




# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

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







class __snake_case			(			a ,  a		):
   UpperCAmelCase__  :    int          =  1







   @register_to_config
   def __init__(      self		:						Optional[Any]					,						_snake_case		:						Tuple=2000					,						_snake_case		:						Tuple=0.1					,						_snake_case		:						Optional[int]=20					,						_snake_case		:						Dict=1e-3):

        """simple docstring"""


        UpperCAmelCase_          =							None
        UpperCAmelCase_          =							None
        UpperCAmelCase_          =							None







   def lowerCamelCase						(      self		:						List[str]					,						_snake_case		:						Dict					,						_snake_case		:						List[str] = None):

        """simple docstring"""


        UpperCAmelCase_          =							torch.linspace(1					,						self.config.sampling_eps					,						_snake_case					,						device=_snake_case)







   def lowerCamelCase						(      self		:						List[str]					,						_snake_case		:						Optional[int]					,						_snake_case		:						Any					,						_snake_case		:						List[str]					,						_snake_case		:						List[Any]=None):

        """simple docstring"""


        if self.timesteps is None:
             raise ValueError(
                 '''`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler''')

        # TODO(Patrick) better comments + non-PyTorch
        # postprocess model score
        UpperCAmelCase_          =							(
            -0.2_5 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
        )
        UpperCAmelCase_          =							torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff))
        UpperCAmelCase_          =							std.flatten()
        while len(std.shape) < len(score.shape):
             UpperCAmelCase_          =							std.unsqueeze(-1)
        UpperCAmelCase_          =							-score / std

        # compute
        UpperCAmelCase_          =							-1.0 / len(self.timesteps)

        UpperCAmelCase_          =							self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
        UpperCAmelCase_          =							beta_t.flatten()
        while len(beta_t.shape) < len(x.shape):
             UpperCAmelCase_          =							beta_t.unsqueeze(-1)
        UpperCAmelCase_          =							-0.5 * beta_t * x

        UpperCAmelCase_          =							torch.sqrt(_snake_case)
        UpperCAmelCase_          =							drift - diffusion**2 * score
        UpperCAmelCase_          =							x + drift * dt

        # add noise
        UpperCAmelCase_          =							randn_tensor(x.shape					,						layout=x.layout					,						generator=_snake_case					,						device=x.device					,						dtype=x.dtype)
        UpperCAmelCase_          =							x_mean + diffusion * math.sqrt(-dt) * noise

        return x, x_mean







   def __len__(      self		:						Optional[Any]):

        """simple docstring"""


        return self.config.num_train_timesteps










from math import isqrt
def 				UpperCAmelCase_					(							__snake_case						)     ->			list[int]:







 """simple docstring"""


 _lowercase							      =[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						):
    _lowercase							      =False

 return [i for i in range(2     ,						__snake_case						) if is_prime[i]]
def 				UpperCAmelCase_					(							__snake_case = 10**8						)     ->			int:







 """simple docstring"""


 _lowercase							      =calculate_prime_numbers(max_number // 2						)

 _lowercase							      =0
 _lowercase							      =0
 _lowercase							      =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() = }''')

