





from __future__ import annotations

from math import gcd



def        __lowercase       (				_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE = 2			,						_SCREAMING_SNAKE_CASE = 1			,						_SCREAMING_SNAKE_CASE = 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(_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE     ) -> int:
            return (pow(_SCREAMING_SNAKE_CASE			,						2     ) + step) % modulus

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

            while True:
                  # At each iteration, the tortoise moves one step and the hare moves two.
                  SCREAMING_SNAKE_CASE		=						rand_fn(_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE     )
                  SCREAMING_SNAKE_CASE		=						rand_fn(_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE     )
                  SCREAMING_SNAKE_CASE		=						rand_fn(_SCREAMING_SNAKE_CASE			,						_SCREAMING_SNAKE_CASE			,						_SCREAMING_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``.
                  SCREAMING_SNAKE_CASE		=						gcd(hare - tortoise			,						_SCREAMING_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.
            SCREAMING_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_						       =	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_						       =	parser.parse_args()

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









import inspect
import unittest

from transformers import RegNetConfig, is_flax_available
from transformers.testing_utils import require_flax, slow
from transformers.utils import cached_property, is_vision_available

from ...test_configuration_common import ConfigTester
from ...test_modeling_flax_common import FlaxModelTesterMixin, floats_tensor


if is_flax_available():
      import jax
      import jax.numpy as jnp

      from transformers.models.regnet.modeling_flax_regnet import FlaxRegNetForImageClassification, FlaxRegNetModel

if is_vision_available():
      from PIL import Image

      from transformers import AutoImageProcessor

class 		UpperCamelCase__			(				unittest.TestCase       ):



     '''simple docstring'''

     def __init__(							self						:   Optional[int]						,lowerCamelCase__						:   List[str]						,lowerCamelCase__						:   Optional[Any]=3						,lowerCamelCase__						:   List[str]=32						,lowerCamelCase__						:   List[Any]=3						,lowerCamelCase__						:   str=10						,lowerCamelCase__						:   Any=[10, 20, 30, 40]						,lowerCamelCase__						:   Optional[Any]=[1, 1, 2, 1]						,lowerCamelCase__						:   Union[str, Any]=True						,lowerCamelCase__						:   int=True						,lowerCamelCase__						:   Tuple="relu"						,lowerCamelCase__						:   Dict=3						,lowerCamelCase__						:   Optional[int]=None						,)					->		Optional[int]:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						parent
           SCREAMING_SNAKE_CASE		=						batch_size
           SCREAMING_SNAKE_CASE		=						image_size
           SCREAMING_SNAKE_CASE		=						num_channels
           SCREAMING_SNAKE_CASE		=						embeddings_size
           SCREAMING_SNAKE_CASE		=						hidden_sizes
           SCREAMING_SNAKE_CASE		=						depths
           SCREAMING_SNAKE_CASE		=						is_training
           SCREAMING_SNAKE_CASE		=						use_labels
           SCREAMING_SNAKE_CASE		=						hidden_act
           SCREAMING_SNAKE_CASE		=						num_labels
           SCREAMING_SNAKE_CASE		=						scope
           SCREAMING_SNAKE_CASE		=						len(lowerCamelCase__	)






     def     SCREAMING_SNAKE_CASE__  (							self						:   Tuple	)					->		Tuple:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						floats_tensor([self.batch_size, self.num_channels, self.image_size, self.image_size]	)

           SCREAMING_SNAKE_CASE		=						self.get_config()

           return config, pixel_values






     def     SCREAMING_SNAKE_CASE__  (							self						:   str	)					->		Optional[int]:




           '''simple docstring'''


           return RegNetConfig(
               num_channels=self.num_channels						,embeddings_size=self.embeddings_size						,hidden_sizes=self.hidden_sizes						,depths=self.depths						,hidden_act=self.hidden_act						,num_labels=self.num_labels						,image_size=self.image_size						,)






     def     SCREAMING_SNAKE_CASE__  (							self						:   Union[str, Any]						,lowerCamelCase__						:   int						,lowerCamelCase__						:   Union[str, Any]	)					->		Any:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						FlaxRegNetModel(config=lowerCamelCase__	)
           SCREAMING_SNAKE_CASE		=						model(lowerCamelCase__	)

           # Output shape (b, c, h, w)
           self.parent.assertEqual(
               result.last_hidden_state.shape						,(self.batch_size, self.hidden_sizes[-1], self.image_size // 32, self.image_size // 32)						,)






     def     SCREAMING_SNAKE_CASE__  (							self						:   Union[str, Any]						,lowerCamelCase__						:   Optional[int]						,lowerCamelCase__						:   Optional[Any]	)					->		Tuple:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						self.num_labels
           SCREAMING_SNAKE_CASE		=						FlaxRegNetForImageClassification(config=lowerCamelCase__	)
           SCREAMING_SNAKE_CASE		=						model(lowerCamelCase__	)
           self.parent.assertEqual(result.logits.shape						,(self.batch_size, self.num_labels)	)






     def     SCREAMING_SNAKE_CASE__  (							self						:   str	)					->		int:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						self.prepare_config_and_inputs()
           SCREAMING_SNAKE_CASE, SCREAMING_SNAKE_CASE		=						config_and_inputs
           SCREAMING_SNAKE_CASE		=						{"""pixel_values""": pixel_values}
           return config, inputs_dict

@require_flax
class 		UpperCamelCase__			(				lowerCAmelCase_							,				unittest.TestCase       ):



     '''simple docstring'''

     __snake_case   :     Union[str, Any]		     =      (FlaxRegNetModel, FlaxRegNetForImageClassification) if is_flax_available() else ()

     __snake_case   :     Tuple		     =      False
     __snake_case   :     int		     =      False
     __snake_case   :     Tuple		     =      False






     def     SCREAMING_SNAKE_CASE__  (							self						:   Union[str, Any]	)					->		None:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						FlaxRegNetModelTester(self	)
           SCREAMING_SNAKE_CASE		=						ConfigTester(self						,config_class=lowerCamelCase__						,has_text_modality=lowerCamelCase__	)






     def     SCREAMING_SNAKE_CASE__  (							self						:   Any	)					->		Optional[int]:




           '''simple docstring'''


           self.create_and_test_config_common_properties()
           self.config_tester.create_and_test_config_to_json_string()
           self.config_tester.create_and_test_config_to_json_file()
           self.config_tester.create_and_test_config_from_and_save_pretrained()
           self.config_tester.create_and_test_config_with_num_labels()
           self.config_tester.check_config_can_be_init_without_params()
           self.config_tester.check_config_arguments_init()






     def     SCREAMING_SNAKE_CASE__  (							self						:   int	)					->		List[str]:




           '''simple docstring'''


           return






     def     SCREAMING_SNAKE_CASE__  (							self						:   Tuple	)					->		List[Any]:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						self.model_tester.prepare_config_and_inputs()
           self.model_tester.create_and_check_model(*lowerCamelCase__	)






     def     SCREAMING_SNAKE_CASE__  (							self						:   Optional[int]	)					->		int:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						self.model_tester.prepare_config_and_inputs()
           self.model_tester.create_and_check_for_image_classification(*lowerCamelCase__	)






     @unittest.skip(reason="""RegNet does not use inputs_embeds"""	)
     def     SCREAMING_SNAKE_CASE__  (							self						:   str	)					->		Any:




           '''simple docstring'''


           pass






     @unittest.skip(reason="""RegNet does not support input and output embeddings"""	)
     def     SCREAMING_SNAKE_CASE__  (							self						:   str	)					->		Any:




           '''simple docstring'''


           pass






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




           '''simple docstring'''


           SCREAMING_SNAKE_CASE, SCREAMING_SNAKE_CASE		=						self.model_tester.prepare_config_and_inputs_for_common()

           for model_class in self.all_model_classes:
                 SCREAMING_SNAKE_CASE		=						model_class(lowerCamelCase__	)
                 SCREAMING_SNAKE_CASE		=						inspect.signature(model.__call__	)
                 # signature.parameters is an OrderedDict => so arg_names order is deterministic
                 SCREAMING_SNAKE_CASE		=						[*signature.parameters.keys()]

                 SCREAMING_SNAKE_CASE		=						["""pixel_values"""]
                 self.assertListEqual(arg_names[:1]						,lowerCamelCase__	)






     def     SCREAMING_SNAKE_CASE__  (							self						:   Optional[Any]	)					->		int:




           '''simple docstring'''


           def check_hidden_states_output(lowerCamelCase__						:   Tuple						,lowerCamelCase__						:   Union[str, Any]						,lowerCamelCase__						:   Optional[int]	):
                 SCREAMING_SNAKE_CASE		=						model_class(lowerCamelCase__	)

                 SCREAMING_SNAKE_CASE		=						model(**self._prepare_for_class(lowerCamelCase__						,lowerCamelCase__	)	)

                 SCREAMING_SNAKE_CASE		=						outputs.encoder_hidden_states if config.is_encoder_decoder else outputs.hidden_states

                 SCREAMING_SNAKE_CASE		=						self.model_tester.num_stages
                 self.assertEqual(len(lowerCamelCase__	)						,expected_num_stages + 1	)

           SCREAMING_SNAKE_CASE, SCREAMING_SNAKE_CASE		=						self.model_tester.prepare_config_and_inputs_for_common()

           for model_class in self.all_model_classes:
                 SCREAMING_SNAKE_CASE		=						True
                 check_hidden_states_output(lowerCamelCase__						,lowerCamelCase__						,lowerCamelCase__	)

                 # check that output_hidden_states also work using config
                 del inputs_dict["output_hidden_states"]
                 SCREAMING_SNAKE_CASE		=						True

                 check_hidden_states_output(lowerCamelCase__						,lowerCamelCase__						,lowerCamelCase__	)






     def     SCREAMING_SNAKE_CASE__  (							self						:   Any	)					->		List[Any]:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE, SCREAMING_SNAKE_CASE		=						self.model_tester.prepare_config_and_inputs_for_common()

           for model_class in self.all_model_classes:
                 with self.subTest(model_class.__name__	):
                       SCREAMING_SNAKE_CASE		=						self._prepare_for_class(lowerCamelCase__						,lowerCamelCase__	)
                       SCREAMING_SNAKE_CASE		=						model_class(lowerCamelCase__	)

                       @jax.jit
                       def model_jitted(lowerCamelCase__						:   Dict						,**lowerCamelCase__						:   Optional[Any]	):
                             return model(pixel_values=lowerCamelCase__						,**lowerCamelCase__	)

                       with self.subTest("""JIT Enabled"""	):
                             SCREAMING_SNAKE_CASE		=						model_jitted(**lowerCamelCase__	).to_tuple()

                       with self.subTest("""JIT Disabled"""	):
                             with jax.disable_jit():
                                   SCREAMING_SNAKE_CASE		=						model_jitted(**lowerCamelCase__	).to_tuple()

                       self.assertEqual(len(lowerCamelCase__	)						,len(lowerCamelCase__	)	)
                       for jitted_output, output in zip(lowerCamelCase__						,lowerCamelCase__	):
                             self.assertEqual(jitted_output.shape						,output.shape	)



def        __lowercase       (				)			->       Union[str, Any]:


      '''simple docstring'''


      SCREAMING_SNAKE_CASE		=						Image.open("""./tests/fixtures/tests_samples/COCO/000000039769.png"""     )
      return image



@require_flax
class 		UpperCamelCase__			(				unittest.TestCase       ):



     '''simple docstring'''

     @cached_property
     def     SCREAMING_SNAKE_CASE__  (							self						:   int	)					->		str:




           '''simple docstring'''


           return AutoImageProcessor.from_pretrained("""facebook/regnet-y-040"""	) if is_vision_available() else None






     @slow
     def     SCREAMING_SNAKE_CASE__  (							self						:   Optional[int]	)					->		List[str]:




           '''simple docstring'''


           SCREAMING_SNAKE_CASE		=						FlaxRegNetForImageClassification.from_pretrained("""facebook/regnet-y-040"""	)

           SCREAMING_SNAKE_CASE		=						self.default_image_processor
           SCREAMING_SNAKE_CASE		=						prepare_img()
           SCREAMING_SNAKE_CASE		=						image_processor(images=lowerCamelCase__						,return_tensors="""np"""	)

           SCREAMING_SNAKE_CASE		=						model(**lowerCamelCase__	)

           # verify the logits
           SCREAMING_SNAKE_CASE		=						(1, 1000)
           self.assertEqual(outputs.logits.shape						,lowerCamelCase__	)

           SCREAMING_SNAKE_CASE		=						jnp.array([-0.4180, -1.5051, -3.4836]	)

           self.assertTrue(jnp.allclose(outputs.logits[0, :3]						,lowerCamelCase__						,atol=1e-4	)	)


