



"""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


A:     int										=	8

def    _snake_case		(		UpperCamelCase		:	Union[str, Any]    ,	UpperCamelCase		:	str=BITS		):
 UpperCAmelCase			:      Tuple			=			x.device

 UpperCAmelCase			:      List[str]			=			(x * 255).int().clamp(0    ,	255		)

 UpperCAmelCase			:      Optional[int]			=			2 ** torch.arange(bits - 1    ,	-1    ,	-1    ,	device=UpperCamelCase		)
 UpperCAmelCase			:      Any			=			rearrange(UpperCamelCase    ,	"""d -> d 1 1"""		)
 UpperCAmelCase			:      Union[str, Any]			=			rearrange(UpperCamelCase    ,	"""b c h w -> b c 1 h w"""		)

 UpperCAmelCase			:      Any			=			((x & mask) != 0).float()
 UpperCAmelCase			:      str			=			rearrange(UpperCamelCase    ,	"""b c d h w -> b (c d) h w"""		)
 UpperCAmelCase			:      List[Any]			=			bits * 2 - 1
 return bits

def    _snake_case		(		UpperCamelCase		:	int    ,	UpperCamelCase		:	Dict=BITS		):
 UpperCAmelCase			:      Tuple			=			x.device

 UpperCAmelCase			:      List[Any]			=			(x > 0).int()
 UpperCAmelCase			:      Dict			=			2 ** torch.arange(bits - 1    ,	-1    ,	-1    ,	device=UpperCamelCase    ,	dtype=torch.intaa		)

 UpperCAmelCase			:      int			=			rearrange(UpperCamelCase    ,	"""d -> d 1 1"""		)
 UpperCAmelCase			:      str			=			rearrange(UpperCamelCase    ,	"""b (c d) h w -> b c d h w"""    ,	d=8		)
 UpperCAmelCase			:      Optional[int]			=			reduce(x * mask    ,	"""b c d h w -> b c h w"""    ,	"""sum"""		)
 return (dec / 255).clamp(0.0    ,	1.0		)

def    _snake_case		(		self		:	Dict    ,	UpperCamelCase		:	torch.FloatTensor    ,	UpperCamelCase		:	int    ,	UpperCamelCase		:	torch.FloatTensor    ,	UpperCamelCase		:	float = 0.0    ,	UpperCamelCase		:	bool = True    ,	UpperCamelCase		:	Dict=None    ,	UpperCamelCase		:	bool = True    ,	):
 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			:      Optional[Any]			=			timestep - self.config.num_train_timesteps // self.num_inference_steps

 # 2. compute alphas, betas
 UpperCAmelCase			:      Any			=			self.alphas_cumprod[timestep]
 UpperCAmelCase			:      List[str]			=			self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

 UpperCAmelCase			:      str			=			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			:      Optional[Any]			=			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

 # 4. Clip "predicted x_0"
 UpperCAmelCase			:      Optional[int]			=			self.bit_scale
 if self.config.clip_sample:
  UpperCAmelCase			:      str			=			torch.clamp(UpperCamelCase    ,	-scale    ,	UpperCamelCase		)

 # 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			:      List[str]			=			self._get_variance(UpperCamelCase    ,	UpperCamelCase		)
 UpperCAmelCase			:      str			=			eta * variance ** 0.5

 if use_clipped_model_output:
  # the model_output is always re-derived from the clipped x_0 in Glide
  UpperCAmelCase			:      List[Any]			=			(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			:      Optional[int]			=			(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			:      str			=			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			:      Union[str, Any]			=			model_output.device if torch.is_tensor(UpperCamelCase		) else """cpu"""
  UpperCAmelCase			:      Optional[int]			=			torch.randn(model_output.shape    ,	dtype=model_output.dtype    ,	generator=UpperCamelCase		).to(UpperCamelCase		)
  UpperCAmelCase			:      Union[str, Any]			=			self._get_variance(UpperCamelCase    ,	UpperCamelCase		) ** 0.5 * eta * noise

  UpperCAmelCase			:      Optional[int]			=			prev_sample + variance

 if not return_dict:
  return (prev_sample,)

 return DDIMSchedulerOutput(prev_sample=UpperCamelCase    ,	pred_original_sample=UpperCamelCase		)

def    _snake_case		(		self		:	List[str]    ,	UpperCamelCase		:	torch.FloatTensor    ,	UpperCamelCase		:	int    ,	UpperCamelCase		:	torch.FloatTensor    ,	UpperCamelCase		:	List[Any]="epsilon"    ,	UpperCamelCase		:	Optional[Any]=None    ,	UpperCamelCase		:	bool = True    ,	):
 UpperCAmelCase			:      int			=			timestep

 if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
  UpperCAmelCase			:      Union[str, Any]			=			torch.split(UpperCamelCase    ,	sample.shape[1]    ,	dim=1		)
 else:
  UpperCAmelCase			:      Optional[int]			=			None

 # 1. compute alphas, betas
 UpperCAmelCase			:      Dict			=			self.alphas_cumprod[t]
 UpperCAmelCase			:      List[str]			=			self.alphas_cumprod[t - 1] if t > 0 else self.one
 UpperCAmelCase			:      List[str]			=			1 - alpha_prod_t
 UpperCAmelCase			:      Optional[Any]			=			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			:      Optional[Any]			=			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
 elif prediction_type == "sample":
  UpperCAmelCase			:      List[str]			=			model_output
 else:
  raise ValueError(F"Unsupported prediction_type {prediction_type}."		)

 # 3. Clip "predicted x_0"
 UpperCAmelCase			:      str			=			self.bit_scale
 if self.config.clip_sample:
  UpperCAmelCase			:      Tuple			=			torch.clamp(UpperCamelCase    ,	-scale    ,	UpperCamelCase		)

 # 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			:      str			=			(alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
 UpperCAmelCase			:      Optional[Any]			=			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			:      Optional[Any]			=			pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

 # 6. Add noise
 UpperCAmelCase			:      Any			=			0
 if t > 0:
  UpperCAmelCase			:      str			=			torch.randn(
      model_output.size()    ,	dtype=model_output.dtype    ,	layout=model_output.layout    ,	generator=UpperCamelCase		).to(model_output.device		)
  UpperCAmelCase			:      List[str]			=			(self._get_variance(UpperCamelCase    ,	predicted_variance=UpperCamelCase		) ** 0.5) * noise

 UpperCAmelCase			:      List[str]			=			pred_prev_sample + variance

 if not return_dict:
  return (pred_prev_sample,)

 return DDPMSchedulerOutput(prev_sample=UpperCamelCase    ,	pred_original_sample=UpperCamelCase		)



class    SCREAMING_SNAKE_CASE__						(      UpperCAmelCase__				):

   def __init__(     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE = 1.0   ,  )						->   Any:





    '''simple docstring'''




    super().__init__()
    UpperCAmelCase			:      Optional[int]			=			bit_scale
    UpperCAmelCase			:      Optional[Any]			=			(
        ddim_bit_scheduler_step if isinstance(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		) else ddpm_bit_scheduler_step
    )

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




   @torch.no_grad()
   def __call__(     self   ,  _SCREAMING_SNAKE_CASE = 256   ,  _SCREAMING_SNAKE_CASE = 256   ,  _SCREAMING_SNAKE_CASE = 50   ,  _SCREAMING_SNAKE_CASE = None   ,  _SCREAMING_SNAKE_CASE = 1   ,  _SCREAMING_SNAKE_CASE = "pil"   ,  _SCREAMING_SNAKE_CASE = True   ,  **_SCREAMING_SNAKE_CASE   ,  )						->   Union[Tuple, ImagePipelineOutput]:





    '''simple docstring'''




    UpperCAmelCase			:      Union[str, Any]			=			torch.randn(
        (batch_size, self.unet.config.in_channels, height, width)   ,  generator=_SCREAMING_SNAKE_CASE   ,  )
    UpperCAmelCase			:      Tuple			=			decimal_to_bits(_SCREAMING_SNAKE_CASE		) * self.bit_scale
    UpperCAmelCase			:      str			=			latents.to(self.device		)

    self.scheduler.set_timesteps(_SCREAMING_SNAKE_CASE		)

    for t in self.progress_bar(self.scheduler.timesteps		):
     # predict the noise residual
     UpperCAmelCase			:      List[Any]			=			self.unet(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		).sample

     # compute the previous noisy sample x_t -> x_t-1
     UpperCAmelCase			:      Optional[int]			=			self.scheduler.step(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		).prev_sample

    UpperCAmelCase			:      Optional[Any]			=			bits_to_decimal(_SCREAMING_SNAKE_CASE		)

    if output_type == "pil":
     UpperCAmelCase			:      Optional[int]			=			self.numpy_to_pil(_SCREAMING_SNAKE_CASE		)

    if not return_dict:
     return (image,)

    return ImagePipelineOutput(images=_SCREAMING_SNAKE_CASE		)











"""simple docstring"""
import math
from datetime import datetime, timedelta

def    _snake_case		(		UpperCamelCase		:	int		):
 UpperCAmelCase			:      Any			=			year % 19
 UpperCAmelCase			:      Any			=			year % 4
 UpperCAmelCase			:      str			=			year % 7
 UpperCAmelCase			:      Union[str, Any]			=			math.floor(year / 100		)
 UpperCAmelCase			:      Optional[Any]			=			math.floor((13 + 8 * leap_day_inhibits) / 25		)
 UpperCAmelCase			:      int			=			leap_day_inhibits / 4
 UpperCAmelCase			:      int			=			(
     15 - lunar_orbit_correction + leap_day_inhibits - leap_day_reinstall_number
 ) % 30
 UpperCAmelCase			:      Tuple			=			(4 + leap_day_inhibits - leap_day_reinstall_number) % 7

 # days to be added to March 21
 UpperCAmelCase			:      int			=			(19 * metonic_cycle + secular_moon_shift) % 30

 # PHM -> Paschal Full Moon
 UpperCAmelCase			:      Tuple			=			(
     2 * julian_leap_year
     + 4 * non_leap_year
     + 6 * days_to_add
     + century_starting_point
 ) % 7

 if days_to_add == 29 and days_from_phm_to_sunday == 6:
  return datetime(UpperCamelCase    ,	4    ,	19		)
 elif days_to_add == 28 and days_from_phm_to_sunday == 6:
  return datetime(UpperCamelCase    ,	4    ,	18		)
 else:
  return datetime(UpperCamelCase    ,	3    ,	22		) + timedelta(
      days=int(days_to_add + days_from_phm_to_sunday		)		)


if __name__ == "__main__":
      for year in (1_9_9_4, 2_0_0_0, 2_0_1_0, 2_0_2_1, 2_0_2_3):
            A:     Any										=	"will be" if year > datetime.now().year else "was"
            print(f"""Easter in {year} {tense} {gauss_easter(year)}""")
