
"""simple docstring"""

import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput






def 							A						(    snake_case				:Optional[Any]    , snake_case				:str=0.999    , snake_case				:List[Any]="cosine"    , )				->     List[Any]:
 if alpha_transform_type == "cosine":

  def alpha_bar_fn(snake_case				:Any		):
   return math.cos((t + 0.008) / 1.008 * math.pi / 2		) ** 2

 elif alpha_transform_type == "exp":

  def alpha_bar_fn(snake_case				:Optional[int]		):
   return math.exp(t * -12.0		)

 else:
  raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}'		)

 __UpperCamelCase      =	[]
 for i in range(snake_case		):
  __UpperCamelCase      =	i / num_diffusion_timesteps
  __UpperCamelCase      =	(i + 1) / num_diffusion_timesteps
  betas.append(min(1 - alpha_bar_fn(snake_case		) / alpha_bar_fn(snake_case		)    , snake_case		)		)
 return torch.tensor(snake_case    , dtype=torch.floataa		)





class __lowerCAmelCase		(				__SCREAMING_SNAKE_CASE      ,  __SCREAMING_SNAKE_CASE      ):
     lowercase						       =						[e.name for e in KarrasDiffusionSchedulers]
     lowercase						       =						2





     @register_to_config
     def __init__(     self     ,					__UpperCAmelCase = 1000     ,					__UpperCAmelCase = 0.0_0_0_8_5     ,					__UpperCAmelCase = 0.0_1_2     ,					__UpperCAmelCase = "linear"     ,					__UpperCAmelCase = None     ,					__UpperCAmelCase = "epsilon"     ,					__UpperCAmelCase = False     ,					__UpperCAmelCase = False     ,					__UpperCAmelCase = 1.0     ,					__UpperCAmelCase = "linspace"     ,					__UpperCAmelCase = 0     ,					):

      '''simple docstring'''




      if trained_betas is not None:
       __UpperCamelCase      =	torch.tensor(__UpperCAmelCase     ,					dtype=torch.floataa				)
      elif beta_schedule == "linear":
       __UpperCamelCase      =	torch.linspace(__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					dtype=torch.floataa				)
      elif beta_schedule == "scaled_linear":
       # this schedule is very specific to the latent diffusion model.
       __UpperCamelCase      =	(
           torch.linspace(beta_start**0.5     ,					beta_end**0.5     ,					__UpperCAmelCase     ,					dtype=torch.floataa				) ** 2
       )
      elif beta_schedule == "squaredcos_cap_v2":
       # Glide cosine schedule
       __UpperCamelCase      =	betas_for_alpha_bar(__UpperCAmelCase     ,					alpha_transform_type='cosine'				)
      elif beta_schedule == "exp":
       __UpperCamelCase      =	betas_for_alpha_bar(__UpperCAmelCase     ,					alpha_transform_type='exp'				)
      else:
       raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'				)

      __UpperCamelCase      =	1.0 - self.betas
      __UpperCamelCase      =	torch.cumprod(self.alphas     ,					dim=0				)

      #  set all values
      self.set_timesteps(__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase				)
      __UpperCamelCase      =	use_karras_sigmas





     def 						UpperCAmelCase (     self     ,					__UpperCAmelCase     ,					__UpperCAmelCase=None				):

      '''simple docstring'''




      if schedule_timesteps is None:
       __UpperCamelCase      =	self.timesteps

      __UpperCamelCase      =	(schedule_timesteps == timestep).nonzero()

      # The sigma index that is taken for the **very** first `step`
      # is always the second index (or the last index if there is only 1)
      # This way we can ensure we don't accidentally skip a sigma in
      # case we start in the middle of the denoising schedule (e.g. for image-to-image)
      if len(self._index_counter				) == 0:
       __UpperCamelCase      =	1 if len(__UpperCAmelCase				) > 1 else 0
      else:
       __UpperCamelCase      =	timestep.cpu().item() if torch.is_tensor(__UpperCAmelCase				) else timestep
       __UpperCamelCase      =	self._index_counter[timestep_int]

      return indices[pos].item()





     @property
     def 						UpperCAmelCase (     self				):

      '''simple docstring'''




      if self.config.timestep_spacing in ["linspace", "trailing"]:
       return self.sigmas.max()

      return (self.sigmas.max() ** 2 + 1) ** 0.5





     def 						UpperCAmelCase (     self     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					):

      '''simple docstring'''




      __UpperCamelCase      =	self.index_for_timestep(__UpperCAmelCase				)

      __UpperCamelCase      =	self.sigmas[step_index]
      __UpperCamelCase      =	sample / ((sigma**2 + 1) ** 0.5)
      return sample





     def 						UpperCAmelCase (     self     ,					__UpperCAmelCase     ,					__UpperCAmelCase = None     ,					__UpperCAmelCase = None     ,					):

      '''simple docstring'''




      __UpperCamelCase      =	num_inference_steps

      __UpperCamelCase      =	num_train_timesteps or self.config.num_train_timesteps

      # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
      if self.config.timestep_spacing == "linspace":
       __UpperCamelCase      =	np.linspace(0     ,					num_train_timesteps - 1     ,					__UpperCAmelCase     ,					dtype=__UpperCAmelCase				)[::-1].copy()
      elif self.config.timestep_spacing == "leading":
       __UpperCamelCase      =	num_train_timesteps // self.num_inference_steps
       # creates integer timesteps by multiplying by ratio
       # casting to int to avoid issues when num_inference_step is power of 3
       __UpperCamelCase      =	(np.arange(0     ,					__UpperCAmelCase				) * step_ratio).round()[::-1].copy().astype(__UpperCAmelCase				)
       timesteps += self.config.steps_offset
      elif self.config.timestep_spacing == "trailing":
       __UpperCamelCase      =	num_train_timesteps / self.num_inference_steps
       # creates integer timesteps by multiplying by ratio
       # casting to int to avoid issues when num_inference_step is power of 3
       __UpperCamelCase      =	(np.arange(__UpperCAmelCase     ,					0     ,					-step_ratio				)).round().copy().astype(__UpperCAmelCase				)
       timesteps -= 1
      else:
       raise ValueError(
           F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'				)

      __UpperCamelCase      =	np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5				)
      __UpperCamelCase      =	np.log(__UpperCAmelCase				)
      __UpperCamelCase      =	np.interp(__UpperCAmelCase     ,					np.arange(0     ,					len(__UpperCAmelCase				)				)     ,					__UpperCAmelCase				)

      if self.config.use_karras_sigmas:
       __UpperCamelCase      =	self._convert_to_karras(in_sigmas=__UpperCAmelCase     ,					num_inference_steps=self.num_inference_steps				)
       __UpperCamelCase      =	np.array([self._sigma_to_t(__UpperCAmelCase     ,					__UpperCAmelCase				) for sigma in sigmas]				)

      __UpperCamelCase      =	np.concatenate([sigmas, [0.0]]				).astype(np.floataa				)
      __UpperCamelCase      =	torch.from_numpy(__UpperCAmelCase				).to(device=__UpperCAmelCase				)
      __UpperCamelCase      =	torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2				), sigmas[-1:]]				)

      __UpperCamelCase      =	torch.from_numpy(__UpperCAmelCase				)
      __UpperCamelCase      =	torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2				)]				)

      if str(__UpperCAmelCase				).startswith('mps'				):
       # mps does not support float64
       __UpperCamelCase      =	timesteps.to(__UpperCAmelCase     ,					dtype=torch.floataa				)
      else:
       __UpperCamelCase      =	timesteps.to(device=__UpperCAmelCase				)

      # empty dt and derivative
      __UpperCamelCase      =	None
      __UpperCamelCase      =	None

      # for exp beta schedules, such as the one for `pipeline_shap_e.py`
      # we need an index counter
      __UpperCamelCase      =	defaultdict(__UpperCAmelCase				)





     def 						UpperCAmelCase (     self     ,					__UpperCAmelCase     ,					__UpperCAmelCase				):

      '''simple docstring'''




      __UpperCamelCase      =	np.log(__UpperCAmelCase				)

      # get distribution
      __UpperCamelCase      =	log_sigma - log_sigmas[:, np.newaxis]

      # get sigmas range
      __UpperCamelCase      =	np.cumsum((dists >= 0)     ,					axis=0				).argmax(axis=0				).clip(max=log_sigmas.shape[0] - 2				)
      __UpperCamelCase      =	low_idx + 1

      __UpperCamelCase      =	log_sigmas[low_idx]
      __UpperCamelCase      =	log_sigmas[high_idx]

      # interpolate sigmas
      __UpperCamelCase      =	(low - log_sigma) / (low - high)
      __UpperCamelCase      =	np.clip(__UpperCAmelCase     ,					0     ,					1				)

      # transform interpolation to time range
      __UpperCamelCase      =	(1 - w) * low_idx + w * high_idx
      __UpperCamelCase      =	t.reshape(sigma.shape				)
      return t





     def 						UpperCAmelCase (     self     ,					__UpperCAmelCase     ,					__UpperCAmelCase				):

      '''simple docstring'''




      __UpperCamelCase      =	in_sigmas[-1].item()
      __UpperCamelCase      =	in_sigmas[0].item()

      __UpperCamelCase      =	7.0  # 7.0 is the value used in the paper
      __UpperCamelCase      =	np.linspace(0     ,					1     ,					__UpperCAmelCase				)
      __UpperCamelCase      =	sigma_min ** (1 / rho)
      __UpperCamelCase      =	sigma_max ** (1 / rho)
      __UpperCamelCase      =	(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
      return sigmas





     @property
     def 						UpperCAmelCase (     self				):

      '''simple docstring'''




      return self.dt is None





     def 						UpperCAmelCase (     self     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase = True     ,					):

      '''simple docstring'''




      __UpperCamelCase      =	self.index_for_timestep(__UpperCAmelCase				)

      # advance index counter by 1
      __UpperCamelCase      =	timestep.cpu().item() if torch.is_tensor(__UpperCAmelCase				) else timestep
      self._index_counter[timestep_int] += 1

      if self.state_in_first_order:
       __UpperCamelCase      =	self.sigmas[step_index]
       __UpperCamelCase      =	self.sigmas[step_index + 1]
      else:
       # 2nd order / Heun's method
       __UpperCamelCase      =	self.sigmas[step_index - 1]
       __UpperCamelCase      =	self.sigmas[step_index]

      # currently only gamma=0 is supported. This usually works best anyways.
      # We can support gamma in the future but then need to scale the timestep before
      # passing it to the model which requires a change in API
      __UpperCamelCase      =	0
      __UpperCamelCase      =	sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

      # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
      if self.config.prediction_type == "epsilon":
       __UpperCamelCase      =	sigma_hat if self.state_in_first_order else sigma_next
       __UpperCamelCase      =	sample - sigma_input * model_output
      elif self.config.prediction_type == "v_prediction":
       __UpperCamelCase      =	sigma_hat if self.state_in_first_order else sigma_next
       __UpperCamelCase      =	model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
           sample / (sigma_input**2 + 1)
       )
      elif self.config.prediction_type == "sample":
       __UpperCamelCase      =	model_output
      else:
       raise ValueError(
           F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'				)

      if self.config.clip_sample:
       __UpperCamelCase      =	pred_original_sample.clamp(
           -self.config.clip_sample_range     ,					self.config.clip_sample_range				)

      if self.state_in_first_order:
       # 2. Convert to an ODE derivative for 1st order
       __UpperCamelCase      =	(sample - pred_original_sample) / sigma_hat
       # 3. delta timestep
       __UpperCamelCase      =	sigma_next - sigma_hat

       # store for 2nd order step
       __UpperCamelCase      =	derivative
       __UpperCamelCase      =	dt
       __UpperCamelCase      =	sample
      else:
       # 2. 2nd order / Heun's method
       __UpperCamelCase      =	(sample - pred_original_sample) / sigma_next
       __UpperCamelCase      =	(self.prev_derivative + derivative) / 2

       # 3. take prev timestep & sample
       __UpperCamelCase      =	self.dt
       __UpperCamelCase      =	self.sample

       # free dt and derivative
       # Note, this puts the scheduler in "first order mode"
       __UpperCamelCase      =	None
       __UpperCamelCase      =	None
       __UpperCamelCase      =	None

      __UpperCamelCase      =	sample + derivative * dt

      if not return_dict:
       return (prev_sample,)

      return SchedulerOutput(prev_sample=__UpperCAmelCase				)





     def 						UpperCAmelCase (     self     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					__UpperCAmelCase     ,					):

      '''simple docstring'''




      __UpperCamelCase      =	self.sigmas.to(device=original_samples.device     ,					dtype=original_samples.dtype				)
      if original_samples.device.type == "mps" and torch.is_floating_point(__UpperCAmelCase				):
       # mps does not support float64
       __UpperCamelCase      =	self.timesteps.to(original_samples.device     ,					dtype=torch.floataa				)
       __UpperCamelCase      =	timesteps.to(original_samples.device     ,					dtype=torch.floataa				)
      else:
       __UpperCamelCase      =	self.timesteps.to(original_samples.device				)
       __UpperCamelCase      =	timesteps.to(original_samples.device				)

      __UpperCamelCase      =	[self.index_for_timestep(__UpperCAmelCase     ,					__UpperCAmelCase				) for t in timesteps]

      __UpperCamelCase      =	sigmas[step_indices].flatten()
      while len(sigma.shape				) < len(original_samples.shape				):
       __UpperCamelCase      =	sigma.unsqueeze(-1				)

      __UpperCamelCase      =	original_samples + noise * sigma
      return noisy_samples







     def __len__(     self				):

      '''simple docstring'''




      return self.config.num_train_timesteps





"""simple docstring"""

from math import isqrt






def 							A						(    snake_case				:int		)				->     list[int]:
 __UpperCamelCase      =	[True] * max_number
 for i in range(2    , isqrt(max_number - 1		) + 1		):
  if is_prime[i]:
   for j in range(i**2    , snake_case    , snake_case		):
    __UpperCamelCase      =	False

 return [i for i in range(2    , snake_case		) if is_prime[i]]






def 							A						(    snake_case				:int = 1_0**8		)				->     int:
 __UpperCamelCase      =	calculate_prime_numbers(max_number // 2		)

 __UpperCamelCase      =	0
 __UpperCamelCase      =	0
 __UpperCamelCase      =	len(snake_case		) - 1
 while left <= right:
  while prime_numbers[left] * prime_numbers[right] >= max_number:
   right -= 1
  semiprimes_count += right - left + 1
  left += 1

 return semiprimes_count


if __name__ == "__main__":
      print(f'''{solution() = }''')



