


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 .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left


@flax.struct.dataclass
class        __lowerCamelCase      :


				"""simple docstring"""







				a_:		Tuple					      =	None
				a_:		Union[str, Any]					      =	None
				a_:		Union[str, Any]					      =	None






				@classmethod
				def        lowerCAmelCase__			(				cls     :    List[str]					):
								return cls()


@dataclass
class        __lowerCamelCase      (				_lowerCAmelCase ):


				"""simple docstring"""







				a_:		Tuple					      =	42
				a_:		Tuple					      =	42
				a_:		Union[str, Any]					      =	None


class        __lowerCamelCase      (				_lowerCAmelCase				,		_lowerCAmelCase ):


				"""simple docstring"""







				@property
				def        lowerCAmelCase__			(				self     :    List[str]					):
								return True






				@register_to_config
				def __init__(				self     :    Any	,							lowerCamelCase_     :    int = 2000	,							lowerCamelCase_     :    float = 0.15	,							lowerCamelCase_     :    float = 0.01	,							lowerCamelCase_     :    float = 1348.0	,							lowerCamelCase_     :    float = 1e-5	,							lowerCamelCase_     :    int = 1	,							):
								pass






				def        lowerCAmelCase__			(				self     :    Dict					):
								_lowerCAmelCase  						=ScoreSdeVeSchedulerState.create()
								return self.set_sigmas(
								    __UpperCAmelCase	,							self.config.num_train_timesteps	,							self.config.sigma_min	,							self.config.sigma_max	,							self.config.sampling_eps	,							)






				def        lowerCAmelCase__			(				self     :    Optional[int]	,							lowerCamelCase_     :    ScoreSdeVeSchedulerState	,							lowerCamelCase_     :    int	,							lowerCamelCase_     :    Tuple = ()	,							lowerCamelCase_     :    float = None					):
								_lowerCAmelCase  						=sampling_eps if sampling_eps is not None else self.config.sampling_eps

								_lowerCAmelCase  						=jnp.linspace(1	,							__UpperCAmelCase	,							__UpperCAmelCase					)
								return state.replace(timesteps=__UpperCAmelCase					)






				def        lowerCAmelCase__			(				self     :    Dict	,							lowerCamelCase_     :    ScoreSdeVeSchedulerState	,							lowerCamelCase_     :    int	,							lowerCamelCase_     :    float = None	,							lowerCamelCase_     :    float = None	,							lowerCamelCase_     :    float = None	,							):
								_lowerCAmelCase  						=sigma_min if sigma_min is not None else self.config.sigma_min
								_lowerCAmelCase  						=sigma_max if sigma_max is not None else self.config.sigma_max
								_lowerCAmelCase  						=sampling_eps if sampling_eps is not None else self.config.sampling_eps
								if state.timesteps is None:
												_lowerCAmelCase  						=self.set_timesteps(__UpperCAmelCase	,							__UpperCAmelCase	,							__UpperCAmelCase					)

								_lowerCAmelCase  						=jnp.exp(jnp.linspace(jnp.log(__UpperCAmelCase					)	,							jnp.log(__UpperCAmelCase					)	,							__UpperCAmelCase					)					)
								_lowerCAmelCase  						=jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]					)

								return state.replace(discrete_sigmas=__UpperCAmelCase	,							sigmas=__UpperCAmelCase					)






				def        lowerCAmelCase__			(				self     :    List[str]	,							lowerCamelCase_     :    Union[str, Any]	,							lowerCamelCase_     :    List[str]	,							lowerCamelCase_     :    Optional[Any]					):
								return jnp.where(timesteps == 0	,							jnp.zeros_like(__UpperCAmelCase					)	,							state.discrete_sigmas[timesteps - 1]					)






				def        lowerCAmelCase__			(				self     :    str	,							lowerCamelCase_     :    ScoreSdeVeSchedulerState	,							lowerCamelCase_     :    jnp.ndarray	,							lowerCamelCase_     :    int	,							lowerCamelCase_     :    jnp.ndarray	,							lowerCamelCase_     :    random.KeyArray	,							lowerCamelCase_     :    bool = True	,							):



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

								_lowerCAmelCase  						=timestep * jnp.ones(
								    sample.shape[0]	,							)
								_lowerCAmelCase  						=(timestep * (len(state.timesteps					) - 1)).long()

								_lowerCAmelCase  						=state.discrete_sigmas[timesteps]
								_lowerCAmelCase  						=self.get_adjacent_sigma(__UpperCAmelCase	,							__UpperCAmelCase	,							__UpperCAmelCase					)
								_lowerCAmelCase  						=jnp.zeros_like(__UpperCAmelCase					)
								_lowerCAmelCase  						=(sigma**2 - adjacent_sigma**2) ** 0.5

								# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
								# also equation 47 shows the analog from SDE models to ancestral sampling methods
								_lowerCAmelCase  						=diffusion.flatten()
								_lowerCAmelCase  						=broadcast_to_shape_from_left(__UpperCAmelCase	,							sample.shape					)
								_lowerCAmelCase  						=drift - diffusion**2 * model_output

								#  equation 6: sample noise for the diffusion term of
								_lowerCAmelCase  						=random.split(__UpperCAmelCase	,							num=1					)
								_lowerCAmelCase  						=random.normal(key=__UpperCAmelCase	,							shape=sample.shape					)
								_lowerCAmelCase  						=sample - drift  # subtract because `dt` is a small negative timestep
								# TODO is the variable diffusion the correct scaling term for the noise?
								_lowerCAmelCase  						=prev_sample_mean + diffusion * noise  # add impact of diffusion field g

								if not return_dict:
												return (prev_sample, prev_sample_mean, state)

								return FlaxSdeVeOutput(prev_sample=__UpperCAmelCase	,							prev_sample_mean=__UpperCAmelCase	,							state=__UpperCAmelCase					)






				def        lowerCAmelCase__			(				self     :    Union[str, Any]	,							lowerCamelCase_     :    ScoreSdeVeSchedulerState	,							lowerCamelCase_     :    jnp.ndarray	,							lowerCamelCase_     :    jnp.ndarray	,							lowerCamelCase_     :    random.KeyArray	,							lowerCamelCase_     :    bool = True	,							):



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

								# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
								# sample noise for correction
								_lowerCAmelCase  						=random.split(__UpperCAmelCase	,							num=1					)
								_lowerCAmelCase  						=random.normal(key=__UpperCAmelCase	,							shape=sample.shape					)

								# compute step size from the model_output, the noise, and the snr
								_lowerCAmelCase  						=jnp.linalg.norm(__UpperCAmelCase					)
								_lowerCAmelCase  						=jnp.linalg.norm(__UpperCAmelCase					)
								_lowerCAmelCase  						=(self.config.snr * noise_norm / grad_norm) ** 2 * 2
								_lowerCAmelCase  						=step_size * jnp.ones(sample.shape[0]					)

								# compute corrected sample: model_output term and noise term
								_lowerCAmelCase  						=step_size.flatten()
								_lowerCAmelCase  						=broadcast_to_shape_from_left(__UpperCAmelCase	,							sample.shape					)
								_lowerCAmelCase  						=sample + step_size * model_output
								_lowerCAmelCase  						=prev_sample_mean + ((step_size * 2) ** 0.5) * noise

								if not return_dict:
												return (prev_sample, state)

								return FlaxSdeVeOutput(prev_sample=__UpperCAmelCase	,							state=__UpperCAmelCase					)






				def __len__(				self     :    int					):
								return self.config.num_train_timesteps


"""simple docstring"""




import math
from collections.abc import Generator



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   Generator  				=					(i for i in range(1							, (max_n + 1)						))
					for i in (n for n in numbers if n > 1):
										for j in range(2							, _lowercase						):
															if (i % j) == 0:
																				break
										else:
															yield i



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   Generator  				=					(i for i in range(1							, (max_n + 1)						))
					for i in (n for n in numbers if n > 1):
										# only need to check for factors up to sqrt(i)
										lowerCamelCase__		:   Tuple  				=					int(math.sqrt(_lowercase						)						) + 1
										for j in range(2							, _lowercase						):
															if (i % j) == 0:
																				break
										else:
															yield i



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   Generator  				=					(i for i in range(1							, (max_n + 1)							, 2						))
					# It's useless to test even numbers as they will not be prime
					if max_n > 2:
										yield 2  # Because 2 will not be tested, it's necessary to yield it now
					for i in (n for n in numbers if n > 1):
										lowerCamelCase__		:   Union[str, Any]  				=					int(math.sqrt(_lowercase						)						) + 1
										for j in range(3							, _lowercase							, 2						):
															# As we removed the even numbers, we don't need them now
															if (i % j) == 0:
																				break
										else:
															yield i



def 				__a       (			):







					"""simple docstring"""





					from timeit import timeit

					lowerCamelCase__		:   Any  				=					'''from __main__ import slow_primes, primes, fast_primes'''
					print(timeit('''slow_primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)
					print(timeit('''primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)
					print(timeit('''fast_primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)


if __name__ == "__main__":
					UpperCAmelCase       :    Tuple									=			int(input("Calculate primes up to:\n>> ").strip())
					for ret in primes(number):
										print(ret)
					benchmark()






