


from __future__ import annotations

from math import gcd







def       _UpperCamelCase (						UpperCamelCase__	, UpperCamelCase__ = 2	, UpperCamelCase__ = 1	, UpperCamelCase__ = 3	, ):



			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(lowerCAmelCase__	, 2   ) + step) % modulus

			for _ in range(lowerCAmelCase__   ):
						# These track the position within the cycle detection logic.
						UpperCAmelCase__					:   int       				=       seed
						UpperCAmelCase__					:   Union[str, Any]       				=       seed

						while True:
									# At each iteration, the tortoise moves one step and the hare moves two.
									UpperCAmelCase__					:   Optional[int]       				=       rand_fn(lowerCAmelCase__	, lowerCAmelCase__	, lowerCAmelCase__   )
									UpperCAmelCase__					:   Optional[int]       				=       rand_fn(lowerCAmelCase__	, lowerCAmelCase__	, lowerCAmelCase__   )
									UpperCAmelCase__					:   int       				=       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``.
									UpperCAmelCase__					:   int       				=       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.
						UpperCAmelCase__					:   str       				=       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}""")



'''simple docstring'''



import unittest

import numpy as np

from transformers import RoFormerConfig, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_modeling_flax_common import FlaxModelTesterMixin, ids_tensor, random_attention_mask


if is_flax_available():
		import jax.numpy as jnp

		from transformers.models.roformer.modeling_flax_roformer import (
		    FlaxRoFormerForMaskedLM,
		    FlaxRoFormerForMultipleChoice,
		    FlaxRoFormerForQuestionAnswering,
		    FlaxRoFormerForSequenceClassification,
		    FlaxRoFormerForTokenClassification,
		    FlaxRoFormerModel,
		)


class 						_snake_case   (       unittest.TestCase		):




					def __init__( self							,							_lowerCamelCase							,							_lowerCamelCase=13							,							_lowerCamelCase=7							,							_lowerCamelCase=True							,							_lowerCamelCase=True							,							_lowerCamelCase=True							,							_lowerCamelCase=True							,							_lowerCamelCase=99							,							_lowerCamelCase=32							,							_lowerCamelCase=5							,							_lowerCamelCase=4							,							_lowerCamelCase=37							,							_lowerCamelCase="gelu"							,							_lowerCamelCase=0.1							,							_lowerCamelCase=0.1							,							_lowerCamelCase=512							,							_lowerCamelCase=16							,							_lowerCamelCase=2							,							_lowerCamelCase=0.02							,							_lowerCamelCase=4							,							):
								UpperCAmelCase__					:   Union[str, Any]       				=       parent
								UpperCAmelCase__					:   str       				=       batch_size
								UpperCAmelCase__					:   Tuple       				=       seq_length
								UpperCAmelCase__					:   Any       				=       is_training
								UpperCAmelCase__					:   Tuple       				=       use_attention_mask
								UpperCAmelCase__					:   Optional[Any]       				=       use_token_type_ids
								UpperCAmelCase__					:   Optional[Any]       				=       use_labels
								UpperCAmelCase__					:   str       				=       vocab_size
								UpperCAmelCase__					:   Dict       				=       hidden_size
								UpperCAmelCase__					:   int       				=       num_hidden_layers
								UpperCAmelCase__					:   Optional[int]       				=       num_attention_heads
								UpperCAmelCase__					:   Optional[int]       				=       intermediate_size
								UpperCAmelCase__					:   Tuple       				=       hidden_act
								UpperCAmelCase__					:   Optional[Any]       				=       hidden_dropout_prob
								UpperCAmelCase__					:   Union[str, Any]       				=       attention_probs_dropout_prob
								UpperCAmelCase__					:   List[Any]       				=       max_position_embeddings
								UpperCAmelCase__					:   Optional[int]       				=       type_vocab_size
								UpperCAmelCase__					:   str       				=       type_sequence_label_size
								UpperCAmelCase__					:   Optional[int]       				=       initializer_range
								UpperCAmelCase__					:   str       				=       num_choices




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   List[str]       				=       ids_tensor([self.batch_size, self.seq_length]							,							self.vocab_size)

								UpperCAmelCase__					:   Union[str, Any]       				=       None
								if self.use_attention_mask:
											UpperCAmelCase__					:   Tuple       				=       random_attention_mask([self.batch_size, self.seq_length])

								UpperCAmelCase__					:   Dict       				=       None
								if self.use_token_type_ids:
											UpperCAmelCase__					:   Any       				=       ids_tensor([self.batch_size, self.seq_length]							,							self.type_vocab_size)

								UpperCAmelCase__					:   Optional[Any]       				=       RoFormerConfig(
								    vocab_size=self.vocab_size							,							hidden_size=self.hidden_size							,							num_hidden_layers=self.num_hidden_layers							,							num_attention_heads=self.num_attention_heads							,							intermediate_size=self.intermediate_size							,							hidden_act=self.hidden_act							,							hidden_dropout_prob=self.hidden_dropout_prob							,							attention_probs_dropout_prob=self.attention_probs_dropout_prob							,							max_position_embeddings=self.max_position_embeddings							,							type_vocab_size=self.type_vocab_size							,							is_decoder=_lowerCamelCase							,							initializer_range=self.initializer_range							,							)

								return config, input_ids, token_type_ids, attention_mask




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   List[Any]       				=       self.prepare_config_and_inputs()
								UpperCAmelCase__				,    UpperCAmelCase__				,    UpperCAmelCase__				,    UpperCAmelCase__					:   Optional[Any]       				=       config_and_inputs
								UpperCAmelCase__					:   Dict       				=       {"""input_ids""": input_ids, """token_type_ids""": token_type_ids, """attention_mask""": attention_mask}
								return config, inputs_dict


@require_flax
class 						_snake_case   (       a__    ,				unittest.TestCase		):
					lowerCAmelCase :Optional[int]						=   True

					lowerCAmelCase :Any						=   (
					    (
					        FlaxRoFormerModel,
					        FlaxRoFormerForMaskedLM,
					        FlaxRoFormerForSequenceClassification,
					        FlaxRoFormerForTokenClassification,
					        FlaxRoFormerForMultipleChoice,
					        FlaxRoFormerForQuestionAnswering,
					    )
					    if is_flax_available()
					    else ()
					)




					def 			snake_case__  ( self):
								UpperCAmelCase__					:   List[str]       				=       FlaxRoFormerModelTester(self)




					@slow
					def 			snake_case__  ( self):
								for model_class_name in self.all_model_classes:
											UpperCAmelCase__					:   List[str]       				=       model_class_name.from_pretrained("""junnyu/roformer_chinese_small"""							,							from_pt=_lowerCamelCase)
											UpperCAmelCase__					:   Dict       				=       model(np.ones((1, 1)))
											self.assertIsNotNone(_lowerCamelCase)


@require_flax
class 						_snake_case   (       unittest.TestCase		):




					@slow
					def 			snake_case__  ( self):
								UpperCAmelCase__					:   Any       				=       FlaxRoFormerForMaskedLM.from_pretrained("""junnyu/roformer_chinese_base""")
								UpperCAmelCase__					:   int       				=       jnp.array([[0, 1, 2, 3, 4, 5]])
								UpperCAmelCase__					:   Optional[int]       				=       model(_lowerCamelCase)[0]

								UpperCAmelCase__					:   Union[str, Any]       				=       5_0000

								UpperCAmelCase__					:   Any       				=       (1, 6, vocab_size)
								self.assertEqual(output.shape							,							_lowerCamelCase)

								UpperCAmelCase__					:   Union[str, Any]       				=       jnp.array(
								    [[[-0.1205, -1.0265, 0.2922], [-1.5134, 0.1974, 0.1519], [-5.0135, -3.9003, -0.8404]]])

								self.assertTrue(jnp.allclose(output[:, :3, :3]							,							_lowerCamelCase							,							atol=1e-4))