"""simple docstring"""



from __future__ import annotations

from math import gcd



def 					_lowerCamelCase(					a ,  a = 2 ,  a = 1 ,  a = 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(a ,  a ,  a							) -> int:
              return (pow(a ,  2							) + step) % modulus

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

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

   SCREAMING_SNAKE_CASE__:Dict			=	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""",
   )
   SCREAMING_SNAKE_CASE__:Dict			=	parser.parse_args()

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

"""simple docstring"""



from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import KarrasVeScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput






class 				snake_case__     (   snake_case_   ):
 _snake_case   :			UNetaDModel
 _snake_case   :			KarrasVeScheduler


 def __init__(				self  ,						lowerCamelCase  ,						lowerCamelCase		):
        super().__init__()
        self.register_modules(unet=lowerCamelCase  ,						scheduler=lowerCamelCase		)






 @torch.no_grad()
 def __call__(				self  ,						lowerCamelCase = 1  ,						lowerCamelCase = 50  ,						lowerCamelCase = None  ,						lowerCamelCase = "pil"  ,						lowerCamelCase = True  ,						**lowerCamelCase  ,						):
        __a     				=  self.unet.config.sample_size
        __a     				=  (batch_size, 3, img_size, img_size)

        __a     				=  self.unet

        # sample x_0 ~ N(0, sigma_0^2 * I)
        __a     				=  randn_tensor(lowerCamelCase  ,						generator=lowerCamelCase  ,						device=self.device		) * self.scheduler.init_noise_sigma

        self.scheduler.set_timesteps(lowerCamelCase		)

        for t in self.progress_bar(self.scheduler.timesteps		):
               # here sigma_t == t_i from the paper
               __a     				=  self.scheduler.schedule[t]
               __a     				=  self.scheduler.schedule[t - 1] if t > 0 else 0

               # 1. Select temporarily increased noise level sigma_hat
               # 2. Add new noise to move from sample_i to sample_hat
               __a				, __a     				=  self.scheduler.add_noise_to_input(lowerCamelCase  ,						lowerCamelCase  ,						generator=lowerCamelCase		)

               # 3. Predict the noise residual given the noise magnitude `sigma_hat`
               # The model inputs and output are adjusted by following eq. (213) in [1].
               __a     				=  (sigma_hat / 2) * model((sample_hat + 1) / 2  ,						sigma_hat / 2		).sample

               # 4. Evaluate dx/dt at sigma_hat
               # 5. Take Euler step from sigma to sigma_prev
               __a     				=  self.scheduler.step(lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase		)

               if sigma_prev != 0:
                      # 6. Apply 2nd order correction
                      # The model inputs and output are adjusted by following eq. (213) in [1].
                      __a     				=  (sigma_prev / 2) * model((step_output.prev_sample + 1) / 2  ,						sigma_prev / 2		).sample
                      __a     				=  self.scheduler.step_correct(
                          lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						step_output.prev_sample  ,						step_output["derivative"]  ,						)
               __a     				=  step_output.prev_sample

        __a     				=  (sample / 2 + 0.5).clamp(0  ,						1		)
        __a     				=  sample.cpu().permute(0  ,						2  ,						3  ,						1		).numpy()
        if output_type == "pil":
               __a     				=  self.numpy_to_pil(lowerCamelCase		)

        if not return_dict:
               return (image,)

        return ImagePipelineOutput(images=lowerCamelCase		)
