
"""simple docstring"""






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

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin




@flax.struct.dataclass
class 			_SCREAMING_SNAKE_CASE					:
			UpperCAmelCase_  :Optional[int]				 =						None
			UpperCAmelCase_  :Optional[jnp.ndarray]				 =						None
			UpperCAmelCase_  :Optional[jnp.ndarray]				 =						None  # sigma(t_i)






			@classmethod
			def  __lowerCAmelCase (					cls       )			->     int:
						return cls()




@dataclass
class 			_SCREAMING_SNAKE_CASE					(			_UpperCAmelCase							):
			UpperCAmelCase_  :jnp.ndarray
			UpperCAmelCase_  :jnp.ndarray
			UpperCAmelCase_  :KarrasVeSchedulerState




class 			_SCREAMING_SNAKE_CASE					(			_UpperCAmelCase	, _UpperCAmelCase							):






			@property
			def  __lowerCAmelCase (					self       )			->     int:
						return True






			@register_to_config
			def __init__(					self       ,   __A = 0.0_2       ,   __A = 100       ,   __A = 1.0_0_7       ,   __A = 80       ,   __A = 0.0_5       ,   __A = 50       ,   )			->     List[str]:
						pass






			def  __lowerCAmelCase (					self       )			->     Union[str, Any]:
						return KarrasVeSchedulerState.create()






			def  __lowerCAmelCase (					self       ,   __A       ,   __A       ,   __A = ()       )			->     KarrasVeSchedulerState:
						lowerCAmelCase_    :str			     =  jnp.arange(0       ,   SCREAMING_SNAKE_CASE_       )[::-1].copy()
						lowerCAmelCase_    :str			     =  [
						    (
						        self.config.sigma_max**2
						        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
						    )
						    for i in timesteps
						]

						return state.replace(
						    num_inference_steps=SCREAMING_SNAKE_CASE_       ,   schedule=jnp.array(SCREAMING_SNAKE_CASE_       ,   dtype=jnp.floataa       )       ,   timesteps=SCREAMING_SNAKE_CASE_       ,   )






			def  __lowerCAmelCase (					self       ,   __A       ,   __A       ,   __A       ,   __A       ,   )			->     Tuple[jnp.ndarray, float]:
						if self.config.s_min <= sigma <= self.config.s_max:
									lowerCAmelCase_    :Union[str, Any]			     =  min(self.config.s_churn / state.num_inference_steps       ,   2**0.5 - 1       )
						else:
									lowerCAmelCase_    :List[str]			     =  0

						# sample eps ~ N(0, S_noise^2 * I)
						lowerCAmelCase_    :Any			     =  random.split(SCREAMING_SNAKE_CASE_       ,   num=1       )
						lowerCAmelCase_    :Tuple			     =  self.config.s_noise * random.normal(key=SCREAMING_SNAKE_CASE_       ,   shape=sample.shape       )
						lowerCAmelCase_    :Tuple			     =  sigma + gamma * sigma
						lowerCAmelCase_    :List[Any]			     =  sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

						return sample_hat, sigma_hat






			def  __lowerCAmelCase (					self       ,   __A       ,   __A       ,   __A       ,   __A       ,   __A       ,   __A = True       ,   )			->     Union[FlaxKarrasVeOutput, Tuple]:
						lowerCAmelCase_    :int			     =  sample_hat + sigma_hat * model_output
						lowerCAmelCase_    :Optional[int]			     =  (sample_hat - pred_original_sample) / sigma_hat
						lowerCAmelCase_    :Any			     =  sample_hat + (sigma_prev - sigma_hat) * derivative

						if not return_dict:
									return (sample_prev, derivative, state)

						return FlaxKarrasVeOutput(prev_sample=SCREAMING_SNAKE_CASE_       ,   derivative=SCREAMING_SNAKE_CASE_       ,   state=SCREAMING_SNAKE_CASE_       )






			def  __lowerCAmelCase (					self       ,   __A       ,   __A       ,   __A       ,   __A       ,   __A       ,   __A       ,   __A       ,   __A = True       ,   )			->     Union[FlaxKarrasVeOutput, Tuple]:
						lowerCAmelCase_    :Optional[int]			     =  sample_prev + sigma_prev * model_output
						lowerCAmelCase_    :int			     =  (sample_prev - pred_original_sample) / sigma_prev
						lowerCAmelCase_    :int			     =  sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

						if not return_dict:
									return (sample_prev, derivative, state)

						return FlaxKarrasVeOutput(prev_sample=SCREAMING_SNAKE_CASE_       ,   derivative=SCREAMING_SNAKE_CASE_       ,   state=SCREAMING_SNAKE_CASE_       )






			def  __lowerCAmelCase (					self       ,   __A       ,   __A       ,   __A       ,   __A       )			->     Optional[Any]:
						raise NotImplementedError()










'''simple docstring'''



from math import isqrt



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				int							)     ->		bool:
     return all(number % divisor != 0 for divisor in range(2      ,    isqrt(UpperCAmelCase_							) + 1							)							)



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				int = 10**6							)     ->		int:
     __lowerCamelCase   :	Optional[Any]								=		0
     __lowerCamelCase   :	Optional[int]								=		1
     __lowerCamelCase   :	List[str]								=		7
     while prime_candidate < max_prime:
          primes_count += is_prime(UpperCAmelCase_							)

          cube_index += 1
          prime_candidate += 6 * cube_index

     return primes_count


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






