
import math
import time
from typing import Dict, List, Optional

from torch.utils.data import Dataset

from transformers import SeqaSeqTrainer, is_torch_tpu_available
from transformers.trainer_utils import PredictionOutput, speed_metrics


if is_torch_tpu_available(check_device=False):
   import torch_xla.core.xla_model as xm
   import torch_xla.debug.metrics as met





class     __UpperCamelCase (							lowerCAmelCase__       ):






     """simple docstring"""







     def __init__(				self							:							Union[str, Any]     ,						*_A							:							Dict     ,						_A							:							List[Any]=None     ,						_A							:							str=None     ,						**_A							:							str ):







       """simple docstring"""




       super().__init__(*_lowerCAmelCase     ,						**_lowerCAmelCase )
       __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		eval_examples
       __SCREAMING_SNAKE_CASE      :	Dict					=		post_process_function



     def  UpperCAmelCase__							(				self							:							Union[str, Any]     ,						_A							:							Optional[Dataset] = None     ,						_A							:							Any=None     ,						_A							:							Optional[List[str]] = None     ,						_A							:							str = "eval"     ,						**_A							:							Tuple     ,						):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE      :	Tuple					=		gen_kwargs.copy()
       __SCREAMING_SNAKE_CASE      :	str					=		(
           gen_kwargs['''max_length'''] if gen_kwargs.get('''max_length''' ) is not None else self.args.generation_max_length
       )
       __SCREAMING_SNAKE_CASE      :	Tuple					=		(
           gen_kwargs['''num_beams'''] if gen_kwargs.get('''num_beams''' ) is not None else self.args.generation_num_beams
       )
       __SCREAMING_SNAKE_CASE      :	List[str]					=		gen_kwargs

       __SCREAMING_SNAKE_CASE      :	Dict					=		self.eval_dataset if eval_dataset is None else eval_dataset
       __SCREAMING_SNAKE_CASE      :	int					=		self.get_eval_dataloader(_lowerCAmelCase )
       __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		self.eval_examples if eval_examples is None else eval_examples

       # Temporarily disable metric computation, we will do it in the loop here.
       __SCREAMING_SNAKE_CASE      :	Optional[int]					=		self.compute_metrics
       __SCREAMING_SNAKE_CASE      :	Dict					=		None
       __SCREAMING_SNAKE_CASE      :	List[Any]					=		time.time()
       __SCREAMING_SNAKE_CASE      :	Dict					=		self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
       try:
         __SCREAMING_SNAKE_CASE      :	Tuple					=		eval_loop(
             _lowerCAmelCase     ,						description='''Evaluation'''     ,						prediction_loss_only=True if compute_metrics is None else None     ,						ignore_keys=_lowerCAmelCase     ,						metric_key_prefix=_lowerCAmelCase     ,						)
       finally:
         __SCREAMING_SNAKE_CASE      :	str					=		compute_metrics
       __SCREAMING_SNAKE_CASE      :	List[str]					=		self.args.eval_batch_size * self.args.world_size
       if F'''{metric_key_prefix}_jit_compilation_time''' in output.metrics:
         start_time += output.metrics[F'''{metric_key_prefix}_jit_compilation_time''']
       output.metrics.update(
           speed_metrics(
               _lowerCAmelCase     ,						_lowerCAmelCase     ,						num_samples=output.num_samples     ,						num_steps=math.ceil(output.num_samples / total_batch_size )     ,						) )

       if self.post_process_function is not None and self.compute_metrics is not None and self.args.should_save:
         # Only the main node write the results by default
         __SCREAMING_SNAKE_CASE      :	Tuple					=		self.post_process_function(_lowerCAmelCase     ,						_lowerCAmelCase     ,						_lowerCAmelCase )
         __SCREAMING_SNAKE_CASE      :	List[Any]					=		self.compute_metrics(_lowerCAmelCase )

         # Prefix all keys with metric_key_prefix + '_'
         for key in list(metrics.keys() ):
           if not key.startswith(F'''{metric_key_prefix}_''' ):
             __SCREAMING_SNAKE_CASE      :	Tuple					=		metrics.pop(_lowerCAmelCase )

         metrics.update(output.metrics )
       else:
         __SCREAMING_SNAKE_CASE      :	Union[str, Any]					=		output.metrics

       if self.args.should_log:
         # Only the main node log the results by default
         self.log(_lowerCAmelCase )

       if self.args.tpu_metrics_debug or self.args.debug:
         # tpu-comment: Logging debug metrics for PyTorch/XLA (compile, execute times, ops, etc.)
         xm.master_print(met.metrics_report() )

       __SCREAMING_SNAKE_CASE      :	List[str]					=		self.callback_handler.on_evaluate(self.args     ,						self.state     ,						self.control     ,						_lowerCAmelCase )
       return metrics




     def  UpperCAmelCase__							(				self							:							Optional[Any]     ,						_A							:							Optional[Any]     ,						_A							:							Union[str, Any]     ,						_A							:							List[str]=None     ,						_A							:							str = "test"     ,						**_A							:							Optional[Any] ):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE      :	List[Any]					=		gen_kwargs.copy()

       __SCREAMING_SNAKE_CASE      :	Any					=		self.get_test_dataloader(_lowerCAmelCase )

       # Temporarily disable metric computation, we will do it in the loop here.
       __SCREAMING_SNAKE_CASE      :	str					=		self.compute_metrics
       __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		None
       __SCREAMING_SNAKE_CASE      :	int					=		time.time()
       __SCREAMING_SNAKE_CASE      :	Dict					=		self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
       try:
         __SCREAMING_SNAKE_CASE      :	str					=		eval_loop(
             _lowerCAmelCase     ,						description='''Prediction'''     ,						prediction_loss_only=True if compute_metrics is None else None     ,						ignore_keys=_lowerCAmelCase     ,						metric_key_prefix=_lowerCAmelCase     ,						)
       finally:
         __SCREAMING_SNAKE_CASE      :	int					=		compute_metrics

       __SCREAMING_SNAKE_CASE      :	Optional[int]					=		self.args.eval_batch_size * self.args.world_size
       if F'''{metric_key_prefix}_jit_compilation_time''' in output.metrics:
         start_time += output.metrics[F'''{metric_key_prefix}_jit_compilation_time''']
       output.metrics.update(
           speed_metrics(
               _lowerCAmelCase     ,						_lowerCAmelCase     ,						num_samples=output.num_samples     ,						num_steps=math.ceil(output.num_samples / total_batch_size )     ,						) )
       if self.post_process_function is None or self.compute_metrics is None:
         return output

       __SCREAMING_SNAKE_CASE      :	Any					=		self.post_process_function(_lowerCAmelCase     ,						_lowerCAmelCase     ,						_lowerCAmelCase     ,						'''predict''' )
       __SCREAMING_SNAKE_CASE      :	str					=		self.compute_metrics(_lowerCAmelCase )

       # Prefix all keys with metric_key_prefix + '_'
       for key in list(metrics.keys() ):
         if not key.startswith(F'''{metric_key_prefix}_''' ):
           __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		metrics.pop(_lowerCAmelCase )
       metrics.update(output.metrics )
       return PredictionOutput(predictions=predictions.predictions     ,						label_ids=predictions.label_ids     ,						metrics=_lowerCAmelCase )




from __future__ import annotations

from math import gcd



def       _lowerCAmelCase    (				lowerCAmelCase_				:int		,    lowerCAmelCase_				:int = 2		,    lowerCAmelCase_				:int = 1		,    lowerCAmelCase_				:int = 3		,    )->int | None:
   '''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(lowerCAmelCase_				:int		,    lowerCAmelCase_				:int		,    lowerCAmelCase_				:int				) -> int:
      return (pow(lowerCAmelCase_		,    2				) + step) % modulus

   for _ in range(lowerCAmelCase_				):
      # These track the position within the cycle detection logic.
      snake_case_            =       seed
      snake_case_            =       seed

      while True:
         # At each iteration, the tortoise moves one step and the hare moves two.
         snake_case_            =       rand_fn(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)
         snake_case_            =       rand_fn(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)
         snake_case_            =       rand_fn(lowerCAmelCase_		,    lowerCAmelCase_		,    lowerCAmelCase_				)

         # 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_            =       gcd(hare - tortoise		,    lowerCAmelCase_				)

         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_            =       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

   SCREAMING_SNAKE_CASE						:Union[str, Any]			=  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''',
   )
   SCREAMING_SNAKE_CASE						:List[str]			=  parser.parse_args()

   SCREAMING_SNAKE_CASE						:List[Any]			=  pollard_rho(args.num, attempts=args.attempts)
   if divisor is None:
      print(F'''{args.num} is probably prime''')
   else:
      SCREAMING_SNAKE_CASE						:List[str]			=  args.num // divisor
      print(F'''{args.num} = {divisor} * {quotient}''')




