




"""simple docstring"""


import unittest

from transformers import is_tf_available
from transformers.testing_utils import require_tf


if is_tf_available():
     import tensorflow as tf
     from tensorflow.python.eager import context
     from tensorflow.python.framework import ops

     from transformers import GradientAccumulator, create_optimizer





@require_tf
class  lowercase(					unittest.TestCase			):







 '''simple docstring'''





 def 			UpperCamelCase_       (    self:		Optional[Any],				a_:		Optional[Any],				a_:		int,				a_:		Union[str, Any]		):




   '''simple docstring'''



   self.assertEqual(len(_A		),				len(_A		)		)
   for a, b in zip(_A,				_A		):
     self.assertAlmostEqual(_A,				_A,				delta=_A		)


 def 			UpperCamelCase_       (    self:		int		):




   '''simple docstring'''



   _snake_case							:		Optional[int]								=  GradientAccumulator()
   accumulator([tf.constant([1.0, 2.0]		)]		)
   accumulator([tf.constant([-2.0, 1.0]		)]		)
   accumulator([tf.constant([-1.0, 2.0]		)]		)
   with self.assertRaises(_A		):
     accumulator([tf.constant([1.0, 1.0]		), tf.constant([2.0, 2.0]		)]		)
   self.assertEqual(accumulator.step,				3		)
   self.assertEqual(len(accumulator.gradients		),				1		)
   self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist(),				[-2.0, 5.0],				tol=1E-2		)
   accumulator.reset()
   self.assertEqual(accumulator.step,				0		)
   self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist(),				[0.0, 0.0],				tol=1E-2		)


 def 			UpperCamelCase_       (    self:		Optional[Any]		):




   '''simple docstring'''



   _snake_case							:		Any								=  None
   ops.enable_eager_execution_internal()
   _snake_case							:		Tuple								=  tf.config.list_physical_devices("""CPU"""		)
   if len(_A		) == 1:
     tf.config.set_logical_device_configuration(
         physical_devices[0],				[tf.config.LogicalDeviceConfiguration(), tf.config.LogicalDeviceConfiguration()]		)
   _snake_case							:		Union[str, Any]								=  tf.config.list_logical_devices(device_type="""CPU"""		)
   _snake_case							:		Dict								=  tf.distribute.MirroredStrategy(devices=devices[:2]		)

   with strategy.scope():
     _snake_case							:		Dict								=  GradientAccumulator()
     _snake_case							:		Any								=  tf.Variable([4.0, 3.0]		)
     _snake_case							:		Dict								=  create_optimizer(5E-5,				10,				5		)
     _snake_case							:		Optional[int]								=  tf.Variable([0.0, 0.0],				trainable=_A		)

   def accumulate_on_replica(a_:		Tuple		):
     accumulator([gradient]		)

   def apply_on_replica():
     optimizer.apply_gradients(list(zip(accumulator.gradients,				[variable]		)		)		)

   @tf.function
   def accumulate(a_:		Optional[Any],				a_:		Union[str, Any]		):
     with strategy.scope():
       _snake_case							:		Tuple								=  strategy.experimental_local_results(_A		)
       local_variables[0].assign(_A		)
       local_variables[1].assign(_A		)
       strategy.run(_A,				args=(gradient_placeholder,)		)

   @tf.function
   def apply_grad():
     with strategy.scope():
       strategy.run(_A		)

   def _check_local_values(a_:		Tuple,				a_:		List[Any]		):
     _snake_case							:		Optional[Any]								=  strategy.experimental_local_results(accumulator._gradients[0]		)
     self.assertListAlmostEqual(values[0].value(),				_A,				tol=1E-2		)
     self.assertListAlmostEqual(values[1].value(),				_A,				tol=1E-2		)

   accumulate([1.0, 2.0],				[-1.0, 1.0]		)
   accumulate([3.0, -1.0],				[-1.0, -1.0]		)
   accumulate([-2.0, 2.0],				[3.0, -2.0]		)
   self.assertEqual(accumulator.step,				3		)
   _check_local_values([2.0, 3.0],				[1.0, -2.0]		)
   apply_grad()
   self.assertListAlmostEqual(variable.value(),				[4.0, 3.0],				tol=1E-2		)
   accumulator.reset()
   self.assertEqual(accumulator.step,				0		)
   _check_local_values([0.0, 0.0],				[0.0, 0.0]		)








"""simple docstring"""


from __future__ import annotations

from math import gcd


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

  for _ in range(snake_case__   ):
    # These track the position within the cycle detection logic.
    _snake_case							:		Optional[int]								=  seed
    _snake_case							:		str								=  seed

    while True:
      # At each iteration, the tortoise moves one step and the hare moves two.
      _snake_case							:		Any								=  rand_fn(snake_case__		,       snake_case__		,       snake_case__   )
      _snake_case							:		Optional[Any]								=  rand_fn(snake_case__		,       snake_case__		,       snake_case__   )
      _snake_case							:		int								=  rand_fn(snake_case__		,       snake_case__		,       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``.
      _snake_case							:		str								=  gcd(hare - tortoise		,       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.
    _snake_case							:		Union[str, Any]								=  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}''')


