'''simple docstring'''




from __future__ import annotations

from math import gcd






def __lowerCAmelCase			(							UpperCamelCase__    ,  UpperCamelCase__ = 2    ,  UpperCamelCase__ = 1    ,  UpperCamelCase__ = 3    ,  )     ->   int | None:
    # A value less than 2 can cause an infinite loop in the algorithm.
    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(UpperCamelCase__    ,  UpperCamelCase__    ,  UpperCamelCase__    ) -> int:
        return (pow(UpperCamelCase__    ,  2    ) + step) % modulus

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

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

            # 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``.
            __lowerCamelCase          =  gcd(hare - tortoise    ,  UpperCamelCase__    )

            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.
        __lowerCamelCase          =  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

  __UpperCAmelCase												=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",
  )
  __UpperCAmelCase												=parser.parse_args()

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

'''simple docstring'''




import time
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch, torch_device

from ..test_modeling_common import ids_tensor


if is_torch_available():
  import torch

  from transformers.generation import (
      MaxLengthCriteria,
      MaxNewTokensCriteria,
      MaxTimeCriteria,
      StoppingCriteriaList,
      validate_stopping_criteria,
  )




@require_torch
class    a__				(       unittest.TestCase			):






     def        SCREAMING_SNAKE_CASE__       (			self		:		Optional[int]  ,    a		:		int   ):





         """simple docstring"""



         __lowerCamelCase          =  3
         __lowerCamelCase          =  2_50

         __lowerCamelCase          =  ids_tensor((batch_size, length)  ,    a   )
         __lowerCamelCase          =  torch.ones((batch_size, length)  ,    device=a  ,    dtype=torch.float   ) / length
         return input_ids, scores






     def        SCREAMING_SNAKE_CASE__       (			self		:		List[Any]   ):





         """simple docstring"""



         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(5   )

         __lowerCamelCase          =  StoppingCriteriaList(
             [
                 MaxLengthCriteria(max_length=10   ),
                 MaxTimeCriteria(max_time=0.1   ),
             ]   )

         self.assertFalse(criteria(a  ,    a   )   )

         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(9   )
         self.assertFalse(criteria(a  ,    a   )   )

         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(10   )
         self.assertTrue(criteria(a  ,    a   )   )






     def        SCREAMING_SNAKE_CASE__       (			self		:		Union[str, Any]   ):





         """simple docstring"""



         __lowerCamelCase          =  MaxLengthCriteria(max_length=10   )

         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(5   )
         self.assertFalse(criteria(a  ,    a   )   )

         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(9   )
         self.assertFalse(criteria(a  ,    a   )   )

         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(10   )
         self.assertTrue(criteria(a  ,    a   )   )






     def        SCREAMING_SNAKE_CASE__       (			self		:		List[Any]   ):





         """simple docstring"""



         __lowerCamelCase          =  MaxNewTokensCriteria(start_length=5  ,    max_new_tokens=5   )

         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(5   )
         self.assertFalse(criteria(a  ,    a   )   )

         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(9   )
         self.assertFalse(criteria(a  ,    a   )   )

         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(10   )
         self.assertTrue(criteria(a  ,    a   )   )

         __lowerCamelCase          =  StoppingCriteriaList([criteria]   )
         self.assertEqual(criteria_list.max_length  ,    10   )






     def        SCREAMING_SNAKE_CASE__       (			self		:		int   ):





         """simple docstring"""



         __lowerCamelCase     ,  __lowerCamelCase          =  self._get_tensors(5   )

         __lowerCamelCase          =  MaxTimeCriteria(max_time=0.1   )
         self.assertFalse(criteria(a  ,    a   )   )

         __lowerCamelCase          =  MaxTimeCriteria(max_time=0.1  ,    initial_timestamp=time.time() - 0.2   )
         self.assertTrue(criteria(a  ,    a   )   )






     def        SCREAMING_SNAKE_CASE__       (			self		:		List[Any]   ):





         """simple docstring"""



         validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10   )]   )  ,    10   )

         with self.assertWarns(a   ):
             validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10   )]   )  ,    11   )

         __lowerCamelCase          =  validate_stopping_criteria(StoppingCriteriaList()  ,    11   )

         self.assertEqual(len(a   )  ,    1   )
