


'''simple docstring'''




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

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					:
	# setable values
	_lowerCamelCase :       Optional[jnp.ndarray]         =			None
	_lowerCamelCase :       Optional[jnp.ndarray]         =			None
	_lowerCamelCase :       Optional[jnp.ndarray]         =			None



	@classmethod
	def 					lowercase  (       cls     ):
		return cls()



@dataclass
class 			lowerCAmelCase					(					a				):
	_lowerCamelCase :       ScoreSdeVeSchedulerState
	_lowerCamelCase :       jnp.ndarray
	_lowerCamelCase :       Optional[jnp.ndarray]         =			None



class 			lowerCAmelCase					(					a   ,					a				):



	@property
	def 					lowercase  (       self     ):
		return True



	@register_to_config
	def __init__(       self			,       snake_case__ = 2000			,       snake_case__ = 0.1_5			,       snake_case__ = 0.0_1			,       snake_case__ = 1_3_4_8.0			,       snake_case__ = 1e-5			,       snake_case__ = 1			,       ):
		pass



	def 					lowercase  (       self     ):
		lowerCAmelCase       :     List[Any]   				=			ScoreSdeVeSchedulerState.create()
		return self.set_sigmas(
		    snake_case__			,       self.config.num_train_timesteps			,       self.config.sigma_min			,       self.config.sigma_max			,       self.config.sampling_eps			,       )



	def 					lowercase  (       self			,       snake_case__			,       snake_case__			,       snake_case__ = ()			,       snake_case__ = None     ):
		lowerCAmelCase       :     Dict   				=			sampling_eps if sampling_eps is not None else self.config.sampling_eps

		lowerCAmelCase       :     int   				=			jnp.linspace(1			,       snake_case__			,       snake_case__     )
		return state.replace(timesteps=snake_case__     )



	def 					lowercase  (       self			,       snake_case__			,       snake_case__			,       snake_case__ = None			,       snake_case__ = None			,       snake_case__ = None			,       ):
		lowerCAmelCase       :     Optional[int]   				=			sigma_min if sigma_min is not None else self.config.sigma_min
		lowerCAmelCase       :     List[Any]   				=			sigma_max if sigma_max is not None else self.config.sigma_max
		lowerCAmelCase       :     Dict   				=			sampling_eps if sampling_eps is not None else self.config.sampling_eps
		if state.timesteps is None:
			lowerCAmelCase       :     int   				=			self.set_timesteps(snake_case__			,       snake_case__			,       snake_case__     )

		lowerCAmelCase       :     Union[str, Any]   				=			jnp.exp(jnp.linspace(jnp.log(snake_case__     )			,       jnp.log(snake_case__     )			,       snake_case__     )     )
		lowerCAmelCase       :     str   				=			jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]     )

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



	def 					lowercase  (       self			,       snake_case__			,       snake_case__			,       snake_case__     ):
		return jnp.where(timesteps == 0			,       jnp.zeros_like(snake_case__     )			,       state.discrete_sigmas[timesteps - 1]     )



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

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

		lowerCAmelCase       :     Optional[int]   				=			state.discrete_sigmas[timesteps]
		lowerCAmelCase       :     Optional[int]   				=			self.get_adjacent_sigma(snake_case__			,       snake_case__			,       snake_case__     )
		lowerCAmelCase       :     Any   				=			jnp.zeros_like(snake_case__     )
		lowerCAmelCase       :     Tuple   				=			(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       :     Union[str, Any]   				=			diffusion.flatten()
		lowerCAmelCase       :     Optional[Any]   				=			broadcast_to_shape_from_left(snake_case__			,       sample.shape     )
		lowerCAmelCase       :     Optional[Any]   				=			drift - diffusion**2 * model_output

		#  equation 6: sample noise for the diffusion term of
		lowerCAmelCase       :     Any   				=			random.split(snake_case__			,       num=1     )
		lowerCAmelCase       :     Dict   				=			random.normal(key=snake_case__			,       shape=sample.shape     )
		lowerCAmelCase       :     Optional[int]   				=			sample - drift  # subtract because `dt` is a small negative timestep
		# TODO is the variable diffusion the correct scaling term for the noise?
		lowerCAmelCase       :     Dict   				=			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=snake_case__			,       prev_sample_mean=snake_case__			,       state=snake_case__     )



	def 					lowercase  (       self			,       snake_case__			,       snake_case__			,       snake_case__			,       snake_case__			,       snake_case__ = 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       :     List[str]   				=			random.split(snake_case__			,       num=1     )
		lowerCAmelCase       :     List[Any]   				=			random.normal(key=snake_case__			,       shape=sample.shape     )

		# compute step size from the model_output, the noise, and the snr
		lowerCAmelCase       :     Tuple   				=			jnp.linalg.norm(snake_case__     )
		lowerCAmelCase       :     Dict   				=			jnp.linalg.norm(snake_case__     )
		lowerCAmelCase       :     Optional[Any]   				=			(self.config.snr * noise_norm / grad_norm) ** 2 * 2
		lowerCAmelCase       :     Optional[int]   				=			step_size * jnp.ones(sample.shape[0]     )

		# compute corrected sample: model_output term and noise term
		lowerCAmelCase       :     Tuple   				=			step_size.flatten()
		lowerCAmelCase       :     Optional[Any]   				=			broadcast_to_shape_from_left(snake_case__			,       sample.shape     )
		lowerCAmelCase       :     int   				=			sample + step_size * model_output
		lowerCAmelCase       :     Optional[Any]   				=			prev_sample_mean + ((step_size * 2) ** 0.5) * noise

		if not return_dict:
			return (prev_sample, state)

		return FlaxSdeVeOutput(prev_sample=snake_case__			,       state=snake_case__     )



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




'''simple docstring'''




import math
from collections.abc import Generator

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""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       , _A					):
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""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       :     List[str]   				=			int(math.sqrt(_A					)					) + 1
		for j in range(2       , _A					):
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     _A     :					int					)     ->   Generator[int, None, None]:




	"""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       :     int   				=			int(math.sqrt(_A					)					) + 1
		for j in range(3       , _A       , 2					):
			# As we removed the even numbers, we don't need them now
			if (i % j) == 0:
				break
		else:
			yield i

def       __UpperCamelCase     (     )     ->   Dict:




	"""simple docstring"""





	from timeit import timeit

	lowerCAmelCase       :     Tuple   				=			'from __main__ import slow_primes, primes, fast_primes'
	print(timeit('slow_primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)
	print(timeit('primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)
	print(timeit('fast_primes(1_000_000_000_000)'       , setup=_A       , number=1_00_00_00					)					)


if __name__ == "__main__":
				_lowerCAmelCase	:		Optional[Any]		  =						int(input('Calculate primes up to:\n>> ').strip())
				for ret in primes(number):
								print(ret)
				benchmark()
