


'''simple docstring'''






from __future__ import annotations

from math import gcd







def 				UpperCamelCase_			(    A__					:   int							,    A__					:   int = 2							,    A__					:   int = 1							,    A__					:   int = 3							,    ):
  '''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(A__					:   int							,    A__					:   int							,    A__					:   int					) -> int:
    return (pow(A__							,    2					) + step) % modulus

  for _ in range(A__					):
    # These track the position within the cycle detection logic.
    lowerCAmelCase_			:      str			=   seed
    lowerCAmelCase_			:      List[str]			=   seed

    while True:
      # At each iteration, the tortoise moves one step and the hare moves two.
      lowerCAmelCase_			:      List[Any]			=   rand_fn(A__							,    A__							,    A__					)
      lowerCAmelCase_			:      Any			=   rand_fn(A__							,    A__							,    A__					)
      lowerCAmelCase_			:      Any			=   rand_fn(A__							,    A__							,    A__					)

      # 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_			:      Union[str, Any]			=   gcd(hare - tortoise							,    A__					)

      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_			:      List[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					:  str											=      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					:  Any											=      parser.parse_args()

  __A					:  Optional[Any]											=      pollard_rho(args.num, attempts=args.attempts)
  if divisor is None:
    print(F'''{args.num} is probably prime''')
  else:
    __A					:  Union[str, Any]											=      args.num // divisor
    print(F'''{args.num} = {divisor} * {quotient}''')







'''simple docstring'''






# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__A					:  Dict											=      {"configuration_timm_backbone": ["TimmBackboneConfig"]}


try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  __A					:  str											=      ["TimmBackbone"]


if TYPE_CHECKING:
  from .configuration_timm_backbone import TimmBackboneConfig

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_timm_backbone import TimmBackbone

else:
  import sys

  __A					:  Dict											=      _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



