

"""simple docstring"""


from __future__ import annotations

from math import gcd




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase = 2  ,					__lowerCAmelCase = 1  ,					__lowerCAmelCase = 3  ,					)       ->				Any:
      # 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(lowercase__  ,					2							) + step) % modulus

      for _ in range(lowercase__							):
            # These track the position within the cycle detection logic.
            SCREAMING_SNAKE_CASE__   :      List[str]      		=	seed
            SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	seed

            while True:
                  # At each iteration, the tortoise moves one step and the hare moves two.
                  SCREAMING_SNAKE_CASE__   :      List[str]      		=	rand_fn(lowercase__  ,					lowercase__  ,					lowercase__							)
                  SCREAMING_SNAKE_CASE__   :      str      		=	rand_fn(lowercase__  ,					lowercase__  ,					lowercase__							)
                  SCREAMING_SNAKE_CASE__   :      List[str]      		=	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__   :      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__   :      str      		=	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					: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",
  )
  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					:Tuple    =       args.num // divisor
    print(f'{args.num} = {divisor} * {quotient}')







"""simple docstring"""


import torch

from diffusers import DDPMScheduler

from .test_schedulers import SchedulerCommonTest

class      __a							(UpperCamelCase_):






     '''simple docstring'''
     _SCREAMING_SNAKE_CASE						:Tuple       = (DDPMScheduler,)

     def 					_a			(						self	,    **_a  )  ->      List[str]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      int      		=	{
               """num_train_timesteps""": 1_000,
               """beta_start""": 0.0_001,
               """beta_end""": 0.02,
               """beta_schedule""": """linear""",
               """variance_type""": """fixed_small""",
               """clip_sample""": True,
           }

           config.update(**_a  )
           return config

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for timesteps in [1, 5, 100, 1_000]:
                 self.check_over_configs(num_train_timesteps=_a  )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for beta_start, beta_end in zip([0.0_001, 0.001, 0.01, 0.1]	,    [0.002, 0.02, 0.2, 2]  ):
                 self.check_over_configs(beta_start=_a	,    beta_end=_a  )

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


           """simple docstring"""


           for schedule in ["linear", "squaredcos_cap_v2"]:
                 self.check_over_configs(beta_schedule=_a  )

     def 					_a			(						self  )  ->      Any:


           """simple docstring"""


           for variance in ["fixed_small", "fixed_large", "other"]:
                 self.check_over_configs(variance_type=_a  )

     def 					_a			(						self  )  ->      Optional[int]:


           """simple docstring"""


           for clip_sample in [True, False]:
                 self.check_over_configs(clip_sample=_a  )

     def 					_a			(						self  )  ->      int:


           """simple docstring"""


           self.check_over_configs(thresholding=_a  )
           for threshold in [0.5, 1.0, 2.0]:
                 for prediction_type in ["epsilon", "sample", "v_prediction"]:
                       self.check_over_configs(
                           thresholding=_a	,    prediction_type=_a	,    sample_max_value=_a	,    )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for prediction_type in ["epsilon", "sample", "v_prediction"]:
                 self.check_over_configs(prediction_type=_a  )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           for t in [0, 500, 999]:
                 self.check_over_forward(time_step=_a  )

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      int      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      Dict      		=	scheduler_class(**_a  )

           assert torch.sum(torch.abs(scheduler._get_variance(0  ) - 0.0  )  ) < 1E-5
           assert torch.sum(torch.abs(scheduler._get_variance(487  ) - 0.00_979  )  ) < 1E-5
           assert torch.sum(torch.abs(scheduler._get_variance(999  ) - 0.02  )  ) < 1E-5

     def 					_a			(						self  )  ->      List[Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      int      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Any      		=	len(_a  )

           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.dummy_model()
           SCREAMING_SNAKE_CASE__   :      str      		=	self.dummy_sample_deter
           SCREAMING_SNAKE_CASE__   :      str      		=	torch.manual_seed(0  )

           for t in reversed(range(_a  )  ):
                 # 1. predict noise residual
                 SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	model(_a	,    _a  )

                 # 2. predict previous mean of sample x_t-1
                 SCREAMING_SNAKE_CASE__   :      int      		=	scheduler.step(_a	,    _a	,    _a	,    generator=_a  ).prev_sample

                 # if t > 0:
                 #     noise = self.dummy_sample_deter
                 #     variance = scheduler.get_variance(t) ** (0.5) * noise
                 #
                 # sample = pred_prev_sample + variance
                 SCREAMING_SNAKE_CASE__   :      str      		=	pred_prev_sample

           SCREAMING_SNAKE_CASE__   :      str      		=	torch.sum(torch.abs(_a  )  )
           SCREAMING_SNAKE_CASE__   :      Any      		=	torch.mean(torch.abs(_a  )  )

           assert abs(result_sum.item() - 258.9_606  ) < 1E-2
           assert abs(result_mean.item() - 0.3_372  ) < 1E-3

     def 					_a			(						self  )  ->      Optional[Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.get_scheduler_config(prediction_type="""v_prediction"""  )
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Dict      		=	len(_a  )

           SCREAMING_SNAKE_CASE__   :      List[str]      		=	self.dummy_model()
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	self.dummy_sample_deter
           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	torch.manual_seed(0  )

           for t in reversed(range(_a  )  ):
                 # 1. predict noise residual
                 SCREAMING_SNAKE_CASE__   :      int      		=	model(_a	,    _a  )

                 # 2. predict previous mean of sample x_t-1
                 SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler.step(_a	,    _a	,    _a	,    generator=_a  ).prev_sample

                 # if t > 0:
                 #     noise = self.dummy_sample_deter
                 #     variance = scheduler.get_variance(t) ** (0.5) * noise
                 #
                 # sample = pred_prev_sample + variance
                 SCREAMING_SNAKE_CASE__   :      Tuple      		=	pred_prev_sample

           SCREAMING_SNAKE_CASE__   :      Any      		=	torch.sum(torch.abs(_a  )  )
           SCREAMING_SNAKE_CASE__   :      int      		=	torch.mean(torch.abs(_a  )  )

           assert abs(result_sum.item() - 202.0_296  ) < 1E-2
           assert abs(result_mean.item() - 0.2_631  ) < 1E-3

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


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      Dict      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	[100, 87, 50, 1, 0]

           scheduler.set_timesteps(timesteps=_a  )

           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	scheduler.timesteps

           for i, timestep in enumerate(_a  ):
                 if i == len(_a  ) - 1:
                       SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	-1
                 else:
                       SCREAMING_SNAKE_CASE__   :      Tuple      		=	timesteps[i + 1]

                 SCREAMING_SNAKE_CASE__   :      int      		=	scheduler.previous_timestep(_a  )
                 SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	prev_t.item()

                 self.assertEqual(_a	,    _a  )

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


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      int      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[100, 87, 50, 51, 0]

           with self.assertRaises(_a	,    msg="""`custom_timesteps` must be in descending order."""  ):
                 scheduler.set_timesteps(timesteps=_a  )

     def 					_a			(						self  )  ->      List[Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      int      		=	[100, 87, 50, 1, 0]
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	len(_a  )

           with self.assertRaises(_a	,    msg="""Can only pass one of `num_inference_steps` or `custom_timesteps`."""  ):
                 scheduler.set_timesteps(num_inference_steps=_a	,    timesteps=_a  )





     def 					_a			(						self  )  ->      Tuple:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.scheduler_classes[0]
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.get_scheduler_config()
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	scheduler_class(**_a  )

           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[scheduler.config.num_train_timesteps]

           with self.assertRaises(
               _a	,    msg="""`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}"""	,    ):
                 scheduler.set_timesteps(timesteps=_a  )




