






'''simple docstring'''





from __future__ import annotations

from math import gcd





def 				snake_case  (     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(A_				,  2					) + step) % modulus

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

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

			# 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``.
			__lowercase             =  gcd(hare - tortoise				,  A_					)

			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.
		__lowercase             =  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      :      str     						=						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      :      Dict     						=						parser.parse_args()

						__UpperCamelCase      :      List[Any]     						=						pollard_rho(args.num, attempts=args.attempts)
						if divisor is None:
												print(F'''{args.num} is probably prime''')
						else:
												__UpperCamelCase      :      Tuple     						=						args.num // divisor
												print(F'''{args.num} = {divisor} * {quotient}''')









import random
import unittest

import torch

from diffusers import IFInpaintingPipeline
from diffusers.utils import floats_tensor
from diffusers.utils.import_utils import is_xformers_available
from diffusers.utils.testing_utils import skip_mps, torch_device

from ..pipeline_params import (
    TEXT_GUIDED_IMAGE_INPAINTING_BATCH_PARAMS,
    TEXT_GUIDED_IMAGE_INPAINTING_PARAMS,
)
from ..test_pipelines_common import PipelineTesterMixin
from . import IFPipelineTesterMixin


@skip_mps
class        __UpperCamelCase    (     _lowerCAmelCase   ,			_lowerCAmelCase   ,			unittest.TestCase   ):
	__snake_case	:Any   =       IFInpaintingPipeline
	__snake_case	:str   =       TEXT_GUIDED_IMAGE_INPAINTING_PARAMS - {'width', 'height'}
	__snake_case	:Optional[int]   =       TEXT_GUIDED_IMAGE_INPAINTING_BATCH_PARAMS
	__snake_case	:str   =       PipelineTesterMixin.required_optional_params - {'latents'}







	def  _a   (  self      :							Union[str, Any]			)		-> Tuple:
		"""simple docstring"""







		return self._get_dummy_components()







	def  _a   (  self      :							Optional[int]       ,				_lowerCAmelCase      :							List[str]       ,				_lowerCAmelCase      :							Dict=0			)		-> Any:
		"""simple docstring"""







		if str(_lowerCAmelCase			).startswith("""mps"""			):
			__lowercase             =  torch.manual_seed(_lowerCAmelCase			)
		else:
			__lowercase             =  torch.Generator(device=_lowerCAmelCase			).manual_seed(_lowerCAmelCase			)

		__lowercase             =  floats_tensor((1, 3, 32, 32)       ,				rng=random.Random(_lowerCAmelCase			)			).to(_lowerCAmelCase			)
		__lowercase             =  floats_tensor((1, 3, 32, 32)       ,				rng=random.Random(_lowerCAmelCase			)			).to(_lowerCAmelCase			)

		__lowercase             =  {
		    """prompt""": """A painting of a squirrel eating a burger""",
		    """image""": image,
		    """mask_image""": mask_image,
		    """generator""": generator,
		    """num_inference_steps""": 2,
		    """output_type""": """numpy""",
		}

		return inputs







	@unittest.skipIf(
	    torch_device != """cuda""" or not is_xformers_available()       ,				reason="""XFormers attention is only available with CUDA and `xformers` installed"""       ,				)
	def  _a   (  self      :							Tuple			)		-> Dict:
		"""simple docstring"""







		self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1e-3			)







	def  _a   (  self      :							Union[str, Any]			)		-> Dict:
		"""simple docstring"""







		self._test_save_load_optional_components()







	@unittest.skipIf(torch_device != """cuda"""       ,				reason="""float16 requires CUDA"""			)
	def  _a   (  self      :							List[str]			)		-> Tuple:
		"""simple docstring"""







		super().test_save_load_floataa(expected_max_diff=1e-1			)







	def  _a   (  self      :							Tuple			)		-> Optional[Any]:
		"""simple docstring"""







		self._test_attention_slicing_forward_pass(expected_max_diff=1e-2			)







	def  _a   (  self      :							str			)		-> Optional[int]:
		"""simple docstring"""







		self._test_save_load_local()







	def  _a   (  self      :							List[str]			)		-> List[Any]:
		"""simple docstring"""







		self._test_inference_batch_single_identical(
		    expected_max_diff=1e-2       ,				)

