



"""simple docstring"""
from __future__ import annotations

from math import gcd





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

   for _ in range(lowercase ):
      # These track the position within the cycle detection logic.
      SCREAMING_SNAKE_CASE_: Any     			=seed
      SCREAMING_SNAKE_CASE_: Dict     			=seed

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

         # 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_: Optional[Any]     			=gcd(hare - tortoise							,			lowercase )

         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_: Dict     			=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

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

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








"""simple docstring"""
import numpy as np
import torch
from torch.utils.data import DataLoader

from accelerate.utils.dataclasses import DistributedType
class 					a	:



  def __init__(						self :					Union[str, Any]       ,		lowerCAmelCase :					List[str]=2       ,		lowerCAmelCase :					int=3       ,		lowerCAmelCase :					Optional[Any]=64       ,		lowerCAmelCase :					Union[str, Any]=None		)     ->					Optional[Any]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: Union[str, Any]     			=np.random.default_rng(lowerCAmelCase		)
     SCREAMING_SNAKE_CASE_: Optional[int]     			=length
     SCREAMING_SNAKE_CASE_: Union[str, Any]     			=rng.normal(size=(length,)		).astype(np.floataa		)
     SCREAMING_SNAKE_CASE_: Tuple     			=a * self.x + b + rng.normal(scale=0.1       ,		size=(length,)		).astype(np.floataa		)



  def __len__(						self :					List[Any]		)     ->					str:


     '''simple docstring'''




     return self.length





  def __getitem__(						self :					Union[str, Any]       ,		lowerCAmelCase :					Any		)     ->					List[str]:


     '''simple docstring'''




     return {"x": self.x[i], "y": self.y[i]}







class 					a	(  torch.nn.Module       ):



  def __init__(						self :					Optional[int]       ,		lowerCAmelCase :					str=0       ,		lowerCAmelCase :					List[Any]=0       ,		lowerCAmelCase :					Optional[int]=False		)     ->					Tuple:


     '''simple docstring'''




     super().__init__()
     SCREAMING_SNAKE_CASE_: int     			=torch.nn.Parameter(torch.tensor([2, 3]		).float()		)
     SCREAMING_SNAKE_CASE_: int     			=torch.nn.Parameter(torch.tensor([2, 3]		).float()		)
     SCREAMING_SNAKE_CASE_: Dict     			=True





  def 	lowerCamelCase__       (						self :					str       ,		lowerCAmelCase :					Tuple=None		)     ->					int:


     '''simple docstring'''




     if self.first_batch:
        print(f'''Model dtype: {self.a.dtype}, {self.b.dtype}. Input dtype: {x.dtype}'''		)
        SCREAMING_SNAKE_CASE_: Union[str, Any]     			=False
     return x * self.a[0] + self.b[0]







class 					a	(  torch.nn.Module       ):



  def __init__(						self :					Union[str, Any]       ,		lowerCAmelCase :					Any=0       ,		lowerCAmelCase :					List[Any]=0       ,		lowerCAmelCase :					List[Any]=False		)     ->					str:


     '''simple docstring'''




     super().__init__()
     SCREAMING_SNAKE_CASE_: List[str]     			=torch.nn.Parameter(torch.tensor(lowerCAmelCase		).float()		)
     SCREAMING_SNAKE_CASE_: Optional[int]     			=torch.nn.Parameter(torch.tensor(lowerCAmelCase		).float()		)
     SCREAMING_SNAKE_CASE_: List[Any]     			=True





  def 	lowerCamelCase__       (						self :					List[str]       ,		lowerCAmelCase :					int=None		)     ->					Any:


     '''simple docstring'''




     if self.first_batch:
        print(f'''Model dtype: {self.a.dtype}, {self.b.dtype}. Input dtype: {x.dtype}'''		)
        SCREAMING_SNAKE_CASE_: Optional[int]     			=False
     return x * self.a + self.b







def      __magic_name__				(							lowercase							,			lowercase = 16 ):
   from datasets import load_dataset
   from transformers import AutoTokenizer

   SCREAMING_SNAKE_CASE_: Optional[Any]     			=AutoTokenizer.from_pretrained("""bert-base-cased""" )
   SCREAMING_SNAKE_CASE_: Optional[int]     			={"""train""": """tests/test_samples/MRPC/train.csv""", """validation""": """tests/test_samples/MRPC/dev.csv"""}
   SCREAMING_SNAKE_CASE_: Any     			=load_dataset("""csv"""							,			data_files=lowercase )
   SCREAMING_SNAKE_CASE_: Any     			=datasets["""train"""].unique("""label""" )

   SCREAMING_SNAKE_CASE_: List[Any]     			={v: i for i, v in enumerate(lowercase )}

   def tokenize_function(lowercase ):
      # max_length=None => use the model max length (it's actually the default)
      SCREAMING_SNAKE_CASE_: Dict     			=tokenizer(
          examples["""sentence1"""]							,			examples["""sentence2"""]							,			truncation=lowercase							,			max_length=lowercase							,			padding="""max_length""" )
      if "label" in examples:
         SCREAMING_SNAKE_CASE_: Optional[int]     			=[label_to_id[l] for l in examples["""label"""]]
      return outputs

   # Apply the method we just defined to all the examples in all the splits of the dataset
   SCREAMING_SNAKE_CASE_: List[Any]     			=datasets.map(
       lowercase							,			batched=lowercase							,			remove_columns=["""sentence1""", """sentence2""", """label"""]							,			)

   def collate_fn(lowercase ):
      # On TPU it's best to pad everything to the same length or training will be very slow.
      if accelerator.distributed_type == DistributedType.TPU:
         return tokenizer.pad(lowercase							,			padding="""max_length"""							,			max_length=128							,			return_tensors="""pt""" )
      return tokenizer.pad(lowercase							,			padding="""longest"""							,			return_tensors="""pt""" )

   # Instantiate dataloaders.
   SCREAMING_SNAKE_CASE_: Optional[int]     			=DataLoader(tokenized_datasets["""train"""]							,			shuffle=lowercase							,			collate_fn=lowercase							,			batch_size=2 )
   SCREAMING_SNAKE_CASE_: Dict     			=DataLoader(tokenized_datasets["""validation"""]							,			shuffle=lowercase							,			collate_fn=lowercase							,			batch_size=1 )

   return train_dataloader, eval_dataloader



