"""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						:     Optional[int]  ,						snake_case__						:     List[Any]=2  ,						snake_case__						:     Any=3  ,						snake_case__						:     Union[str, Any]=64  ,						snake_case__						:     Any=None     ):
							lowerCAmelCase__        =   np.random.default_rng(snake_case__     )
							lowerCAmelCase__        =   length
							lowerCAmelCase__        =   rng.normal(size=(length,)     ).astype(np.floataa     )
							lowerCAmelCase__        =   a * self.x + b + rng.normal(scale=0.1  ,						size=(length,)     ).astype(np.floataa     )




					def __len__(	self						:     Optional[Any]     ):
							return self.length




					def __getitem__(	self						:     List[str]  ,						snake_case__						:     Optional[int]     ):
							return {"x": self.x[i], "y": self.y[i]}

class       a_      (     torch.nn.Module			):




					def __init__(	self						:     List[str]  ,						snake_case__						:     str=0  ,						snake_case__						:     Dict=0  ,						snake_case__						:     Any=False     ):
							super().__init__()
							lowerCAmelCase__        =   torch.nn.Parameter(torch.tensor([2, 3]     ).float()     )
							lowerCAmelCase__        =   torch.nn.Parameter(torch.tensor([2, 3]     ).float()     )
							lowerCAmelCase__        =   True




					def 						_SCREAMING_SNAKE_CASE						(	self						:     int  ,						snake_case__						:     Any=None     ):
							if self.first_batch:
									print(F"""Model dtype: {self.a.dtype}, {self.b.dtype}. Input dtype: {x.dtype}"""     )
									lowerCAmelCase__        =   False
							return x * self.a[0] + self.b[0]

class       a_      (     torch.nn.Module			):




					def __init__(	self						:     Any  ,						snake_case__						:     Union[str, Any]=0  ,						snake_case__						:     Union[str, Any]=0  ,						snake_case__						:     List[Any]=False     ):
							super().__init__()
							lowerCAmelCase__        =   torch.nn.Parameter(torch.tensor(snake_case__     ).float()     )
							lowerCAmelCase__        =   torch.nn.Parameter(torch.tensor(snake_case__     ).float()     )
							lowerCAmelCase__        =   True




					def 						_SCREAMING_SNAKE_CASE						(	self						:     Tuple  ,						snake_case__						:     Optional[Any]=None     ):
							if self.first_batch:
									print(F"""Model dtype: {self.a.dtype}, {self.b.dtype}. Input dtype: {x.dtype}"""     )
									lowerCAmelCase__        =   False
							return x * self.a + self.b







def 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__ = 16     ):





		"""simple docstring"""




		from datasets import load_dataset
		from transformers import AutoTokenizer

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

		lowerCAmelCase__        =   {v: i for i, v in enumerate(lowerCamelCase__     )}

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

		def collate_fn(lowerCamelCase__     ):
				# 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(lowerCamelCase__			,  padding="""max_length"""			,  max_length=128			,  return_tensors="""pt"""     )
				return tokenizer.pad(lowerCamelCase__			,  padding="""longest"""			,  return_tensors="""pt"""     )

		# Instantiate dataloaders.
		lowerCAmelCase__        =   DataLoader(tokenized_datasets["""train"""]			,  shuffle=lowerCamelCase__			,  collate_fn=lowerCamelCase__			,  batch_size=2     )
		lowerCAmelCase__        =   DataLoader(tokenized_datasets["""validation"""]			,  shuffle=lowerCamelCase__			,  collate_fn=lowerCamelCase__			,  batch_size=1     )

		return train_dataloader, eval_dataloader





"""simple docstring"""




from __future__ import annotations

from math import gcd







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

		for _ in range(lowerCamelCase__     ):
				# These track the position within the cycle detection logic.
				lowerCAmelCase__        =   seed
				lowerCAmelCase__        =   seed

				while True:
						# At each iteration, the tortoise moves one step and the hare moves two.
						lowerCAmelCase__        =   rand_fn(lowerCamelCase__			,  lowerCamelCase__			,  lowerCamelCase__     )
						lowerCAmelCase__        =   rand_fn(lowerCamelCase__			,  lowerCamelCase__			,  lowerCamelCase__     )
						lowerCAmelCase__        =   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__        =   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__        =   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    :							Union[str, Any]													=						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    :							List[str]													=						parser.parse_args()

			__lowerCAmelCase    :							Dict													=						pollard_rho(args.num, attempts=args.attempts)
			if divisor is None:
						print(F"{args.num} is probably prime")
			else:
						__lowerCAmelCase    :							List[str]													=						args.num // divisor
						print(F"{args.num} = {divisor} * {quotient}")




