




'''simple docstring'''


import os
import re
import shutil
import sys
import tempfile
import unittest

import black


_snake_case : str  				=						os.path.abspath(os.path.dirname(os.path.dirname(os.path.dirname(__file__))))
sys.path.append(os.path.join(git_repo_path, 'utils'))

import check_copies  # noqa: E402


# This is the reference code that will be used in the tests.
# If DDPMSchedulerOutput is changed in scheduling_ddpm.py, this code needs to be manually updated.
_snake_case : List[str]  				=						'    \"""\n    Output class for the scheduler\'s step function output.\n\n    Args:\n        prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):\n            Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the\n            denoising loop.\n        pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):\n            The predicted denoised sample (x_{0}) based on the model output from the current timestep.\n            `pred_original_sample` can be used to preview progress or for guidance.\n    \"""\n\n    prev_sample: torch.FloatTensor\n    pred_original_sample: Optional[torch.FloatTensor] = None\n'

class      A       (						unittest.TestCase       ):







							def   __lowerCAmelCase     (    self			:    int   )     ->				List[Any]:


														"""simple docstring"""


														_a      	=							tempfile.mkdtemp()
														os.makedirs(os.path.join(self.diffusers_dir				,     '''schedulers/'''   )   )
														_a      	=							self.diffusers_dir
														shutil.copy(
														    os.path.join(lowerCAmelCase_				,     '''src/diffusers/schedulers/scheduling_ddpm.py'''   )				,     os.path.join(self.diffusers_dir				,     '''schedulers/scheduling_ddpm.py'''   )				,     )







							def   __lowerCAmelCase     (    self			:    Dict   )     ->				int:


														"""simple docstring"""


														_a      	=							'''src/diffusers'''
														shutil.rmtree(self.diffusers_dir   )







							def   __lowerCAmelCase     (    self			:    int				,     lowerCAmelCase_			:    str				,     lowerCAmelCase_			:    List[Any]				,     lowerCAmelCase_			:    Union[str, Any]				,     lowerCAmelCase_			:    str=None   )     ->				Union[str, Any]:


														"""simple docstring"""


														_a      	=							comment + F'\nclass {class_name}(nn.Module):\n' + class_code
														if overwrite_result is not None:
																					_a      	=							comment + F'\nclass {class_name}(nn.Module):\n' + overwrite_result
														_a      	=							black.Mode(target_versions={black.TargetVersion.PYaa}				,     line_length=1_19   )
														_a      	=							black.format_str(lowerCAmelCase_				,     mode=lowerCAmelCase_   )
														_a      	=							os.path.join(self.diffusers_dir				,     '''new_code.py'''   )
														with open(lowerCAmelCase_				,     '''w'''				,     newline='''\n'''   ) as f:
																					f.write(lowerCAmelCase_   )
														if overwrite_result is None:
																					self.assertTrue(len(check_copies.is_copy_consistent(lowerCAmelCase_   )   ) == 0   )
														else:
																					check_copies.is_copy_consistent(f.name				,     overwrite=lowerCAmelCase_   )
																					with open(lowerCAmelCase_				,     '''r'''   ) as f:
																												self.assertTrue(f.read()				,     lowerCAmelCase_   )







							def   __lowerCAmelCase     (    self			:    Optional[Any]   )     ->				Union[str, Any]:


														"""simple docstring"""


														_a      	=							check_copies.find_code_in_diffusers('''schedulers.scheduling_ddpm.DDPMSchedulerOutput'''   )
														self.assertEqual(lowerCAmelCase_				,     lowerCAmelCase_   )







							def   __lowerCAmelCase     (    self			:    Dict   )     ->				Union[str, Any]:


														"""simple docstring"""


														self.check_copy_consistency(
														    '''# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput'''				,     '''DDPMSchedulerOutput'''				,     REFERENCE_CODE + '''\n'''				,     )

														# With no empty line at the end
														self.check_copy_consistency(
														    '''# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput'''				,     '''DDPMSchedulerOutput'''				,     lowerCAmelCase_				,     )

														# Copy consistency with rename
														self.check_copy_consistency(
														    '''# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->Test'''				,     '''TestSchedulerOutput'''				,     re.sub('''DDPM'''				,     '''Test'''				,     lowerCAmelCase_   )				,     )

														# Copy consistency with a really long name
														_a      	=							'''TestClassWithAReallyLongNameBecauseSomePeopleLikeThatForSomeReason'''
														self.check_copy_consistency(
														    F'# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->{long_class_name}'				,     F'{long_class_name}SchedulerOutput'				,     re.sub('''Bert'''				,     lowerCAmelCase_				,     lowerCAmelCase_   )				,     )

														# Copy consistency with overwrite
														self.check_copy_consistency(
														    '''# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->Test'''				,     '''TestSchedulerOutput'''				,     lowerCAmelCase_				,     overwrite_result=re.sub('''DDPM'''				,     '''Test'''				,     lowerCAmelCase_   )				,     )






'''simple docstring'''

from __future__ import annotations

from math import gcd



def 	__lowerCamelCase	( lowerCAmelCase_		,     lowerCAmelCase_ = 2		,     lowerCAmelCase_ = 1		,     lowerCAmelCase_ = 3		,     )     -> int | None:
		# 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(lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    ) -> int:
				return (pow(lowerCAmelCase_		,     2    ) + step) % modulus

		for _ in range(lowerCAmelCase_    ):
				# These track the position within the cycle detection logic.
				_a	: Optional[int]								=				seed
				_a	: str								=				seed

				while True:
						# At each iteration, the tortoise moves one step and the hare moves two.
						_a	: str								=				rand_fn(lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    )
						_a	: Dict								=				rand_fn(lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    )
						_a	: Tuple								=				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``.
						_a	: Optional[Any]								=				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.
				_a	: Union[str, 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}""")




