


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


lowerCAmelCase       =							8
def 			_a (      SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE=BITS     ):


		"""simple docstring"""




		lowercase__            =      x.device

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

		lowercase__            =      2 ** torch.arange(bits - 1						,				-1						,				-1						,				device=SCREAMING_SNAKE_CASE     )
		lowercase__            =      rearrange(SCREAMING_SNAKE_CASE						,				'''d -> d 1 1'''     )
		lowercase__            =      rearrange(SCREAMING_SNAKE_CASE						,				'''b c h w -> b c 1 h w'''     )

		lowercase__            =      ((x & mask) != 0).float()
		lowercase__            =      rearrange(SCREAMING_SNAKE_CASE						,				'''b c d h w -> b (c d) h w'''     )
		lowercase__            =      bits * 2 - 1
		return bits
def 			_a (      SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE=BITS     ):


		"""simple docstring"""




		lowercase__            =      x.device

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

		lowercase__            =      rearrange(SCREAMING_SNAKE_CASE						,				'''d -> d 1 1'''     )
		lowercase__            =      rearrange(SCREAMING_SNAKE_CASE						,				'''b (c d) h w -> b c d h w'''						,				d=8     )
		lowercase__            =      reduce(x * mask						,				'''b c d h w -> b c h w'''						,				'''sum'''     )
		return (dec / 2_55).clamp(0.0						,				1.0     )
def 			_a (      self						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE = 0.0						,				SCREAMING_SNAKE_CASE = True						,				SCREAMING_SNAKE_CASE=None						,				SCREAMING_SNAKE_CASE = True						,				):


		"""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)
		lowercase__            =      timestep - self.config.num_train_timesteps // self.num_inference_steps

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

		lowercase__            =      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
		lowercase__            =      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

		# 4. Clip "predicted x_0"
		lowercase__            =      self.bit_scale
		if self.config.clip_sample:
				lowercase__            =      torch.clamp(SCREAMING_SNAKE_CASE						,				-scale						,				SCREAMING_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)
		lowercase__            =      self._get_variance(SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE     )
		lowercase__            =      eta * variance ** 0.5

		if use_clipped_model_output:
				# the model_output is always re-derived from the clipped x_0 in Glide
				lowercase__            =      (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
		lowercase__            =      (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
		lowercase__            =      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
				lowercase__            =      model_output.device if torch.is_tensor(SCREAMING_SNAKE_CASE     ) else '''cpu'''
				lowercase__            =      torch.randn(model_output.shape						,				dtype=model_output.dtype						,				generator=SCREAMING_SNAKE_CASE     ).to(SCREAMING_SNAKE_CASE     )
				lowercase__            =      self._get_variance(SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE     ) ** 0.5 * eta * noise

				lowercase__            =      prev_sample + variance

		if not return_dict:
				return (prev_sample,)

		return DDIMSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE						,				pred_original_sample=SCREAMING_SNAKE_CASE     )
def 			_a (      self						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE="epsilon"						,				SCREAMING_SNAKE_CASE=None						,				SCREAMING_SNAKE_CASE = True						,				):


		"""simple docstring"""




		lowercase__            =      timestep

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

		# 1. compute alphas, betas
		lowercase__            =      self.alphas_cumprod[t]
		lowercase__            =      self.alphas_cumprod[t - 1] if t > 0 else self.one
		lowercase__            =      1 - alpha_prod_t
		lowercase__            =      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":
				lowercase__            =      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
		elif prediction_type == "sample":
				lowercase__            =      model_output
		else:
				raise ValueError(f'Unsupported prediction_type {prediction_type}.'     )

		# 3. Clip "predicted x_0"
		lowercase__            =      self.bit_scale
		if self.config.clip_sample:
				lowercase__            =      torch.clamp(SCREAMING_SNAKE_CASE						,				-scale						,				SCREAMING_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
		lowercase__            =      (alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
		lowercase__            =      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
		lowercase__            =      pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

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

		lowercase__            =      pred_prev_sample + variance

		if not return_dict:
				return (pred_prev_sample,)

		return DDPMSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE						,				pred_original_sample=SCREAMING_SNAKE_CASE     )


class        _a							(			UpperCamelCase__			):

							def __init__(							self:	int    ,						UpperCamelCase_:	UNetaDConditionModel    ,						UpperCamelCase_:	Union[DDIMScheduler, DDPMScheduler]    ,						UpperCamelCase_:	Optional[float] = 1.0    ,						)			->   Optional[int]:





									"""simple docstring"""







									super().__init__()
									lowercase__            =      bit_scale
									lowercase__            =      (
									    ddim_bit_scheduler_step if isinstance(UpperCamelCase_    ,						UpperCamelCase_							) else ddpm_bit_scheduler_step
									)

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


							@torch.no_grad()
							def __call__(							self:	str    ,						UpperCamelCase_:	Optional[int] = 256    ,						UpperCamelCase_:	Optional[int] = 256    ,						UpperCamelCase_:	Optional[int] = 50    ,						UpperCamelCase_:	Optional[torch.Generator] = None    ,						UpperCamelCase_:	Optional[int] = 1    ,						UpperCamelCase_:	Optional[str] = "pil"    ,						UpperCamelCase_:	bool = True    ,						**UpperCamelCase_:	str    ,						)			->   Union[Tuple, ImagePipelineOutput]:





									"""simple docstring"""







									lowercase__            =      torch.randn(
									    (batch_size, self.unet.config.in_channels, height, width)    ,						generator=UpperCamelCase_    ,						)
									lowercase__            =      decimal_to_bits(UpperCamelCase_							) * self.bit_scale
									lowercase__            =      latents.to(self.device							)

									self.scheduler.set_timesteps(UpperCamelCase_							)

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

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

									lowercase__            =      bits_to_decimal(UpperCamelCase_							)

									if output_type == "pil":
											lowercase__            =      self.numpy_to_pil(UpperCamelCase_							)

									if not return_dict:
											return (image,)

									return ImagePipelineOutput(images=UpperCamelCase_							)






from __future__ import annotations
def 			_a (      SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		lowercase__            =      0
		lowercase__            =      len(SCREAMING_SNAKE_CASE     ) - 1

		while i < j:
				if nums[i] + nums[j] == target:
						return [i, j]
				elif nums[i] + nums[j] < target:
						lowercase__            =      i + 1
				else:
						lowercase__            =      j - 1

		return []


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			print(f"""{two_pointer([2, 7, 11, 15], 9) = }""")


