





import random
import unittest

import numpy as np

import transformers
from transformers import is_flax_available, is_torch_available
from transformers.testing_utils import is_pt_flax_cross_test, require_flax


if is_flax_available():
   import os

   import jax.numpy as jnp
   from jax import jit

   from transformers import AutoTokenizer, FlaxAutoModelForCausalLM
   from transformers.modeling_flax_pytorch_utils import load_flax_weights_in_pytorch_model

   UpperCAmelCase_           =	"0.12"  # assumed parallelism: 8


if is_torch_available():
   import torch
def      A__       (    SCREAMING_SNAKE_CASE_   :      int				,	SCREAMING_SNAKE_CASE_   :      Optional[int]				,	SCREAMING_SNAKE_CASE_   :      Tuple=None						)  ->  Dict:






   """simple docstring"""







   if rng is None:
      _UpperCAmelCase           =   random.Random()

   _UpperCAmelCase           =   1
   for dim in shape:
      total_dims *= dim

   _UpperCAmelCase           =   []
   for _ in range(SCREAMING_SNAKE_CASE_						):
      values.append(rng.randint(0				,	vocab_size - 1						)						)

   _UpperCAmelCase           =   np.array(SCREAMING_SNAKE_CASE_				,	dtype=jnp.intaa						).reshape(SCREAMING_SNAKE_CASE_						)

   return output
def      A__       (    SCREAMING_SNAKE_CASE_   :      Any				,	SCREAMING_SNAKE_CASE_   :      Optional[int]=None						)  ->  int:






   """simple docstring"""







   _UpperCAmelCase           =   ids_tensor(SCREAMING_SNAKE_CASE_				,	vocab_size=2				,	rng=SCREAMING_SNAKE_CASE_						)
   # make sure that at least one token is attended to for each batch
   _UpperCAmelCase           =   1
   return attn_mask




@require_flax
class 			__UpperCamelCase    :
     __A	:  Optional[Any]							  =   None
     __A	:  Tuple							  =   ()





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase           =   self.model_tester.prepare_config_and_inputs_for_common()

        # cut to half length & take max batch_size 3
        _UpperCAmelCase           =   2
        _UpperCAmelCase           =   inputs['''input_ids'''].shape[-1] // 2
        _UpperCAmelCase           =   inputs['''input_ids'''][:max_batch_size, :sequence_length]

        _UpperCAmelCase           =   jnp.ones_like(_UpperCamelCase					)
        _UpperCAmelCase           =   attention_mask[:max_batch_size, :sequence_length]

        # generate max 5 tokens
        _UpperCAmelCase           =   input_ids.shape[-1] + 5
        if config.eos_token_id is not None and config.pad_token_id is None:
           # hack to allow generate for models such as GPT2 as is done in `generate()`
           _UpperCAmelCase           =   config.eos_token_id
        return config, input_ids, attention_mask, max_length





     @is_pt_flax_cross_test
     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()
        _UpperCAmelCase           =   False
        _UpperCAmelCase           =   max_length
        _UpperCAmelCase           =   0

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model_class.__name__[4:]  # Skip the "Flax" at the beginning
           _UpperCAmelCase           =   getattr(_UpperCamelCase				,							_UpperCamelCase					)
           _UpperCAmelCase           =   pt_model_class(_UpperCamelCase					).eval()
           _UpperCAmelCase           =   load_flax_weights_in_pytorch_model(_UpperCamelCase				,							flax_model.params					)

           _UpperCAmelCase           =   flax_model.generate(_UpperCamelCase					).sequences
           _UpperCAmelCase           =   pt_model.generate(torch.tensor(_UpperCamelCase				,							dtype=torch.long					)					)

           if flax_generation_outputs.shape[-1] > pt_generation_outputs.shape[-1]:
              _UpperCAmelCase           =   flax_generation_outputs[:, : pt_generation_outputs.shape[-1]]

           self.assertListEqual(pt_generation_outputs.numpy().tolist()				,							flax_generation_outputs.tolist()					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()
        _UpperCAmelCase           =   False
        _UpperCAmelCase           =   max_length

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[-1]				,							_UpperCamelCase					)

           _UpperCAmelCase           =   jit(model.generate					)
           _UpperCAmelCase           =   jit_generate(_UpperCamelCase					).sequences

           self.assertListEqual(generation_outputs.tolist()				,							jit_generation_outputs.tolist()					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()
        _UpperCAmelCase           =   True
        _UpperCAmelCase           =   max_length

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[-1]				,							_UpperCamelCase					)

           _UpperCAmelCase           =   jit(model.generate					)
           _UpperCAmelCase           =   jit_generate(_UpperCamelCase					).sequences

           self.assertListEqual(generation_outputs.tolist()				,							jit_generation_outputs.tolist()					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()
        _UpperCAmelCase           =   False
        _UpperCAmelCase           =   max_length
        _UpperCAmelCase           =   2

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[-1]				,							_UpperCamelCase					)

           _UpperCAmelCase           =   jit(model.generate					)
           _UpperCAmelCase           =   jit_generate(_UpperCamelCase					).sequences

           self.assertListEqual(generation_outputs.tolist()				,							jit_generation_outputs.tolist()					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()
        _UpperCAmelCase           =   False
        _UpperCAmelCase           =   max_length
        _UpperCAmelCase           =   2
        _UpperCAmelCase           =   2

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[0]				,							input_ids.shape[0] * config.num_return_sequences					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()
        _UpperCAmelCase           =   True
        _UpperCAmelCase           =   max_length
        _UpperCAmelCase           =   0.8
        _UpperCAmelCase           =   10
        _UpperCAmelCase           =   0.3
        _UpperCAmelCase           =   1
        _UpperCAmelCase           =   8
        _UpperCAmelCase           =   9

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[-1]				,							_UpperCamelCase					)

           _UpperCAmelCase           =   jit(model.generate					)
           _UpperCAmelCase           =   jit_generate(_UpperCamelCase					).sequences

           self.assertListEqual(generation_outputs.tolist()				,							jit_generation_outputs.tolist()					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()
        _UpperCAmelCase           =   max_length
        _UpperCAmelCase           =   1
        _UpperCAmelCase           =   8
        _UpperCAmelCase           =   9

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[-1]				,							_UpperCamelCase					)

           _UpperCAmelCase           =   jit(model.generate					)
           _UpperCAmelCase           =   jit_generate(_UpperCamelCase					).sequences

           self.assertListEqual(generation_outputs.tolist()				,							jit_generation_outputs.tolist()					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()
        _UpperCAmelCase           =   max_length
        _UpperCAmelCase           =   2
        _UpperCAmelCase           =   1
        _UpperCAmelCase           =   8
        _UpperCAmelCase           =   9

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[-1]				,							_UpperCamelCase					)

           _UpperCAmelCase           =   jit(model.generate					)
           _UpperCAmelCase           =   jit_generate(_UpperCamelCase					).sequences

           self.assertListEqual(generation_outputs.tolist()				,							jit_generation_outputs.tolist()					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()

        # pad attention mask on the left
        _UpperCAmelCase           =   attention_mask.at[(0, 0)].set(0					)

        _UpperCAmelCase           =   False
        _UpperCAmelCase           =   max_length

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase				,							attention_mask=_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[-1]				,							_UpperCamelCase					)

           _UpperCAmelCase           =   jit(model.generate					)
           _UpperCAmelCase           =   jit_generate(_UpperCamelCase				,							attention_mask=_UpperCamelCase					).sequences

           self.assertListEqual(generation_outputs.tolist()				,							jit_generation_outputs.tolist()					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()

        # pad attention mask on the left
        _UpperCAmelCase           =   attention_mask.at[(0, 0)].set(0					)

        _UpperCAmelCase           =   True
        _UpperCAmelCase           =   max_length

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase				,							attention_mask=_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[-1]				,							_UpperCamelCase					)

           _UpperCAmelCase           =   jit(model.generate					)
           _UpperCAmelCase           =   jit_generate(_UpperCamelCase				,							attention_mask=_UpperCamelCase					).sequences

           self.assertListEqual(generation_outputs.tolist()				,							jit_generation_outputs.tolist()					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase       ,      _UpperCAmelCase           =   self._get_input_ids_and_config()

        # pad attention mask on the left
        _UpperCAmelCase           =   attention_mask.at[(0, 0)].set(0					)

        _UpperCAmelCase           =   2
        _UpperCAmelCase           =   max_length

        for model_class in self.all_generative_model_classes:
           _UpperCAmelCase           =   model_class(_UpperCamelCase					)

           _UpperCAmelCase           =   model.generate(_UpperCamelCase				,							attention_mask=_UpperCamelCase					).sequences
           self.assertEqual(generation_outputs.shape[-1]				,							_UpperCamelCase					)

           _UpperCAmelCase           =   jit(model.generate					)
           _UpperCAmelCase           =   jit_generate(_UpperCamelCase				,							attention_mask=_UpperCamelCase					).sequences

           self.assertListEqual(generation_outputs.tolist()				,							jit_generation_outputs.tolist()					)




@require_flax
class 			__UpperCamelCase    (							unittest.TestCase    ):





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase           =   AutoTokenizer.from_pretrained('''hf-internal-testing/tiny-bert'''					)
        _UpperCAmelCase           =   FlaxAutoModelForCausalLM.from_pretrained('''hf-internal-testing/tiny-bert-flax-only'''					)

        _UpperCAmelCase           =   '''Hello world'''
        _UpperCAmelCase           =   tokenizer(_UpperCamelCase				,							return_tensors='''np'''					).input_ids

        # typos are quickly detected (the correct argument is `do_sample`)
        with self.assertRaisesRegex(_UpperCamelCase				,							'''do_samples'''					):
           model.generate(_UpperCamelCase				,							do_samples=_UpperCamelCase					)

        # arbitrary arguments that will not be used anywhere are also not accepted
        with self.assertRaisesRegex(_UpperCamelCase				,							'''foo'''					):
           _UpperCAmelCase           =   {'''foo''': '''bar'''}
           model.generate(_UpperCamelCase				,							**_UpperCamelCase					)


from __future__ import annotations

from math import gcd


def 							__lowerCAmelCase     (							_UpperCamelCase		:	int		,				_UpperCamelCase		:	int = 2		,				_UpperCamelCase		:	int = 1		,				_UpperCamelCase		:	int = 3		,				)		->				int | None:
 '''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(_UpperCamelCase		:	int		,				_UpperCamelCase		:	int		,				_UpperCamelCase		:	int						) -> int:
  return (pow(_UpperCamelCase		,				2						) + step) % modulus

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

  while True:
   # At each iteration, the tortoise moves one step and the hare moves two.
   SCREAMING_SNAKE_CASE		    =      rand_fn(_UpperCamelCase		,				_UpperCamelCase		,				_UpperCamelCase						)
   SCREAMING_SNAKE_CASE		    =      rand_fn(_UpperCamelCase		,				_UpperCamelCase		,				_UpperCamelCase						)
   SCREAMING_SNAKE_CASE		    =      rand_fn(_UpperCamelCase		,				_UpperCamelCase		,				_UpperCamelCase						)

   # 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		    =      gcd(hare - tortoise		,				_UpperCamelCase						)

   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		    =      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_     :    int     		=   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_     :    Tuple     		=   parser.parse_args()

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

