





'''simple docstring'''





from typing import List, Optional, Union

import torch

from ...models import UNetaDConditionModel, VQModel
from ...pipelines import DiffusionPipeline
from ...pipelines.pipeline_utils import ImagePipelineOutput
from ...schedulers import DDPMScheduler
from ...utils import (
    is_accelerate_available,
    is_accelerate_version,
    logging,
    randn_tensor,
    replace_example_docstring,
)


UpperCAmelCase_  							=				logging.get_logger(__name__)  # pylint: disable=invalid-name

UpperCAmelCase_  							=				'\n    Examples:\n        ```py\n        >>> from diffusers import KandinskyV22Pipeline, KandinskyV22PriorPipeline\n        >>> import torch\n\n        >>> pipe_prior = KandinskyV22PriorPipeline.from_pretrained("kandinsky-community/kandinsky-2-2-prior")\n        >>> pipe_prior.to("cuda")\n        >>> prompt = "red cat, 4k photo"\n        >>> out = pipe_prior(prompt)\n        >>> image_emb = out.image_embeds\n        >>> zero_image_emb = out.negative_image_embeds\n        >>> pipe = KandinskyV22Pipeline.from_pretrained("kandinsky-community/kandinsky-2-2-decoder")\n        >>> pipe.to("cuda")\n        >>> image = pipe(\n        ...     image_embeds=image_emb,\n        ...     negative_image_embeds=zero_image_emb,\n        ...     height=768,\n        ...     width=768,\n        ...     num_inference_steps=50,\n        ... ).images\n        >>> image[0].save("cat.png")\n        ```\n'




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Union[str, Any]	,     __UpperCAmelCase:    Any	,     __UpperCAmelCase:    Optional[Any]=8   )   ->			int:
    UpperCamelCase__							:       Optional[int]      =   height // scale_factor**2
    if height % scale_factor**2 != 0:
        new_height += 1
    UpperCamelCase__							:       Optional[Any]      =   width // scale_factor**2
    if width % scale_factor**2 != 0:
        new_width += 1
    return new_height * scale_factor, new_width * scale_factor






class 					lowercase__ (			__lowerCamelCase       ):

   '''simple docstring'''


   def __init__(					self,	__magic_name__,	__magic_name__,	__magic_name__,	)				->   List[Any]:






       """simple docstring"""
       super().__init__()

       self.register_modules(
           unet=__magic_name__,	scheduler=__magic_name__,	movq=__magic_name__,	)
       UpperCamelCase__							:       Optional[int]      =   2 ** (len(self.movq.config.block_out_channels							) - 1)




   def    UpperCamelCase__						(					self,	__magic_name__,	__magic_name__,	__magic_name__,	__magic_name__,	__magic_name__,	__magic_name__							)				->   int:






       """simple docstring"""
       if latents is None:
           UpperCamelCase__							:       List[str]      =   randn_tensor(__magic_name__,	generator=__magic_name__,	device=__magic_name__,	dtype=__magic_name__							)
       else:
           if latents.shape != shape:
               raise ValueError(f"Unexpected latents shape, got {latents.shape}, expected {shape}"							)
           UpperCamelCase__							:       List[Any]      =   latents.to(__magic_name__							)

       UpperCamelCase__							:       str      =   latents * scheduler.init_noise_sigma
       return latents




   def    UpperCamelCase__						(					self,	__magic_name__=0							)				->   Optional[int]:






       """simple docstring"""
       if is_accelerate_available():
           from accelerate import cpu_offload
       else:
           raise ImportError('''Please install accelerate via `pip install accelerate`'''							)

       UpperCamelCase__							:       List[Any]      =   torch.device(f"cuda:{gpu_id}"							)

       UpperCamelCase__							:       Optional[Any]      =   [
           self.unet,
           self.movq,
       ]
       for cpu_offloaded_model in models:
           if cpu_offloaded_model is not None:
               cpu_offload(__magic_name__,	__magic_name__							)




   def    UpperCamelCase__						(					self,	__magic_name__=0							)				->   Optional[int]:






       """simple docstring"""
       if is_accelerate_available() and is_accelerate_version('''>=''',	'''0.17.0.dev0'''							):
           from accelerate import cpu_offload_with_hook
       else:
           raise ImportError('''`enable_model_cpu_offload` requires `accelerate v0.17.0` or higher.'''							)

       UpperCamelCase__							:       List[str]      =   torch.device(f"cuda:{gpu_id}"							)

       if self.device.type != "cpu":
           self.to('''cpu''',	silence_dtype_warnings=__magic_name__							)
           torch.cuda.empty_cache()  # otherwise we don't see the memory savings (but they probably exist)

       UpperCamelCase__							:       Any      =   None
       for cpu_offloaded_model in [self.unet, self.movq]:
           UpperCamelCase__							:       Any      =   cpu_offload_with_hook(__magic_name__,	__magic_name__,	prev_module_hook=__magic_name__							)

       # We'll offload the last model manually.
       UpperCamelCase__							:       Optional[Any]      =   hook




   @property
   # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline._execution_device
   def    UpperCamelCase__						(					self							)				->   List[str]:






       """simple docstring"""
       if not hasattr(self.unet,	'''_hf_hook'''							):
           return self.device
       for module in self.unet.modules():
           if (
               hasattr(__magic_name__,	'''_hf_hook'''							)
               and hasattr(module._hf_hook,	'''execution_device'''							)
               and module._hf_hook.execution_device is not None
           ):
               return torch.device(module._hf_hook.execution_device							)
       return self.device




   @torch.no_grad()
   @replace_example_docstring(__magic_name__							)
   def __call__(					self,	__magic_name__,	__magic_name__,	__magic_name__ = 512,	__magic_name__ = 512,	__magic_name__ = 100,	__magic_name__ = 4.0,	__magic_name__ = 1,	__magic_name__ = None,	__magic_name__ = None,	__magic_name__ = "pil",	__magic_name__ = True,	)				->   str:






       """simple docstring"""
       UpperCamelCase__							:       List[str]      =   self._execution_device

       UpperCamelCase__							:       List[str]      =   guidance_scale > 1.0

       if isinstance(__magic_name__,	__magic_name__							):
           UpperCamelCase__							:       List[Any]      =   torch.cat(__magic_name__,	dim=0							)
       UpperCamelCase__							:       int      =   image_embeds.shape[0] * num_images_per_prompt
       if isinstance(__magic_name__,	__magic_name__							):
           UpperCamelCase__							:       int      =   torch.cat(__magic_name__,	dim=0							)

       if do_classifier_free_guidance:
           UpperCamelCase__							:       Optional[Any]      =   image_embeds.repeat_interleave(__magic_name__,	dim=0							)
           UpperCamelCase__							:       Union[str, Any]      =   negative_image_embeds.repeat_interleave(__magic_name__,	dim=0							)

       UpperCamelCase__							:       Optional[Any]      =   torch.cat([negative_image_embeds, image_embeds],	dim=0							).to(dtype=self.unet.dtype,	device=__magic_name__							)

       self.scheduler.set_timesteps(__magic_name__,	device=__magic_name__							)
       UpperCamelCase__							:       List[str]      =   self.scheduler.timesteps

       UpperCamelCase__							:       List[str]      =   self.unet.config.in_channels

       UpperCamelCase__							:       int      =   downscale_height_and_width(__magic_name__,	__magic_name__,	self.movq_scale_factor							)

       # create initial latent
       UpperCamelCase__							:       Union[str, Any]      =   self.prepare_latents(
           (batch_size, num_channels_latents, height, width),	image_embeds.dtype,	__magic_name__,	__magic_name__,	__magic_name__,	self.scheduler,	)

       for i, t in enumerate(self.progress_bar(__magic_name__							)							):
           # expand the latents if we are doing classifier free guidance
           UpperCamelCase__							:       Tuple      =   torch.cat([latents] * 2							) if do_classifier_free_guidance else latents

           UpperCamelCase__							:       Optional[Any]      =   {'''image_embeds''': image_embeds}
           UpperCamelCase__							:       Tuple      =   self.unet(
               sample=__magic_name__,	timestep=__magic_name__,	encoder_hidden_states=__magic_name__,	added_cond_kwargs=__magic_name__,	return_dict=__magic_name__,	)[0]

           if do_classifier_free_guidance:
               UpperCamelCase__							:       str      =   noise_pred.split(latents.shape[1],	dim=1							)
               UpperCamelCase__							:       Any      =   noise_pred.chunk(2							)
               UpperCamelCase__							:       Tuple      =   variance_pred.chunk(2							)
               UpperCamelCase__							:       Optional[int]      =   noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
               UpperCamelCase__							:       Dict      =   torch.cat([noise_pred, variance_pred_text],	dim=1							)

           if not (
               hasattr(self.scheduler.config,	'''variance_type'''							)
               and self.scheduler.config.variance_type in ["learned", "learned_range"]
           ):
               UpperCamelCase__							:       List[str]      =   noise_pred.split(latents.shape[1],	dim=1							)

           # compute the previous noisy sample x_t -> x_t-1
           UpperCamelCase__							:       Dict      =   self.scheduler.step(
               __magic_name__,	__magic_name__,	__magic_name__,	generator=__magic_name__,	)[0]
       # post-processing
       UpperCamelCase__							:       Dict      =   self.movq.decode(__magic_name__,	force_not_quantize=__magic_name__							)['''sample''']

       if output_type not in ["pt", "np", "pil"]:
           raise ValueError(f"Only the output types `pt`, `pil` and `np` are supported not output_type={output_type}"							)

       if output_type in ["np", "pil"]:
           UpperCamelCase__							:       Union[str, Any]      =   image * 0.5 + 0.5
           UpperCamelCase__							:       str      =   image.clamp(0,	1							)
           UpperCamelCase__							:       int      =   image.cpu().permute(0,	2,	3,	1							).float().numpy()

       if output_type == "pil":
           UpperCamelCase__							:       List[Any]      =   self.numpy_to_pil(__magic_name__							)

       if not return_dict:
           return (image,)

       return ImagePipelineOutput(images=__magic_name__							)








from __future__ import annotations

from math import gcd




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

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

        while True:
            # At each iteration, the tortoise moves one step and the hare moves two.
            UpperCamelCase__							:       Optional[int]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )
            UpperCamelCase__							:       List[str]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )
            UpperCamelCase__							:       Optional[int]      =   rand_fn(__UpperCAmelCase	,     __UpperCAmelCase	,     __UpperCAmelCase   )

            # 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``.
            UpperCamelCase__							:       Optional[int]      =   gcd(hare - tortoise	,     __UpperCAmelCase   )

            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.
        UpperCamelCase__							:       List[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

  UpperCAmelCase_  							=				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_  							=				parser.parse_args()

  UpperCAmelCase_  							=				pollard_rho(args.num, attempts=args.attempts)
  if divisor is None:
    print(F'''{args.num} is probably prime''')
  else:
    UpperCAmelCase_  							=				args.num // divisor
    print(F'''{args.num} = {divisor} * {quotient}''')

