.0,				device=input_ids.device		), input_ids
        else:
          return input_ids






class  lowercase(					__a			):







 '''simple docstring'''





 @require_torch_neuroncore
 def 			UpperCamelCase_       (    self:		Union[str, Any]		):




   '''simple docstring'''



   _snake_case							:		List[str]								=  f"--nproc_per_node=2\n            --master_port={get_torch_dist_unique_port()}\n            {self.test_file_dir}/test_trainer_distributed.py\n        ".split()
   _snake_case							:		List[str]								=  self.get_auto_remove_tmp_dir()
   _snake_case							:		int								=  f"--output_dir {output_dir}".split()
   _snake_case							:		Any								=  ["""torchrun"""] + distributed_args + args
   execute_subprocess_async(a_,				env=self.get_env()		)
   # successful return here == success - any errors would have caused an error in the sub-call







class  lowercase(					__a			):







 '''simple docstring'''





 @require_torch_multi_gpu
 def 			UpperCamelCase_       (    self:		str		):




   '''simple docstring'''



   _snake_case							:		Dict								=  f"--nproc_per_node={torch.cuda.device_count()}\n            --master_port={get_torch_dist_unique_port()}\n            {self.test_file_dir}/test_trainer_distributed.py\n        ".split()
   _snake_case							:		str								=  self.get_auto_remove_tmp_dir()
   _snake_case							:		Optional[Any]								=  f"--output_dir {output_dir}".split()
   _snake_case							:		Dict								=  ["""torchrun"""] + distributed_args + args
   execute_subprocess_async(a_,				env=self.get_env()		)
   # successful return here == success - any errors would have caused an error in the sub-call


if __name__ == "__main__":
     # The script below is meant to be run under torch.distributed, on a machine with multiple GPUs:
     #
     # PYTHONPATH="src" python -m torch.distributed.run --nproc_per_node 2 --output_dir output_dir ./tests/test_trainer_distributed.py

     A_      =    HfArgumentParser((TrainingArguments,))
     A_      =    parser.parse_args_into_dataclasses()[0]

     logger.warning(
         F'''Process rank: {training_args.local_rank}, device: {training_args.device}, n_gpu: {training_args.n_gpu}, '''
         F'''distributed training: {training_args.parallel_mode != ParallelMode.NOT_DISTRIBUTED}'''
     )

     # Essentially, what we want to verify in the distributed case is that we get all samples back,
     # in the right order. (this is crucial for prediction for instance)
     for dataset_length in [1_01, 40, 7]:
          A_      =    DummyDataset(dataset_length)


          def  UpperCAmelCase__	(snake_case__							: EvalPrediction   ):
            """simple docstring"""

            _snake_case							:		Any								=  list(range(len(snake_case__   )   )   )
            _snake_case							:		List[str]								=  p.predictions.tolist() == sequential and p.label_ids.tolist() == sequential
            if not success and training_args.local_rank == 0:
              logger.warning(
                  """Predictions and/or labels do not match expected results:\n  - predictions: """
                  F"{p.predictions.tolist()}\n  - labels: {p.label_ids.tolist()}\n  - expected: {sequential}"   )
            return {"success": success}

          A_      =    Trainer(
              model=DummyModel(),
              args=training_args,
              data_collator=DummyDataCollator(),
              eval_dataset=dataset,
              compute_metrics=compute_metrics,
          )
          A_      =    trainer.evaluate()
          logger.info(metrics)
          if metrics["eval_success"] is not True:
               logger.error(metrics)
               exit(1)

          A_      =    trainer.predict(dataset)
          logger.info(p.metrics)
          if p.metrics["test_success"] is not True:
               logger.error(p.metrics)
               exit(1)

          A_      =    2

          A_      =    trainer.evaluate()
          logger.info(metrics)
          if metrics["eval_success"] is not True:
               logger.error(metrics)
               exit(1)

          A_      =    trainer.predict(dataset)
          logger.info(p.metrics)
          if p.metrics["test_success"] is not True:
               logger.error(p.metrics)
               exit(1)






          A_      =    None








"""simple docstring"""


from __future__ import annotations

from math import gcd


def  UpperCAmelCase__	(snake_case__							: int		,       snake_case__							: int = 2		,       snake_case__							: int = 1		,       snake_case__							: int = 3		,       ):
  """simple docstring"""

  if num < 2:
    raise ValueError("""The input value cannot be less than 2"""   )

  # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
  # algorithm struggles to find factors that are divisible by two.
  # As a workaround, we specifically check for two and even inputs.
  #   See: https://math.stackexchange.com/a/2856214/165820
  if num > 2 and num % 2 == 0:
    return 2

  # Pollard's Rho algorithm requires a function that returns pseudorandom
  # values between 0 <= X < ``num``.  It doesn't need to be random in the
  # sense that the output value is cryptographically secure or difficult
  # to calculate, it only needs to be random in the sense that all output
  # values should be equally likely to appear.
  # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
  # However, the success of Pollard's algorithm isn't guaranteed and is
  # determined in part by the initial seed and the chosen random function.
  # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
  # where ``C`` is a value that we can modify between each attempt.
  def rand_fn(snake_case__							: int		,       snake_case__							: int		,       snake_case__							: int   ) -> int:
    return (pow(snake_case__		,       2   ) + step) % modulus

  for _ in range(snake_case__   ):
    # These track the position within the cycle detection logic.
    _snake_case							:		Optional[int]								=  seed
    _snake_case							:		str								=  seed

    while True:
      # At each iteration, the tortoise moves one step and the hare moves two.
      _snake_case							:		Any								=  rand_fn(snake_case__		,       snake_case__		,       snake_case__   )
      _snake_case							:		Optional[Any]								=  rand_fn(snake_case__		,       snake_case__		,       snake_case__   )
      _snake_case							:		int								=  rand_fn(snake_case__		,       snake_case__		,       snake_case__   )

      # At some point both the tortoise and the hare will enter a cycle whose
      # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
      # the tortoise and hare will end up on the same value modulo ``p``.
      # We can detect when this happens because the position difference between
      # the tortoise and the hare will share a common divisor with ``num``.
      _snake_case							:		str								=  gcd(hare - tortoise		,       snake_case__   )

      if divisor == 1:
        # No common divisor yet, just keep searching.
        continue
      else:
        # We found a common divisor!
        if divisor == num:
          # Unfortunately, the divisor is ``num`` itself and is useless.
          break
        else:
          # The divisor is a nontrivial factor of ``num``!
          return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
    _snake_case							:		Union[str, Any]								=  hare

    # The new step value for the random function can just be incremented.
    # At first the results will be similar to what the old function would
    # have produced, but the value will quickly diverge after a bit.
    step += 1

  # We haven't found a divisor within the requested number of attempts.
  # We were unlucky or ``num`` itself is actually prime.
  return None


if __name__ == "__main__":
     import argparse

     A_      =    argparse.ArgumentParser()
     parser.add_argument(
         '''num''',
         type=int,
         help='''The value to find a divisor of''',
     )
     parser.add_argument(
         '''--attempts''',
         type=int,
         default=3,
         help='''The number of attempts before giving up''',
     )
     A_      =    parser.parse_args()

     A_      =    pollard_rho(args.num, attempts=args.attempts)
     if divisor is None:
          print(F'''{args.num} is probably prime''')
     else:
          A_      =    args.num // divisor
          print(F'''{args.num} = {divisor} * {quotient}''')


