"""simple docstring"""



def 					_lowerCamelCase(					a ,  a = False							):
       if n == 2:
              return True
       if not n % 2 or n < 2:
              return False
       if n > 5 and n % 1_0 not in (1, 3, 7, 9):  # can quickly check last digit
              return False
       if n > 3_3_1_7_0_4_4_0_6_4_6_7_9_8_8_7_3_8_5_9_6_1_9_8_1 and not allow_probable:
              raise ValueError(
                  "Warning: upper bound of deterministic test is exceeded. "
                  "Pass allow_probable=True to allow probabilistic test. "
                  "A return value of True indicates a probable prime."							)
       # array bounds provided by analysis
       __a     				=  [
           2_0_4_7,
           1_3_7_3_6_5_3,
           2_5_3_2_6_0_0_1,
           3_2_1_5_0_3_1_7_5_1,
           2_1_5_2_3_0_2_8_9_8_7_4_7,
           3_4_7_4_7_4_9_6_6_0_3_8_3,
           3_4_1_5_5_0_0_7_1_7_2_8_3_2_1,
           1,
           3_8_2_5_1_2_3_0_5_6_5_4_6_4_1_3_0_5_1,
           1,
           1,
           3_1_8_6_6_5_8_5_7_8_3_4_0_3_1_1_5_1_1_6_7_4_6_1,
           3_3_1_7_0_4_4_0_6_4_6_7_9_8_8_7_3_8_5_9_6_1_9_8_1,
       ]

       __a     				=  [2, 3, 5, 7, 1_1, 1_3, 1_7, 1_9, 2_3, 2_9, 3_1, 3_7, 4_1]
       for idx, _p in enumerate(a ,  1							):
              if n < _p:
                     # then we have our last prime to check
                     __a     				=  primes[:idx]
                     break
       __a				, __a     				=  n - 1, 0
       # break up n -1 into a power of 2 (s) and
       # remaining odd component
       # essentially, solve for d * 2 ** s == n - 1
       while d % 2 == 0:
              d //= 2
              s += 1
       for prime in plist:
              __a     				=  False
              for r in range(a							):
                     __a     				=  pow(a ,  d * 2**r ,  a							)
                     # see article for analysis explanation for m
                     if (r == 0 and m == 1) or ((m + 1) % n == 0):
                            __a     				=  True
                            # this loop will not determine compositeness
                            break
              if pr:
                     continue
              # if pr is False, then the above loop never evaluated to true,
              # and the n MUST be composite
              return False
       return True



def 					_lowerCamelCase(					):
       assert not miller_rabin(5_6_1							)
       assert miller_rabin(5_6_3							)
       # 2047

       assert not miller_rabin(8_3_8_2_0_1							)
       assert miller_rabin(8_3_8_2_0_7							)
       # 1_373_653

       assert not miller_rabin(1_7_3_1_6_0_0_1							)
       assert miller_rabin(1_7_3_1_6_0_1_7							)
       # 25_326_001

       assert not miller_rabin(3_0_7_8_3_8_6_6_4_1							)
       assert miller_rabin(3_0_7_8_3_8_6_6_5_3							)
       # 3_215_031_751

       assert not miller_rabin(1_7_1_3_0_4_5_5_7_4_8_0_1							)
       assert miller_rabin(1_7_1_3_0_4_5_5_7_4_8_1_9							)
       # 2_152_302_898_747

       assert not miller_rabin(2_7_7_9_7_9_9_7_2_8_3_0_7							)
       assert miller_rabin(2_7_7_9_7_9_9_7_2_8_3_2_7							)
       # 3_474_749_660_383

       assert not miller_rabin(1_1_3_8_5_0_0_2_3_9_0_9_4_4_1							)
       assert miller_rabin(1_1_3_8_5_0_0_2_3_9_0_9_5_2_7							)
       # 341_550_071_728_321

       assert not miller_rabin(1_2_7_5_0_4_1_0_1_8_8_4_8_8_0_4_3_5_1							)
       assert miller_rabin(1_2_7_5_0_4_1_0_1_8_8_4_8_8_0_4_3_9_1							)
       # 3_825_123_056_546_413_051

       assert not miller_rabin(7_9_6_6_6_4_6_4_4_5_8_5_0_7_7_8_7_7_9_1_8_6_7							)
       assert miller_rabin(7_9_6_6_6_4_6_4_4_5_8_5_0_7_7_8_7_7_9_1_9_5_1							)
       # 318_665_857_834_031_151_167_461

       assert not miller_rabin(5_5_2_8_4_0_6_7_7_4_4_6_6_4_7_8_9_7_6_6_0_3_3_3							)
       assert miller_rabin(5_5_2_8_4_0_6_7_7_4_4_6_6_4_7_8_9_7_6_6_0_3_5_9							)
       # 3_317_044_064_679_887_385_961_981
       # upper limit for probabilistic test


if __name__ == "__main__":
   test_miller_rabin()

"""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		)
