



"""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 gc
import unittest

from diffusers import FlaxDPMSolverMultistepScheduler, FlaxStableDiffusionPipeline
from diffusers.utils import is_flax_available, slow
from diffusers.utils.testing_utils import require_flax


if is_flax_available():
   import jax
   import jax.numpy as jnp
   from flax.jax_utils import replicate
   from flax.training.common_utils import shard
@slow
@require_flax
class 					a	(  unittest.TestCase       ):



  def 	lowerCamelCase__       (						self :					Dict		)     ->					str:


     '''simple docstring'''




     super().tearDown()
     gc.collect()



  def 	lowerCamelCase__       (						self :					Optional[Any]		)     ->					int:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_			,		SCREAMING_SNAKE_CASE_: Dict     			=FlaxStableDiffusionPipeline.from_pretrained(
         """stabilityai/stable-diffusion-2"""       ,		revision="""bf16"""       ,		dtype=jnp.bfloataa       ,		)

     SCREAMING_SNAKE_CASE_: Union[str, Any]     			="""A painting of a squirrel eating a burger"""
     SCREAMING_SNAKE_CASE_: Any     			=jax.device_count()
     SCREAMING_SNAKE_CASE_: Dict     			=num_samples * [prompt]
     SCREAMING_SNAKE_CASE_: List[Any]     			=sd_pipe.prepare_inputs(lowerCAmelCase		)

     SCREAMING_SNAKE_CASE_: Union[str, Any]     			=replicate(lowerCAmelCase		)
     SCREAMING_SNAKE_CASE_: Optional[int]     			=shard(lowerCAmelCase		)

     SCREAMING_SNAKE_CASE_: Dict     			=jax.random.PRNGKey(0		)
     SCREAMING_SNAKE_CASE_: Union[str, Any]     			=jax.random.split(lowerCAmelCase       ,		jax.device_count()		)

     SCREAMING_SNAKE_CASE_: Tuple     			=sd_pipe(lowerCAmelCase       ,		lowerCAmelCase       ,		lowerCAmelCase       ,		num_inference_steps=25       ,		jit=lowerCAmelCase		)[0]
     assert images.shape == (jax.device_count(), 1, 768, 768, 3)

     SCREAMING_SNAKE_CASE_: Dict     			=images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:]		)
     SCREAMING_SNAKE_CASE_: Dict     			=images[0, 253:256, 253:256, -1]

     SCREAMING_SNAKE_CASE_: Optional[int]     			=jnp.asarray(jax.device_get(image_slice.flatten()		)		)
     SCREAMING_SNAKE_CASE_: Optional[int]     			=jnp.array([0.4_2_3_8, 0.4_4_1_4, 0.4_3_9_5, 0.4_4_5_3, 0.4_6_2_9, 0.4_5_9_0, 0.4_5_3_1, 0.4_5_5_0_8, 0.4_5_1_2]		)
     print(f'''output_slice: {output_slice}'''		)
     assert jnp.abs(output_slice - expected_slice		).max() < 1E-2





  def 	lowerCamelCase__       (						self :					List[str]		)     ->					Dict:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: int     			="""stabilityai/stable-diffusion-2"""
     SCREAMING_SNAKE_CASE_			,		SCREAMING_SNAKE_CASE_: Optional[int]     			=FlaxDPMSolverMultistepScheduler.from_pretrained(lowerCAmelCase       ,		subfolder="""scheduler"""		)
     SCREAMING_SNAKE_CASE_			,		SCREAMING_SNAKE_CASE_: Optional[int]     			=FlaxStableDiffusionPipeline.from_pretrained(
         lowerCAmelCase       ,		scheduler=lowerCAmelCase       ,		revision="""bf16"""       ,		dtype=jnp.bfloataa       ,		)
     SCREAMING_SNAKE_CASE_: Optional[int]     			=scheduler_params

     SCREAMING_SNAKE_CASE_: Tuple     			="""A painting of a squirrel eating a burger"""
     SCREAMING_SNAKE_CASE_: Union[str, Any]     			=jax.device_count()
     SCREAMING_SNAKE_CASE_: Optional[Any]     			=num_samples * [prompt]
     SCREAMING_SNAKE_CASE_: List[Any]     			=sd_pipe.prepare_inputs(lowerCAmelCase		)

     SCREAMING_SNAKE_CASE_: Tuple     			=replicate(lowerCAmelCase		)
     SCREAMING_SNAKE_CASE_: Optional[int]     			=shard(lowerCAmelCase		)

     SCREAMING_SNAKE_CASE_: Any     			=jax.random.PRNGKey(0		)
     SCREAMING_SNAKE_CASE_: Any     			=jax.random.split(lowerCAmelCase       ,		jax.device_count()		)

     SCREAMING_SNAKE_CASE_: Tuple     			=sd_pipe(lowerCAmelCase       ,		lowerCAmelCase       ,		lowerCAmelCase       ,		num_inference_steps=25       ,		jit=lowerCAmelCase		)[0]
     assert images.shape == (jax.device_count(), 1, 768, 768, 3)

     SCREAMING_SNAKE_CASE_: str     			=images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:]		)
     SCREAMING_SNAKE_CASE_: Any     			=images[0, 253:256, 253:256, -1]

     SCREAMING_SNAKE_CASE_: Optional[Any]     			=jnp.asarray(jax.device_get(image_slice.flatten()		)		)
     SCREAMING_SNAKE_CASE_: Optional[int]     			=jnp.array([0.4_3_3_6, 0.4_2_9_6_9, 0.4_4_5_3, 0.4_1_9_9, 0.4_2_9_7, 0.4_5_3_1, 0.4_4_3_4, 0.4_4_3_4, 0.4_2_9_7]		)
     print(f'''output_slice: {output_slice}'''		)
     assert jnp.abs(output_slice - expected_slice		).max() < 1E-2



