'''simple docstring'''





from typing import Optional, Tuple, Union

import torch
from einops import rearrange, reduce

from diffusers import DDIMScheduler, DDPMScheduler, DiffusionPipeline, ImagePipelineOutput, UNetaDConditionModel
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from diffusers.schedulers.scheduling_ddpm import DDPMSchedulerOutput


SCREAMING_SNAKE_CASE_:	Optional[int]    =8





def       lowerCAmelCase_							(   snake_case_			:					Optional[int]   ,       snake_case_			:					List[Any]=BITS     )       -> Tuple:


     '''simple docstring'''




     UpperCAmelCase_			       =  x.device

     UpperCAmelCase_			       =  (x * 2_55).int().clamp(0   ,       2_55     )

     UpperCAmelCase_			       =  2 ** torch.arange(bits - 1   ,       -1   ,       -1   ,       device=snake_case_     )
     UpperCAmelCase_			       =  rearrange(snake_case_   ,       "d -> d 1 1"     )
     UpperCAmelCase_			       =  rearrange(snake_case_   ,       "b c h w -> b c 1 h w"     )

     UpperCAmelCase_			       =  ((x & mask) != 0).float()
     UpperCAmelCase_			       =  rearrange(snake_case_   ,       "b c d h w -> b (c d) h w"     )
     UpperCAmelCase_			       =  bits * 2 - 1
     return bits





def       lowerCAmelCase_							(   snake_case_			:					List[Any]   ,       snake_case_			:					str=BITS     )       -> Union[str, Any]:


     '''simple docstring'''




     UpperCAmelCase_			       =  x.device

     UpperCAmelCase_			       =  (x > 0).int()
     UpperCAmelCase_			       =  2 ** torch.arange(bits - 1   ,       -1   ,       -1   ,       device=snake_case_   ,       dtype=torch.intaa     )

     UpperCAmelCase_			       =  rearrange(snake_case_   ,       "d -> d 1 1"     )
     UpperCAmelCase_			       =  rearrange(snake_case_   ,       "b (c d) h w -> b c d h w"   ,       d=8     )
     UpperCAmelCase_			       =  reduce(x * mask   ,       "b c d h w -> b c h w"   ,       "sum"     )
     return (dec / 2_55).clamp(0.0   ,       1.0     )





def       lowerCAmelCase_							(   self			:					Optional[int]   ,       snake_case_			:					torch.FloatTensor   ,       snake_case_			:					int   ,       snake_case_			:					torch.FloatTensor   ,       snake_case_			:					float = 0.0   ,       snake_case_			:					bool = True   ,       snake_case_			:					Optional[int]=None   ,       snake_case_			:					bool = True   ,       )       -> Union[DDIMSchedulerOutput, Tuple]:


     '''simple docstring'''




     if self.num_inference_steps is None:
          raise ValueError(
              "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"     )

     # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
     # Ideally, read DDIM paper in-detail understanding

     # Notation (<variable name> -> <name in paper>
     # - pred_noise_t -> e_theta(x_t, t)
     # - pred_original_sample -> f_theta(x_t, t) or x_0
     # - std_dev_t -> sigma_t
     # - eta -> η
     # - pred_sample_direction -> "direction pointing to x_t"
     # - pred_prev_sample -> "x_t-1"

     # 1. get previous step value (=t-1)
     UpperCAmelCase_			       =  timestep - self.config.num_train_timesteps // self.num_inference_steps

     # 2. compute alphas, betas
     UpperCAmelCase_			       =  self.alphas_cumprod[timestep]
     UpperCAmelCase_			       =  self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

     UpperCAmelCase_			       =  1 - alpha_prod_t

     # 3. compute predicted original sample from predicted noise also called
     # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
     UpperCAmelCase_			       =  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

     # 4. Clip "predicted x_0"
     UpperCAmelCase_			       =  self.bit_scale
     if self.config.clip_sample:
          UpperCAmelCase_			       =  torch.clamp(snake_case_   ,       -scale   ,       snake_case_     )

     # 5. compute variance: "sigma_t(η)" -> see formula (16)
     # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
     UpperCAmelCase_			       =  self._get_variance(snake_case_   ,       snake_case_     )
     UpperCAmelCase_			       =  eta * variance ** 0.5

     if use_clipped_model_output:
          # the model_output is always re-derived from the clipped x_0 in Glide
          UpperCAmelCase_			       =  (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5

     # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
     UpperCAmelCase_			       =  (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

     # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
     UpperCAmelCase_			       =  alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

     if eta > 0:
          # randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
          UpperCAmelCase_			       =  model_output.device if torch.is_tensor(snake_case_     ) else "cpu"
          UpperCAmelCase_			       =  torch.randn(model_output.shape   ,       dtype=model_output.dtype   ,       generator=snake_case_     ).to(snake_case_     )
          UpperCAmelCase_			       =  self._get_variance(snake_case_   ,       snake_case_     ) ** 0.5 * eta * noise

          UpperCAmelCase_			       =  prev_sample + variance

     if not return_dict:
          return (prev_sample,)

     return DDIMSchedulerOutput(prev_sample=snake_case_   ,       pred_original_sample=snake_case_     )





def       lowerCAmelCase_							(   self			:					Union[str, Any]   ,       snake_case_			:					torch.FloatTensor   ,       snake_case_			:					int   ,       snake_case_			:					torch.FloatTensor   ,       snake_case_			:					List[Any]="epsilon"   ,       snake_case_			:					List[str]=None   ,       snake_case_			:					bool = True   ,       )       -> Union[DDPMSchedulerOutput, Tuple]:


     '''simple docstring'''




     UpperCAmelCase_			       =  timestep

     if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
          UpperCAmelCase_       ,					UpperCAmelCase_			       =  torch.split(snake_case_   ,       sample.shape[1]   ,       dim=1     )
     else:
          UpperCAmelCase_			       =  None

     # 1. compute alphas, betas
     UpperCAmelCase_			       =  self.alphas_cumprod[t]
     UpperCAmelCase_			       =  self.alphas_cumprod[t - 1] if t > 0 else self.one
     UpperCAmelCase_			       =  1 - alpha_prod_t
     UpperCAmelCase_			       =  1 - alpha_prod_t_prev

     # 2. compute predicted original sample from predicted noise also called
     # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
     if prediction_type == "epsilon":
          UpperCAmelCase_			       =  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
     elif prediction_type == "sample":
          UpperCAmelCase_			       =  model_output
     else:
          raise ValueError(f"""Unsupported prediction_type {prediction_type}."""     )

     # 3. Clip "predicted x_0"
     UpperCAmelCase_			       =  self.bit_scale
     if self.config.clip_sample:
          UpperCAmelCase_			       =  torch.clamp(snake_case_   ,       -scale   ,       snake_case_     )

     # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
     # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
     UpperCAmelCase_			       =  (alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
     UpperCAmelCase_			       =  self.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

     # 5. Compute predicted previous sample µ_t
     # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
     UpperCAmelCase_			       =  pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

     # 6. Add noise
     UpperCAmelCase_			       =  0
     if t > 0:
          UpperCAmelCase_			       =  torch.randn(
              model_output.size()   ,       dtype=model_output.dtype   ,       layout=model_output.layout   ,       generator=snake_case_     ).to(model_output.device     )
          UpperCAmelCase_			       =  (self._get_variance(snake_case_   ,       predicted_variance=snake_case_     ) ** 0.5) * noise

     UpperCAmelCase_			       =  pred_prev_sample + variance

     if not return_dict:
          return (pred_prev_sample,)

     return DDPMSchedulerOutput(prev_sample=snake_case_   ,       pred_original_sample=snake_case_     )






class 			__A (					UpperCamelCase__      ):



    def __init__(self       :       str  ,     __a       :       UNetaDConditionModel  ,     __a       :       Union[DDIMScheduler, DDPMScheduler]  ,     __a       :       Optional[float] = 1.0  ,     ):
         super().__init__()
         UpperCAmelCase_			       =  bit_scale
         UpperCAmelCase_			       =  (
             ddim_bit_scheduler_step if isinstance(__a  ,     __a					) else ddpm_bit_scheduler_step
         )

         self.register_modules(unet=__a  ,     scheduler=__a					)






    @torch.no_grad()
    def __call__(self       :       Union[str, Any]  ,     __a       :       Optional[int] = 256  ,     __a       :       Optional[int] = 256  ,     __a       :       Optional[int] = 50  ,     __a       :       Optional[torch.Generator] = None  ,     __a       :       Optional[int] = 1  ,     __a       :       Optional[str] = "pil"  ,     __a       :       bool = True  ,     **__a       :       Tuple  ,     ):
         UpperCAmelCase_			       =  torch.randn(
             (batch_size, self.unet.config.in_channels, height, width)  ,     generator=__a  ,     )
         UpperCAmelCase_			       =  decimal_to_bits(__a					) * self.bit_scale
         UpperCAmelCase_			       =  latents.to(self.device					)

         self.scheduler.set_timesteps(__a					)

         for t in self.progress_bar(self.scheduler.timesteps					):
              # predict the noise residual
              UpperCAmelCase_			       =  self.unet(__a  ,     __a					).sample

              # compute the previous noisy sample x_t -> x_t-1
              UpperCAmelCase_			       =  self.scheduler.step(__a  ,     __a  ,     __a					).prev_sample

         UpperCAmelCase_			       =  bits_to_decimal(__a					)

         if output_type == "pil":
              UpperCAmelCase_			       =  self.numpy_to_pil(__a					)

         if not return_dict:
              return (image,)

         return ImagePipelineOutput(images=__a					)







'''simple docstring'''

def 							_UpperCamelCase				(   lowerCAmelCase__:					int = 1000   )      -> int:
							SCREAMING_SNAKE_CASE_				=				2**power
							SCREAMING_SNAKE_CASE_				=				str(lowerCAmelCase__   )
							SCREAMING_SNAKE_CASE_				=				list(lowerCAmelCase__   )
							SCREAMING_SNAKE_CASE_				=				0

							for i in list_num:
														sum_of_num += int(lowerCAmelCase__   )

							return sum_of_num


if __name__ == "__main__":
							SCREAMING_SNAKE_CASE							:				Tuple     	=			int(input("Enter the power of 2: ").strip())
							print("2 ^ ", power, " = ", 2**power)
							SCREAMING_SNAKE_CASE							:				str     	=			solution(power)
							print("Sum of the digits is: ", result)





