
import math
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 							lowercase   (						__UpperCAmelCase  ):
		__lowercase			:			Union[str, Any]      	=							42
		__lowercase			:			Optional[int]      	=							42






def  A			(   lowercase       ,			lowercase=0.9_9_9       ,			lowercase="cosine"       ,			)  ->    Optional[int]:
		'''simple docstring'''

		if alpha_transform_type == "cosine":

				def alpha_bar_fn(lowercase					):
						return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2					) ** 2

		elif alpha_transform_type == "exp":

				def alpha_bar_fn(lowercase					):
						return math.exp(t * -12.0					)

		else:
				raise ValueError(f'''Unsupported alpha_tranform_type: {alpha_transform_type}'''					)

		UpperCamelCase            =	[]
		for i in range(lowercase__					):
				UpperCamelCase            =	i / num_diffusion_timesteps
				UpperCamelCase            =	(i + 1) / num_diffusion_timesteps
				betas.append(min(1 - alpha_bar_fn(lowercase__					) / alpha_bar_fn(lowercase__					)       ,			lowercase__					)					)
		return torch.tensor(lowercase__       ,			dtype=torch.floataa					)


class 							lowercase   (						__UpperCAmelCase    ,  __UpperCAmelCase  ):
		__lowercase			:			List[Any]      	=							1



		@register_to_config
		def __init__(					self							, A_ = 1_000							, A_ = 0.0001							, A_ = 0.02							, A_ = "linear"							, A_ = 0.0							, A_ = None							, A_ = True							, )    ->   Optional[int]:
				"""simple docstring"""





				if trained_betas is not None:
						UpperCamelCase            =	torch.from_numpy(__snake_case			)
				elif beta_schedule == "linear":
						UpperCamelCase            =	torch.linspace(__snake_case							, __snake_case							, __snake_case							, dtype=torch.floataa			)
				elif beta_schedule == "scaled_linear":
						# this schedule is very specific to the latent diffusion model.
						UpperCamelCase            =	(
						    torch.linspace(beta_start**0.5							, beta_end**0.5							, __snake_case							, dtype=torch.floataa			) ** 2
						)
				elif beta_schedule == "squaredcos_cap_v2":
						# Glide cosine schedule
						UpperCamelCase            =	betas_for_alpha_bar(__snake_case			)
				elif beta_schedule == "sigmoid":
						# GeoDiff sigmoid schedule
						UpperCamelCase            =	torch.linspace(-6							, 6							, __snake_case			)
						UpperCamelCase            =	torch.sigmoid(__snake_case			) * (beta_end - beta_start) + beta_start
				else:
						raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''			)

				UpperCamelCase            =	1.0 - self.betas
				UpperCamelCase            =	torch.cumprod(self.alphas							, dim=0			)
				UpperCamelCase            =	torch.tensor(1.0			)

				UpperCamelCase            =	torch.tensor(1.0			)

				# standard deviation of the initial noise distribution
				UpperCamelCase            =	1.0

				# setable values
				UpperCamelCase            =	None
				UpperCamelCase            =	torch.from_numpy(np.arange(0							, __snake_case			)[::-1].copy()			)

				UpperCamelCase            =	eta



		def __UpperCamelCase					(					self							, A_							, A_ = None			)    ->   str:
				"""simple docstring"""
				return sample



		def __UpperCamelCase					(					self							, A_							, A_ = 10							, A_ = 10							, A_ = None							, )    ->   Any:
				"""simple docstring"""
				UpperCamelCase            =	min(self.config.num_train_timesteps							, __snake_case			)
				UpperCamelCase            =	num_inference_steps

				UpperCamelCase            =	[]

				UpperCamelCase            =	{}
				for j in range(0							, num_inference_steps - jump_length							, __snake_case			):
						UpperCamelCase            =	jump_n_sample - 1

				UpperCamelCase            =	num_inference_steps
				while t >= 1:
						UpperCamelCase            =	t - 1
						timesteps.append(__snake_case			)

						if jumps.get(__snake_case							, 0			) > 0:
								UpperCamelCase            =	jumps[t] - 1
								for _ in range(__snake_case			):
										UpperCamelCase            =	t + 1
										timesteps.append(__snake_case			)

				UpperCamelCase            =	np.array(__snake_case			) * (self.config.num_train_timesteps // self.num_inference_steps)
				UpperCamelCase            =	torch.from_numpy(__snake_case			).to(__snake_case			)



		def __UpperCamelCase					(					self							, A_			)    ->   Tuple:
				"""simple docstring"""
				UpperCamelCase            =	t - self.config.num_train_timesteps // self.num_inference_steps

				UpperCamelCase            =	self.alphas_cumprod[t]
				UpperCamelCase            =	self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
				UpperCamelCase            =	1 - alpha_prod_t
				UpperCamelCase            =	1 - alpha_prod_t_prev

				# For t > 0, compute predicted variance βt (see formula (6) and (7) from
				# https://arxiv.org/pdf/2006.11239.pdf) and sample from it to get
				# previous sample x_{t-1} ~ N(pred_prev_sample, variance) == add
				# variance to pred_sample
				# Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
				# without eta.
				# variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
				UpperCamelCase            =	(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

				return variance



		def __UpperCamelCase					(					self							, A_							, A_							, A_							, A_							, A_							, A_ = None							, A_ = True							, )    ->   Optional[Any]:
				"""simple docstring"""
				UpperCamelCase            =	timestep
				UpperCamelCase            =	timestep - self.config.num_train_timesteps // self.num_inference_steps

				# 1. compute alphas, betas
				UpperCamelCase            =	self.alphas_cumprod[t]
				UpperCamelCase            =	self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
				UpperCamelCase            =	1 - alpha_prod_t

				# 2. compute predicted original sample from predicted noise also called
				# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
				UpperCamelCase            =	(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

				# 3. Clip "predicted x_0"
				if self.config.clip_sample:
						UpperCamelCase            =	torch.clamp(__snake_case							, -1							, 1			)

				# We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
				# substitute formula (7) in the algorithm coming from DDPM paper
				# (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
				# DDIM schedule gives the same results as DDPM with eta = 1.0
				# Noise is being reused in 7. and 8., but no impact on quality has
				# been observed.

				# 5. Add noise
				UpperCamelCase            =	model_output.device
				UpperCamelCase            =	randn_tensor(model_output.shape							, generator=__snake_case							, device=__snake_case							, dtype=model_output.dtype			)
				UpperCamelCase            =	self.eta * self._get_variance(__snake_case			) ** 0.5

				UpperCamelCase            =	0
				if t > 0 and self.eta > 0:
						UpperCamelCase            =	std_dev_t * noise

				# 6. compute "direction pointing to x_t" of formula (12)
				# from https://arxiv.org/pdf/2010.02502.pdf
				UpperCamelCase            =	(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

				# 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
				UpperCamelCase            =	alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance

				# 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
				UpperCamelCase            =	(alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise

				# 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
				UpperCamelCase            =	mask * prev_known_part + (1.0 - mask) * prev_unknown_part

				if not return_dict:
						return (
						    pred_prev_sample,
						    pred_original_sample,
						)

				return RePaintSchedulerOutput(prev_sample=__snake_case							, pred_original_sample=__snake_case			)



		def __UpperCamelCase					(					self							, A_							, A_							, A_=None			)    ->   str:
				"""simple docstring"""
				UpperCamelCase            =	self.config.num_train_timesteps // self.num_inference_steps

				for i in range(__snake_case			):
						UpperCamelCase            =	self.betas[timestep + i]
						if sample.device.type == "mps":
								# randn does not work reproducibly on mps
								UpperCamelCase            =	randn_tensor(sample.shape							, dtype=sample.dtype							, generator=__snake_case			)
								UpperCamelCase            =	noise.to(sample.device			)
						else:
								UpperCamelCase            =	randn_tensor(sample.shape							, generator=__snake_case							, device=sample.device							, dtype=sample.dtype			)

						# 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
						UpperCamelCase            =	(1 - beta) ** 0.5 * sample + beta**0.5 * noise

				return sample



		def __UpperCamelCase					(					self							, A_							, A_							, A_							, )    ->   Optional[Any]:
				"""simple docstring"""
				raise NotImplementedError('Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.'			)



		def __len__(					self			)    ->   List[str]:
				"""simple docstring"""
				return self.config.num_train_timesteps







'''simple docstring'''






import math
from collections.abc import Generator





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: 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    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: 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)
												_snake_case: int	       =		int(math.sqrt(lowercase__    )    ) + 1
												for j in range(2					,	lowercase__    ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: 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):
												_snake_case: List[str]	       =		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    lowercase_   (		) ->Optional[int]:
						from timeit import timeit

						_snake_case: Dict	       =		'from __main__ import slow_primes, primes, fast_primes'
						print(timeit('slow_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('fast_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )


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





