

# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class   UpperCamelCase			(  SCREAMING_SNAKE_CASE ):
    __UpperCamelCase    =42
    __UpperCamelCase    =None


def 							__lowerCAmelCase     (							_UpperCamelCase		:	Union[str, Any]		,				_UpperCamelCase		:	Union[str, Any]=0.9_99		,				_UpperCamelCase		:	Union[str, Any]="cosine"		,				)		->				int:
 '''simple docstring'''


 if alpha_transform_type == "cosine":

  def alpha_bar_fn(_UpperCamelCase		:	str						):
   return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2						) ** 2

 elif alpha_transform_type == "exp":

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

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

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




class   UpperCamelCase			(  SCREAMING_SNAKE_CASE						,      SCREAMING_SNAKE_CASE ):
    __UpperCamelCase    =1

    @register_to_config
    def __init__(      self			:   int				,     snake_case__			:   int = 1_0_0_0				,     snake_case__			:   float = 0.0_001				,     snake_case__			:   float = 0.02				,     snake_case__			:   str = "linear"				,     snake_case__			:   Optional[Union[np.ndarray, List[float]]] = None				,     snake_case__			:   bool = True				,     snake_case__			:   bool = True				,     snake_case__			:   int = 0				,     snake_case__			:   str = "epsilon"				,     snake_case__			:   float = 1.0				,     **snake_case__			:   Any				,     ):

     """simple docstring"""






     if kwargs.get('set_alpha_to_one'				,     snake_case__     ) is not None:
      SCREAMING_SNAKE_CASE		    =      (
          'The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead.'
      )
      deprecate('set_alpha_to_one'				,     '1.0.0'				,     snake_case__				,     standard_warn=snake_case__     )
      SCREAMING_SNAKE_CASE		    =      kwargs['set_alpha_to_one']
     if trained_betas is not None:
      SCREAMING_SNAKE_CASE		    =      torch.tensor(snake_case__				,     dtype=torch.floataa     )
     elif beta_schedule == "linear":
      SCREAMING_SNAKE_CASE		    =      torch.linspace(snake_case__				,     snake_case__				,     snake_case__				,     dtype=torch.floataa     )
     elif beta_schedule == "scaled_linear":
      # this schedule is very specific to the latent diffusion model.
      SCREAMING_SNAKE_CASE		    =      (
          torch.linspace(beta_start**0.5				,     beta_end**0.5				,     snake_case__				,     dtype=torch.floataa     ) ** 2
      )
     elif beta_schedule == "squaredcos_cap_v2":
      # Glide cosine schedule
      SCREAMING_SNAKE_CASE		    =      betas_for_alpha_bar(snake_case__     )
     else:
      raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""     )

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

     # At every step in inverted ddim, we are looking into the next alphas_cumprod
     # For the final step, there is no next alphas_cumprod, and the index is out of bounds
     # `set_alpha_to_zero` decides whether we set this parameter simply to zero
     # in this case, self.step() just output the predicted noise
     # or whether we use the final alpha of the "non-previous" one.
     SCREAMING_SNAKE_CASE		    =      torch.tensor(0.0     ) if set_alpha_to_zero else self.alphas_cumprod[-1]

     # standard deviation of the initial noise distribution
     SCREAMING_SNAKE_CASE		    =      1.0

     # setable values
     SCREAMING_SNAKE_CASE		    =      None
     SCREAMING_SNAKE_CASE		    =      torch.from_numpy(np.arange(0				,     snake_case__     ).copy().astype(np.intaa     )     )

    def UpperCamelCase      (      self			:   List[str]				,     snake_case__			:   torch.FloatTensor				,     snake_case__			:   Optional[int] = None     ):

     """simple docstring"""






     return sample

    def UpperCamelCase      (      self			:   List[str]				,     snake_case__			:   int				,     snake_case__			:   Union[str, torch.device] = None     ):

     """simple docstring"""






     if num_inference_steps > self.config.num_train_timesteps:
      raise ValueError(
          F"""`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"""
          F""" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"""
          F""" maximal {self.config.num_train_timesteps} timesteps."""     )

     SCREAMING_SNAKE_CASE		    =      num_inference_steps
     SCREAMING_SNAKE_CASE		    =      self.config.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
     SCREAMING_SNAKE_CASE		    =      (np.arange(0				,     snake_case__     ) * step_ratio).round().copy().astype(np.intaa     )
     SCREAMING_SNAKE_CASE		    =      torch.from_numpy(snake_case__     ).to(snake_case__     )
     self.timesteps += self.config.steps_offset

    def UpperCamelCase      (      self			:   Any				,     snake_case__			:   torch.FloatTensor				,     snake_case__			:   int				,     snake_case__			:   torch.FloatTensor				,     snake_case__			:   float = 0.0				,     snake_case__			:   bool = False				,     snake_case__			:   Optional[torch.FloatTensor] = None				,     snake_case__			:   bool = True				,     ):

     """simple docstring"""






     SCREAMING_SNAKE_CASE		    =      timestep + self.config.num_train_timesteps // self.num_inference_steps

     # 2. compute alphas, betas
     # change original implementation to exactly match noise levels for analogous forward process
     SCREAMING_SNAKE_CASE		    =      self.alphas_cumprod[timestep]
     SCREAMING_SNAKE_CASE		    =      (
         self.alphas_cumprod[prev_timestep]
         if prev_timestep < self.config.num_train_timesteps
         else self.final_alpha_cumprod
     )

     SCREAMING_SNAKE_CASE		    =      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
     if self.config.prediction_type == "epsilon":
      SCREAMING_SNAKE_CASE		    =      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
      SCREAMING_SNAKE_CASE		    =      model_output
     elif self.config.prediction_type == "sample":
      SCREAMING_SNAKE_CASE		    =      model_output
      SCREAMING_SNAKE_CASE		    =      (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
     elif self.config.prediction_type == "v_prediction":
      SCREAMING_SNAKE_CASE		    =      (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
      SCREAMING_SNAKE_CASE		    =      (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
     else:
      raise ValueError(
          F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"""
          ' `v_prediction`'     )

     # 4. Clip or threshold "predicted x_0"
     if self.config.clip_sample:
      SCREAMING_SNAKE_CASE		    =      pred_original_sample.clamp(
          -self.config.clip_sample_range				,     self.config.clip_sample_range     )

     # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
     SCREAMING_SNAKE_CASE		    =      (1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

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

     if not return_dict:
      return (prev_sample, pred_original_sample)
     return DDIMSchedulerOutput(prev_sample=snake_case__				,     pred_original_sample=snake_case__     )




    def __len__(      self			:   Optional[Any]     ):

     """simple docstring"""






     return self.config.num_train_timesteps




import math


def 							__lowerCAmelCase     (							_UpperCamelCase		:	int						)		->				list[int]:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE		    =      []
 SCREAMING_SNAKE_CASE		    =      2
 SCREAMING_SNAKE_CASE		    =      int(math.sqrt(_UpperCamelCase						)						)  # Size of every segment
 SCREAMING_SNAKE_CASE		    =      [True] * (end + 1)
 SCREAMING_SNAKE_CASE		    =      []

 while start <= end:
  if temp[start] is True:
   in_prime.append(_UpperCamelCase						)
   for i in range(start * start		,				end + 1		,				_UpperCamelCase						):
    SCREAMING_SNAKE_CASE		    =      False
  start += 1
 prime += in_prime

 SCREAMING_SNAKE_CASE		    =      end + 1
 SCREAMING_SNAKE_CASE		    =      min(2 * end		,				_UpperCamelCase						)

 while low <= n:
  SCREAMING_SNAKE_CASE		    =      [True] * (high - low + 1)
  for each in in_prime:
   SCREAMING_SNAKE_CASE		    =      math.floor(low / each						) * each
   if t < low:
    t += each

   for j in range(_UpperCamelCase		,				high + 1		,				_UpperCamelCase						):
    SCREAMING_SNAKE_CASE		    =      False

  for j in range(len(_UpperCamelCase						)						):
   if temp[j] is True:
    prime.append(j + low						)

  SCREAMING_SNAKE_CASE		    =      high + 1
  SCREAMING_SNAKE_CASE		    =      min(high + end		,				_UpperCamelCase						)

 return prime




print(sieve(10**6))

