





'''simple docstring'''

from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_tf_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_tf_available():
  import tensorflow as tf


__lowerCAmelCase							:     Union[str, Any]		     =logging.get_logger(__name__)






@dataclass
class        UpperCAmelCase     (	UpperCamelCase__    ):
 __lowercase       		=    [
     """no_inference""",
     """no_cuda""",
     """no_tpu""",
     """no_speed""",
     """no_memory""",
     """no_env_print""",
     """no_multi_process""",
 ]
 def __init__(    self				:Tuple						,	**lowercase_				:List[str]							)->							str:
     for deprecated_arg in self.deprecated_args:
         if deprecated_arg in kwargs:
             A__    =      deprecated_arg[3:]
             A__    =      not kwargs.pop(lowercase_							)
             logger.warning(
                 F"{deprecated_arg} is depreciated. Please use --no-{positive_arg} or"
                 F" {positive_arg}={kwargs[positive_arg]}"							)
     A__    =      kwargs.pop("tpu_name"						,	self.tpu_name							)
     A__    =      kwargs.pop("device_idx"						,	self.device_idx							)
     A__    =      kwargs.pop("eager_mode"						,	self.eager_mode							)
     A__    =      kwargs.pop("use_xla"						,	self.use_xla							)
     super().__init__(**lowercase_							)

 __lowercase       		=    field(
     default=UpperCamelCase__      ,	metadata={"""help""": """Name of TPU"""}      ,	)
 __lowercase       		=    field(
     default=0      ,	metadata={"""help""": """CPU / GPU device index. Defaults to 0."""}      ,	)
 __lowercase       		=    field(default=UpperCamelCase__      ,	metadata={"""help""": """Benchmark models in eager model."""}    )
 __lowercase       		=    field(
     default=UpperCamelCase__      ,	metadata={
         """help""": """Benchmark models using XLA JIT compilation. Note that `eager_model` has to be set to `False`."""
     }      ,	)
 @cached_property
 def 					UpperCAmelCase_							(    self				:int							)->							Tuple["tf.distribute.cluster_resolver.TPUClusterResolver"]:
     requires_backends(self						,	["tf"]							)
     A__    =      None
     if self.tpu:
         try:
             if self.tpu_name:
                 A__    =      tf.distribute.cluster_resolver.TPUClusterResolver(self.tpu_name							)
             else:
                 A__    =      tf.distribute.cluster_resolver.TPUClusterResolver()
         except ValueError:
             A__    =      None
     return tpu
 @cached_property
 def 					UpperCAmelCase_							(    self				:int							)->							Tuple["tf.distribute.Strategy", "tf.distribute.cluster_resolver.TPUClusterResolver"]:
     requires_backends(self						,	["tf"]							)
     if self.is_tpu:
         tf.config.experimental_connect_to_cluster(self._setup_tpu							)
         tf.tpu.experimental.initialize_tpu_system(self._setup_tpu							)

         A__    =      tf.distribute.TPUStrategy(self._setup_tpu							)
     else:
         # currently no multi gpu is allowed
         if self.is_gpu:
             # TODO: Currently only single GPU is supported
             tf.config.set_visible_devices(self.gpu_list[self.device_idx]						,	"GPU"							)
             A__    =      tf.distribute.OneDeviceStrategy(device=F"/gpu:{self.device_idx}"							)
         else:
             tf.config.set_visible_devices([]						,	"GPU"							)  # disable GPU
             A__    =      tf.distribute.OneDeviceStrategy(device=F"/cpu:{self.device_idx}"							)

     return strategy
 @property
 def 					UpperCAmelCase_							(    self				:List[str]							)->							bool:
     requires_backends(self						,	["tf"]							)
     return self._setup_tpu is not None
 @property
 def 					UpperCAmelCase_							(    self				:Tuple							)->							"tf.distribute.Strategy":
     requires_backends(self						,	["tf"]							)
     return self._setup_strategy
 @property
 def 					UpperCAmelCase_							(    self				:Optional[Any]							)->							Union[str, Any]:
     requires_backends(self						,	["tf"]							)
     return tf.config.list_physical_devices("GPU"							)
 @property
 def 					UpperCAmelCase_							(    self				:str							)->							int:
     requires_backends(self						,	["tf"]							)
     if self.cuda:
         return len(self.gpu_list							)
     return 0



 @property
 def 					UpperCAmelCase_							(    self				:int							)->							bool:
     return self.n_gpu > 0










'''simple docstring'''

from __future__ import annotations

from math import gcd





def 						UpperCamelCase    (							_lowerCamelCase : int						,	_lowerCamelCase : int = 2						,	_lowerCamelCase : int = 1						,	_lowerCamelCase : int = 3						,	):
    # 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.
        A__    =      seed
        A__    =      seed

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

  __lowerCAmelCase							:     Optional[int]		     =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",
  )
  __lowerCAmelCase							:     Optional[int]		     =parser.parse_args()

  __lowerCAmelCase							:     Dict		     =pollard_rho(args.num, attempts=args.attempts)
  if divisor is None:
    print(f"""{args.num} is probably prime""")
  else:
    __lowerCAmelCase							:     Optional[Any]		     =args.num // divisor
    print(f"""{args.num} = {divisor} * {quotient}""")



