





'''simple docstring'''






import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

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





def    lowercase_   (		lowercase__					,	lowercase__=0.9_9_9					,	lowercase__="cosine"					,	) ->List[Any]:
						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 * -1_2.0    )

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

						_snake_case: Union[str, Any]	       =		[]
						for i in range(lowercase__    ):
												_snake_case: Optional[Any]	       =		i / num_diffusion_timesteps
												_snake_case: str	       =		(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       lowerCamelCase       (    __UpperCAmelCase  ,				__UpperCAmelCase	):
					_SCREAMING_SNAKE_CASE				 =     [e.name for e in KarrasDiffusionSchedulers]
					_SCREAMING_SNAKE_CASE				 =     2


					@register_to_config
					def __init__(       self						:	List[Any]							,  __snake_case						:	int = 10_00							,  __snake_case						:	float = 0.00_085							,  __snake_case						:	float = 0.012							,  __snake_case						:	str = "linear"							,  __snake_case						:	Optional[Union[np.ndarray, List[float]]] = None							,  __snake_case						:	str = "epsilon"							,  __snake_case						:	str = "linspace"							,  __snake_case						:	int = 0							,  ):





											'''simple docstring'''





											if trained_betas is not None:
																	_snake_case: Optional[int]	       =		torch.tensor(__snake_case							,  dtype=torch.floataa							)
											elif beta_schedule == "linear":
																	_snake_case: Any	       =		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.
																	_snake_case: str	       =		(
																	    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
																	_snake_case: Tuple	       =		betas_for_alpha_bar(__snake_case							)
											else:
																	raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''							)

											_snake_case: Union[str, Any]	       =		1.0 - self.betas
											_snake_case: Optional[Any]	       =		torch.cumprod(self.alphas							,  dim=0							)

											#  set all values
											self.set_timesteps(__snake_case							,  __snake_case							,  __snake_case							)


					def  SCREAMING_SNAKE_CASE_		(       self						:	int							,  __snake_case						:	Dict							,  __snake_case						:	List[Any]=None							):





											'''simple docstring'''





											if schedule_timesteps is None:
																	_snake_case: Dict	       =		self.timesteps

											_snake_case: Any	       =		(schedule_timesteps == timestep).nonzero()

											# The sigma index that is taken for the **very** first `step`
											# is always the second index (or the last index if there is only 1)
											# This way we can ensure we don't accidentally skip a sigma in
											# case we start in the middle of the denoising schedule (e.g. for image-to-image)
											if len(self._index_counter							) == 0:
																	_snake_case: Optional[Any]	       =		1 if len(__snake_case							) > 1 else 0
											else:
																	_snake_case: Optional[int]	       =		timestep.cpu().item() if torch.is_tensor(__snake_case							) else timestep
																	_snake_case: int	       =		self._index_counter[timestep_int]

											return indices[pos].item()


					@property
					def  SCREAMING_SNAKE_CASE_		(       self						:	Optional[Any]							):





											'''simple docstring'''





											if self.config.timestep_spacing in ["linspace", "trailing"]:
																	return self.sigmas.max()

											return (self.sigmas.max() ** 2 + 1) ** 0.5


					def  SCREAMING_SNAKE_CASE_		(       self						:	Dict							,  __snake_case						:	torch.FloatTensor							,  __snake_case						:	Union[float, torch.FloatTensor]							,  ):





											'''simple docstring'''





											_snake_case: int	       =		self.index_for_timestep(__snake_case							)

											if self.state_in_first_order:
																	_snake_case: List[str]	       =		self.sigmas[step_index]
											else:
																	_snake_case: int	       =		self.sigmas_interpol[step_index - 1]

											_snake_case: List[str]	       =		sample / ((sigma**2 + 1) ** 0.5)
											return sample


					def  SCREAMING_SNAKE_CASE_		(       self						:	Optional[Any]							,  __snake_case						:	int							,  __snake_case						:	Union[str, torch.device] = None							,  __snake_case						:	Optional[int] = None							,  ):





											'''simple docstring'''





											_snake_case: Union[str, Any]	       =		num_inference_steps

											_snake_case: Optional[Any]	       =		num_train_timesteps or self.config.num_train_timesteps

											# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
											if self.config.timestep_spacing == "linspace":
																	_snake_case: Tuple	       =		np.linspace(0							,  num_train_timesteps - 1							,  __snake_case							,  dtype=__snake_case							)[::-1].copy()
											elif self.config.timestep_spacing == "leading":
																	_snake_case: int	       =		num_train_timesteps // self.num_inference_steps
																	# creates integer timesteps by multiplying by ratio
																	# casting to int to avoid issues when num_inference_step is power of 3
																	_snake_case: Optional[int]	       =		(np.arange(0							,  __snake_case							) * step_ratio).round()[::-1].copy().astype(__snake_case							)
																	timesteps += self.config.steps_offset
											elif self.config.timestep_spacing == "trailing":
																	_snake_case: Any	       =		num_train_timesteps / self.num_inference_steps
																	# creates integer timesteps by multiplying by ratio
																	# casting to int to avoid issues when num_inference_step is power of 3
																	_snake_case: str	       =		(np.arange(__snake_case							,  0							,  -step_ratio							)).round().copy().astype(__snake_case							)
																	timesteps -= 1
											else:
																	raise ValueError(
																	    f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''							)

											_snake_case: Union[str, Any]	       =		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
											_snake_case: str	       =		torch.from_numpy(np.log(__snake_case							)							).to(__snake_case							)

											_snake_case: str	       =		np.interp(__snake_case							,  np.arange(0							,  len(__snake_case							)							)							,  __snake_case							)
											_snake_case: Tuple	       =		np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)
											_snake_case: Optional[int]	       =		torch.from_numpy(__snake_case							).to(device=__snake_case							)

											# compute up and down sigmas
											_snake_case: List[Any]	       =		sigmas.roll(-1							)
											_snake_case: Tuple	       =		0.0
											_snake_case: List[str]	       =		(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
											_snake_case: Union[str, Any]	       =		(sigmas_next**2 - sigmas_up**2) ** 0.5
											_snake_case: Any	       =		0.0

											# compute interpolated sigmas
											_snake_case: int	       =		sigmas.log().lerp(sigmas_down.log()							,  0.5							).exp()
											_snake_case: Optional[int]	       =		0.0

											# set sigmas
											_snake_case: Optional[int]	       =		torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2							), sigmas[-1:]]							)
											_snake_case: Union[str, Any]	       =		torch.cat(
											    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2							), sigmas_interpol[-1:]]							)
											_snake_case: int	       =		torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2							), sigmas_up[-1:]]							)
											_snake_case: Optional[int]	       =		torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2							), sigmas_down[-1:]]							)

											if str(__snake_case							).startswith('mps'							):
																	# mps does not support float64
																	_snake_case: Optional[Any]	       =		torch.from_numpy(__snake_case							).to(__snake_case							,  dtype=torch.floataa							)
											else:
																	_snake_case: List[str]	       =		torch.from_numpy(__snake_case							).to(__snake_case							)

											_snake_case: Dict	       =		self.sigma_to_t(__snake_case							).to(__snake_case							,  dtype=timesteps.dtype							)
											_snake_case: Optional[Any]	       =		torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])							,  dim=-1							).flatten()

											_snake_case: Optional[int]	       =		torch.cat([timesteps[:1], interleaved_timesteps]							)

											_snake_case: Union[str, Any]	       =		None

											# for exp beta schedules, such as the one for `pipeline_shap_e.py`
											# we need an index counter
											_snake_case: Union[str, Any]	       =		defaultdict(__snake_case							)


					def  SCREAMING_SNAKE_CASE_		(       self						:	List[str]							,  __snake_case						:	Tuple							):





											'''simple docstring'''





											_snake_case: Any	       =		sigma.log()

											# get distribution
											_snake_case: Tuple	       =		log_sigma - self.log_sigmas[:, None]

											# get sigmas range
											_snake_case: Union[str, Any]	       =		dists.ge(0							).cumsum(dim=0							).argmax(dim=0							).clamp(max=self.log_sigmas.shape[0] - 2							)
											_snake_case: Optional[Any]	       =		low_idx + 1

											_snake_case: Tuple	       =		self.log_sigmas[low_idx]
											_snake_case: Tuple	       =		self.log_sigmas[high_idx]

											# interpolate sigmas
											_snake_case: Tuple	       =		(low - log_sigma) / (low - high)
											_snake_case: Tuple	       =		w.clamp(0							,  1							)

											# transform interpolation to time range
											_snake_case: Dict	       =		(1 - w) * low_idx + w * high_idx
											_snake_case: str	       =		t.view(sigma.shape							)
											return t


					@property
					def  SCREAMING_SNAKE_CASE_		(       self						:	int							):





											'''simple docstring'''





											return self.sample is None


					def  SCREAMING_SNAKE_CASE_		(       self						:	List[str]							,  __snake_case						:	Union[torch.FloatTensor, np.ndarray]							,  __snake_case						:	Union[float, torch.FloatTensor]							,  __snake_case						:	Union[torch.FloatTensor, np.ndarray]							,  __snake_case						:	Optional[torch.Generator] = None							,  __snake_case						:	bool = True							,  ):





											'''simple docstring'''





											_snake_case: Tuple	       =		self.index_for_timestep(__snake_case							)

											# advance index counter by 1
											_snake_case: Tuple	       =		timestep.cpu().item() if torch.is_tensor(__snake_case							) else timestep
											self._index_counter[timestep_int] += 1

											if self.state_in_first_order:
																	_snake_case: Optional[Any]	       =		self.sigmas[step_index]
																	_snake_case: Union[str, Any]	       =		self.sigmas_interpol[step_index]
																	_snake_case: Optional[Any]	       =		self.sigmas_up[step_index]
																	_snake_case: List[str]	       =		self.sigmas_down[step_index - 1]
											else:
																	# 2nd order / KPDM2's method
																	_snake_case: Any	       =		self.sigmas[step_index - 1]
																	_snake_case: Dict	       =		self.sigmas_interpol[step_index - 1]
																	_snake_case: List[str]	       =		self.sigmas_up[step_index - 1]
																	_snake_case: Any	       =		self.sigmas_down[step_index - 1]

											# currently only gamma=0 is supported. This usually works best anyways.
											# We can support gamma in the future but then need to scale the timestep before
											# passing it to the model which requires a change in API
											_snake_case: Optional[int]	       =		0
											_snake_case: Union[str, Any]	       =		sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

											_snake_case: List[Any]	       =		model_output.device
											_snake_case: Tuple	       =		randn_tensor(model_output.shape							,  dtype=model_output.dtype							,  device=__snake_case							,  generator=__snake_case							)

											# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
											if self.config.prediction_type == "epsilon":
																	_snake_case: int	       =		sigma_hat if self.state_in_first_order else sigma_interpol
																	_snake_case: Dict	       =		sample - sigma_input * model_output
											elif self.config.prediction_type == "v_prediction":
																	_snake_case: Any	       =		sigma_hat if self.state_in_first_order else sigma_interpol
																	_snake_case: Union[str, Any]	       =		model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
																	    sample / (sigma_input**2 + 1)
																	)
											elif self.config.prediction_type == "sample":
																	raise NotImplementedError('prediction_type not implemented yet: sample'							)
											else:
																	raise ValueError(
																	    f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''							)

											if self.state_in_first_order:
																	# 2. Convert to an ODE derivative for 1st order
																	_snake_case: Dict	       =		(sample - pred_original_sample) / sigma_hat
																	# 3. delta timestep
																	_snake_case: Optional[int]	       =		sigma_interpol - sigma_hat

																	# store for 2nd order step
																	_snake_case: Optional[int]	       =		sample
																	_snake_case: Tuple	       =		dt
																	_snake_case: int	       =		sample + derivative * dt
											else:
																	# DPM-Solver-2
																	# 2. Convert to an ODE derivative for 2nd order
																	_snake_case: str	       =		(sample - pred_original_sample) / sigma_interpol
																	# 3. delta timestep
																	_snake_case: Dict	       =		sigma_down - sigma_hat

																	_snake_case: Optional[Any]	       =		self.sample
																	_snake_case: List[Any]	       =		None

																	_snake_case: List[Any]	       =		sample + derivative * dt
																	_snake_case: Dict	       =		prev_sample + noise * sigma_up

											if not return_dict:
																	return (prev_sample,)

											return SchedulerOutput(prev_sample=__snake_case							)


					def  SCREAMING_SNAKE_CASE_		(       self						:	Any							,  __snake_case						:	torch.FloatTensor							,  __snake_case						:	torch.FloatTensor							,  __snake_case						:	torch.FloatTensor							,  ):





											'''simple docstring'''





											_snake_case: Union[str, Any]	       =		self.sigmas.to(device=original_samples.device							,  dtype=original_samples.dtype							)
											if original_samples.device.type == "mps" and torch.is_floating_point(__snake_case							):
																	# mps does not support float64
																	_snake_case: List[str]	       =		self.timesteps.to(original_samples.device							,  dtype=torch.floataa							)
																	_snake_case: Union[str, Any]	       =		timesteps.to(original_samples.device							,  dtype=torch.floataa							)
											else:
																	_snake_case: int	       =		self.timesteps.to(original_samples.device							)
																	_snake_case: str	       =		timesteps.to(original_samples.device							)

											_snake_case: Dict	       =		[self.index_for_timestep(__snake_case							,  __snake_case							) for t in timesteps]

											_snake_case: str	       =		sigmas[step_indices].flatten()
											while len(sigma.shape							) < len(original_samples.shape							):
																	_snake_case: Union[str, Any]	       =		sigma.unsqueeze(-1							)

											_snake_case: Union[str, Any]	       =		original_samples + noise * sigma
											return noisy_samples




					def __len__(       self						:	Optional[Any]							):





											'''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()





