





'''simple docstring'''

from __future__ import annotations

from math import gcd





def lowerCamelCase						(     __lowerCamelCase :    int					,       __lowerCamelCase :    int = 2					,       __lowerCamelCase :    int = 1					,       __lowerCamelCase :    int = 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(__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.
        _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(__lowerCamelCase					,       __lowerCamelCase					,       __lowerCamelCase    )
            _SCREAMING_SNAKE_CASE									=			rand_fn(__lowerCamelCase					,       __lowerCamelCase					,       __lowerCamelCase    )
            _SCREAMING_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``.
            _SCREAMING_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.
        _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

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

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





import os
import tempfile
import unittest
from pathlib import Path

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


if is_torch_available():
					from transformers import PyTorchBenchmark, PyTorchBenchmarkArguments


@require_torch
class 				lowercase					(		unittest.TestCase   ):



		def __UpperCamelCase ( self				,      A_       )  ->					List[str]:
				"""simple docstring"""
				for model_result in results.values():
						for batch_size, sequence_length in zip(model_result['bs']				,      model_result['ss']       ):
								UpperCamelCase		=     model_result['result'][batch_size][sequence_length]
								self.assertIsNotNone(A_       )



		def __UpperCamelCase ( self       )  ->					Tuple:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result       )
				self.check_results_dict_not_empty(results.memory_inference_result       )



		def __UpperCamelCase ( self       )  ->					Any:
				"""simple docstring"""
				UpperCamelCase		=     'sgugger/tiny-distilbert-classification'
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      only_pretrain_model=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result       )
				self.check_results_dict_not_empty(results.memory_inference_result       )



		def __UpperCamelCase ( self       )  ->					Any:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      torchscript=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result       )
				self.check_results_dict_not_empty(results.memory_inference_result       )



		@unittest.skipIf(torch_device == 'cpu'				,      'Cant do half precision'       )
		def __UpperCamelCase ( self       )  ->					List[str]:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      fpaa=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result       )
				self.check_results_dict_not_empty(results.memory_inference_result       )



		def __UpperCamelCase ( self       )  ->					str:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'
				UpperCamelCase		=     AutoConfig.from_pretrained(A_       )
				# set architectures equal to `None`
				UpperCamelCase		=     None
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_				,      configs=[config]       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result       )
				self.check_results_dict_not_empty(results.memory_inference_result       )



		def __UpperCamelCase ( self       )  ->					List[str]:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_train_result       )
				self.check_results_dict_not_empty(results.memory_train_result       )



		@unittest.skipIf(torch_device == 'cpu'				,      'Can\'t do half precision'       )
		def __UpperCamelCase ( self       )  ->					Tuple:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      fpaa=A_				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_train_result       )
				self.check_results_dict_not_empty(results.memory_train_result       )



		def __UpperCamelCase ( self       )  ->					Tuple:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'
				UpperCamelCase		=     AutoConfig.from_pretrained(A_       )
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_				,      configs=[config]       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result       )
				self.check_results_dict_not_empty(results.memory_inference_result       )



		def __UpperCamelCase ( self       )  ->					Optional[Any]:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tinier_bart'
				UpperCamelCase		=     AutoConfig.from_pretrained(A_       )
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_				,      configs=[config]       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_inference_result       )
				self.check_results_dict_not_empty(results.memory_inference_result       )



		def __UpperCamelCase ( self       )  ->					Optional[Any]:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'
				UpperCamelCase		=     AutoConfig.from_pretrained(A_       )
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_				,      configs=[config]       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_train_result       )
				self.check_results_dict_not_empty(results.memory_train_result       )



		def __UpperCamelCase ( self       )  ->					Any:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tinier_bart'
				UpperCamelCase		=     AutoConfig.from_pretrained(A_       )
				UpperCamelCase		=     PyTorchBenchmarkArguments(
				    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      multi_process=A_				,      )
				UpperCamelCase		=     PyTorchBenchmark(A_				,      configs=[config]       )
				UpperCamelCase		=     benchmark.run()
				self.check_results_dict_not_empty(results.time_train_result       )
				self.check_results_dict_not_empty(results.memory_train_result       )



		def __UpperCamelCase ( self       )  ->					str:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'
				with tempfile.TemporaryDirectory() as tmp_dir:
						UpperCamelCase		=     PyTorchBenchmarkArguments(
						    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      save_to_csv=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      inference_time_csv_file=os.path.join(A_				,      'inf_time.csv'       )				,      train_memory_csv_file=os.path.join(A_				,      'train_mem.csv'       )				,      inference_memory_csv_file=os.path.join(A_				,      'inf_mem.csv'       )				,      train_time_csv_file=os.path.join(A_				,      'train_time.csv'       )				,      env_info_csv_file=os.path.join(A_				,      'env.csv'       )				,      multi_process=A_				,      )
						UpperCamelCase		=     PyTorchBenchmark(A_       )
						benchmark.run()
						self.assertTrue(Path(os.path.join(A_				,      'inf_time.csv'       )       ).exists()       )
						self.assertTrue(Path(os.path.join(A_				,      'train_time.csv'       )       ).exists()       )
						self.assertTrue(Path(os.path.join(A_				,      'inf_mem.csv'       )       ).exists()       )
						self.assertTrue(Path(os.path.join(A_				,      'train_mem.csv'       )       ).exists()       )
						self.assertTrue(Path(os.path.join(A_				,      'env.csv'       )       ).exists()       )



		def __UpperCamelCase ( self       )  ->					List[Any]:
				"""simple docstring"""
				UpperCamelCase		=     'sshleifer/tiny-gpt2'

				def _check_summary_is_not_empty(A_       ):
						self.assertTrue(hasattr(A_				,      'sequential'       )       )
						self.assertTrue(hasattr(A_				,      'cumulative'       )       )
						self.assertTrue(hasattr(A_				,      'current'       )       )
						self.assertTrue(hasattr(A_				,      'total'       )       )

				with tempfile.TemporaryDirectory() as tmp_dir:
						UpperCamelCase		=     PyTorchBenchmarkArguments(
						    models=[MODEL_ID]				,      training=A_				,      inference=A_				,      sequence_lengths=[8]				,      batch_sizes=[1]				,      log_filename=os.path.join(A_				,      'log.txt'       )				,      log_print=A_				,      trace_memory_line_by_line=A_				,      multi_process=A_				,      )
						UpperCamelCase		=     PyTorchBenchmark(A_       )
						UpperCamelCase		=     benchmark.run()
						_check_summary_is_not_empty(result.inference_summary       )
						_check_summary_is_not_empty(result.train_summary       )
						self.assertTrue(Path(os.path.join(A_				,      'log.txt'       )       ).exists()       )
