
from __future__ import annotations

from math import gcd





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

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

  while True:
   # At each iteration, the tortoise moves one step and the hare moves two.
   lowerCamelCase		:	int							=      rand_fn(lowerCamelCase,	lowerCamelCase,	lowerCamelCase							)
   lowerCamelCase		:	List[str]							=      rand_fn(lowerCamelCase,	lowerCamelCase,	lowerCamelCase							)
   lowerCamelCase		:	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``.
   lowerCamelCase		:	Any							=      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.
  lowerCamelCase		:	Tuple							=      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					   =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					   =parser.parse_args()

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






import json
import os
import tempfile

import transformers

import datasets
from utils import generate_example_dataset, get_duration


_lowerCamelCase					   =5_0_0_0_0_0

_lowerCamelCase   ,  _lowerCamelCase					   =os.path.split(__file__)
_lowerCamelCase					   =os.path.join(RESULTS_BASEPATH, """results""", RESULTS_FILENAME.replace(""".py""", """.json"""))





@get_duration
def     _a					(						lowerCamelCase,	**lowerCamelCase							):
 lowerCamelCase		:	Optional[Any]							=      dataset.map(**lowerCamelCase							)





@get_duration
def     _a					(						lowerCamelCase,	**lowerCamelCase							):
 lowerCamelCase		:	Optional[Any]							=      dataset.filter(**lowerCamelCase							)





def     _a					(						):
 lowerCamelCase		:	Optional[Any]							=      {"""num examples""": SPEED_TEST_N_EXAMPLES}
 with tempfile.TemporaryDirectory() as tmp_dir:
  lowerCamelCase		:	Any							=      datasets.Features({"""text""": datasets.Value("""string"""							), """numbers""": datasets.Value("""float32"""							)}							)
  lowerCamelCase		:	Tuple							=      generate_example_dataset(
      os.path.join(lowerCamelCase,	"""dataset.arrow"""							),	lowerCamelCase,	num_examples=lowerCamelCase							)

  lowerCamelCase		:	Tuple							=      transformers.AutoTokenizer.from_pretrained("""bert-base-cased""",	use_fast=lowerCamelCase							)

  def tokenize(lowerCamelCase							):
   return tokenizer(examples["""text"""]							)

  lowerCamelCase		:	List[str]							=      map(lowerCamelCase							)

  lowerCamelCase		:	int							=      map(lowerCamelCase,	batched=lowerCamelCase							)

  lowerCamelCase		:	int							=      map(lowerCamelCase,	function=lambda lowerCamelCase							: None,	batched=lowerCamelCase							)

  with dataset.formatted_as(type="""numpy"""							):
   lowerCamelCase		:	Optional[int]							=      map(lowerCamelCase,	function=lambda lowerCamelCase							: None,	batched=lowerCamelCase							)

  with dataset.formatted_as(type="""pandas"""							):
   lowerCamelCase		:	List[str]							=      map(lowerCamelCase,	function=lambda lowerCamelCase							: None,	batched=lowerCamelCase							)

  with dataset.formatted_as(type="""torch""",	columns="""numbers"""							):
   lowerCamelCase		:	List[str]							=      map(lowerCamelCase,	function=lambda lowerCamelCase							: None,	batched=lowerCamelCase							)

  with dataset.formatted_as(type="""tensorflow""",	columns="""numbers"""							):
   lowerCamelCase		:	Optional[int]							=      map(lowerCamelCase,	function=lambda lowerCamelCase							: None,	batched=lowerCamelCase							)

  lowerCamelCase		:	int							=      map(lowerCamelCase,	function=lowerCamelCase,	batched=lowerCamelCase							)

  lowerCamelCase		:	Union[str, Any]							=      filter(lowerCamelCase							)

  # Activate later when tokenizer support batched inputs
  # with dataset.formatted_as(type='numpy'):
  #     times[func.__name__ + " fast-tokenizer batched numpy"] = func(dataset, function=tokenize, batched=True)

 with open(lowerCamelCase,	"""wb"""							) as f:
  f.write(json.dumps(lowerCamelCase							).encode("""utf-8"""							)							)


if __name__ == "__main__":  # useful to run the profiler
      benchmark_map_filter()




