






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[Any]          =						seed
          __snake_case			:Tuple          =						seed

          while True:
               # At each iteration, the tortoise moves one step and the hare moves two.
               __snake_case			:str          =						rand_fn(snake_case__	,snake_case__	,snake_case__  )
               __snake_case			:Optional[Any]          =						rand_fn(snake_case__	,snake_case__	,snake_case__  )
               __snake_case			:Tuple          =						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			:Dict          =						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			: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

     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 numpy as np
import torch
from torch.utils.data import DataLoader

from accelerate.utils.dataclasses import DistributedType




class 			snake_case__   :

       '''simple docstring'''



       def __init__(							self			,						a__=2			,						a__=3			,						a__=64			,						a__=None    ) ->      int:






            '''simple docstring'''





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



       def __len__(							self    ) ->      str:






            '''simple docstring'''





            return self.length



       def __getitem__(							self			,						a__    ) ->      int:






            '''simple docstring'''





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




class 			snake_case__   (							torch.nn.Module):

       '''simple docstring'''



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






            '''simple docstring'''





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



       def 					__lowercase						(							self			,						a__=None    ) ->      Optional[Any]:






            '''simple docstring'''





            if self.first_batch:
                 print(F'''Model dtype: {self.a.dtype}, {self.b.dtype}. Input dtype: {x.dtype}'''    )
                 __snake_case			:Tuple          =						False
            return x * self.a[0] + self.b[0]




class 			snake_case__   (							torch.nn.Module):

       '''simple docstring'''



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






            '''simple docstring'''





            super().__init__()
            __snake_case			:Optional[int]          =						torch.nn.Parameter(torch.tensor(a__    ).float()    )
            __snake_case			:List[str]          =						torch.nn.Parameter(torch.tensor(a__    ).float()    )
            __snake_case			:str          =						True



       def 					__lowercase						(							self			,						a__=None    ) ->      str:






            '''simple docstring'''





            if self.first_batch:
                 print(F'''Model dtype: {self.a.dtype}, {self.b.dtype}. Input dtype: {x.dtype}'''    )
                 __snake_case			:List[Any]          =						False
            return x * self.a + self.b






def   UpperCamelCase  (       snake_case__     :   Optional[int]	,snake_case__     :   int = 16  ):




     '''simple docstring'''






     from datasets import load_dataset
     from transformers import AutoTokenizer

     __snake_case			:Union[str, Any]          =						AutoTokenizer.from_pretrained("""bert-base-cased"""  )
     __snake_case			:Dict          =						{"""train""": """tests/test_samples/MRPC/train.csv""", """validation""": """tests/test_samples/MRPC/dev.csv"""}
     __snake_case			:Any          =						load_dataset("""csv"""	,data_files=snake_case__  )
     __snake_case			:Dict          =						datasets["""train"""].unique("""label"""  )

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

     def tokenize_function(snake_case__     :   List[Any]  ):
          # max_length=None => use the model max length (it's actually the default)
          __snake_case			:Optional[Any]          =						tokenizer(
              examples["""sentence1"""]	,examples["""sentence2"""]	,truncation=snake_case__	,max_length=snake_case__	,padding="""max_length"""  )
          if "label" in examples:
               __snake_case			:Dict          =						[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
     __snake_case			:List[str]          =						datasets.map(
         snake_case__	,batched=snake_case__	,remove_columns=["""sentence1""", """sentence2""", """label"""]	,)

     def collate_fn(snake_case__     :   Optional[int]  ):
          # 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(snake_case__	,padding="""max_length"""	,max_length=128	,return_tensors="""pt"""  )
          return tokenizer.pad(snake_case__	,padding="""longest"""	,return_tensors="""pt"""  )

     # Instantiate dataloaders.
     __snake_case			:List[Any]          =						DataLoader(tokenized_datasets["""train"""]	,shuffle=snake_case__	,collate_fn=snake_case__	,batch_size=2  )
     __snake_case			:str          =						DataLoader(tokenized_datasets["""validation"""]	,shuffle=snake_case__	,collate_fn=snake_case__	,batch_size=1  )

     return train_dataloader, eval_dataloader


