

from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin


@dataclass
class       SCREAMING_SNAKE_CASE__					(__snake_case     ):
    __lowerCamelCase						:       torch.FloatTensor
    __lowerCamelCase						:       torch.FloatTensor
    __lowerCamelCase						:       Optional[torch.FloatTensor]														=     None



class       SCREAMING_SNAKE_CASE__					(__snake_case		,       __snake_case     ):
    __lowerCamelCase						:       str														=     2





    @register_to_config
    def __init__(      self						,   a = 0.02						,   a = 100						,   a = 1.007						,   a = 80						,   a = 0.05						,   a = 50						,   ):
         # standard deviation of the initial noise distribution
         lowercase__    :   int      =       sigma_max

         # setable values
         lowercase__    :   int      =       None
         lowercase__    :   np.IntTensor      =       None
         lowercase__    :   torch.FloatTensor      =       None  # sigma(t_i)





    def       snake_case_				(      self						,   a						,   a = None):
         return sample





    def       snake_case_				(      self						,   a						,   a = None):
         lowercase__    :   Optional[int]      =       num_inference_steps
         lowercase__    :   Dict      =       np.arange(0						,   self.num_inference_steps)[::-1].copy()
         lowercase__    :   Optional[int]      =       torch.from_numpy(a).to(a)
         lowercase__    :   Dict      =       [
             (
                 self.config.sigma_max**2
                 * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
             )
             for i in self.timesteps
         ]
         lowercase__    :   Optional[Any]      =       torch.tensor(a						,   dtype=torch.floataa						,   device=a)





    def       snake_case_				(      self						,   a						,   a						,   a = None):
         if self.config.s_min <= sigma <= self.config.s_max:
              lowercase__    :   Any      =       min(self.config.s_churn / self.num_inference_steps						,   2**0.5 - 1)
         else:
              lowercase__    :   Optional[Any]      =       0

         # sample eps ~ N(0, S_noise^2 * I)
         lowercase__    :   Dict      =       self.config.s_noise * randn_tensor(sample.shape						,   generator=a).to(sample.device)
         lowercase__    :   Optional[int]      =       sigma + gamma * sigma
         lowercase__    :   Optional[Any]      =       sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

         return sample_hat, sigma_hat





    def       snake_case_				(      self						,   a						,   a						,   a						,   a						,   a = True						,   ):
         lowercase__    :   str      =       sample_hat + sigma_hat * model_output
         lowercase__    :   Dict      =       (sample_hat - pred_original_sample) / sigma_hat
         lowercase__    :   Union[str, Any]      =       sample_hat + (sigma_prev - sigma_hat) * derivative

         if not return_dict:
              return (sample_prev, derivative)

         return KarrasVeOutput(
             prev_sample=a						,   derivative=a						,   pred_original_sample=a)





    def       snake_case_				(      self						,   a						,   a						,   a						,   a						,   a						,   a						,   a = True						,   ):
         lowercase__    :   List[Any]      =       sample_prev + sigma_prev * model_output
         lowercase__    :   List[Any]      =       (sample_prev - pred_original_sample) / sigma_prev
         lowercase__    :   Union[str, Any]      =       sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

         if not return_dict:
              return (sample_prev, derivative)

         return KarrasVeOutput(
             prev_sample=a						,   derivative=a						,   pred_original_sample=a)





    def       snake_case_				(      self						,   a						,   a						,   a):
         raise NotImplementedError()




import math

def 	snake_case__			(    SCREAMING_SNAKE_CASE_		:    int			):



     '''simple docstring'''





     lowercase__    :   Optional[Any]      =       []
     lowercase__    :   str      =       2
     lowercase__    :   Optional[Any]      =       int(math.sqrt(SCREAMING_SNAKE_CASE_			)			)  # Size of every segment
     lowercase__    :   Dict      =       [True] * (end + 1)
     lowercase__    :   Union[str, Any]      =       []

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

     lowercase__    :   Optional[int]      =       end + 1
     lowercase__    :   List[str]      =       min(2 * end	,     SCREAMING_SNAKE_CASE_			)

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

               for j in range(SCREAMING_SNAKE_CASE_	,     high + 1	,     SCREAMING_SNAKE_CASE_			):
                    lowercase__    :   Optional[Any]      =       False

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

          lowercase__    :   Optional[Any]      =       high + 1
          lowercase__    :   Optional[int]      =       min(high + end	,     SCREAMING_SNAKE_CASE_			)

     return prime

print(sieve(10**6))

