



"""simple docstring"""




import math
from collections.abc import Generator


def 	lowercase__  (      _UpperCAmelCase					)  ->      Generator[int, None, None]:






      '''simple docstring'''


      lowercase	:   str											= (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						,   _UpperCAmelCase					):
                  if (i % j) == 0:
                        break
            else:
                  yield i


def 	lowercase__  (      _UpperCAmelCase					)  ->      Generator[int, None, None]:






      '''simple docstring'''


      lowercase	:   str											= (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)
            lowercase	:   Optional[Any]											= int(math.sqrt(_UpperCAmelCase					)					) + 1
            for j in range(2						,   _UpperCAmelCase					):
                  if (i % j) == 0:
                        break
            else:
                  yield i


def 	lowercase__  (      _UpperCAmelCase					)  ->      Generator[int, None, None]:






      '''simple docstring'''


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


def 	lowercase__  (      )  ->      Dict:






      '''simple docstring'''


      from timeit import timeit

      lowercase	:   Optional[int]											= 'from __main__ import slow_primes, primes, fast_primes'
      print(timeit('slow_primes(1_000_000_000_000)'						,   setup=_UpperCAmelCase						,   number=1_00_00_00					)					)
      print(timeit('primes(1_000_000_000_000)'						,   setup=_UpperCAmelCase						,   number=1_00_00_00					)					)
      print(timeit('fast_primes(1_000_000_000_000)'						,   setup=_UpperCAmelCase						,   number=1_00_00_00					)					)


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







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

import flax
import jax.numpy as jnp
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    broadcast_to_shape_from_left,
)

@flax.struct.dataclass
class SCREAMING_SNAKE_CASE_			:





					"""simple docstring"""


					A__								=     42

					# setable values
					A__								=     42
					A__								=     42
					A__								=     42
					A__								=     None

					# running values
					A__								=     None





					@classmethod
					def        __magic_name__			(			cls						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						):
										return cls(common=_lowerCAmelCase						,	init_noise_sigma=_lowerCAmelCase						,	timesteps=_lowerCAmelCase						,	sigmas=_lowerCAmelCase						)

@dataclass
class SCREAMING_SNAKE_CASE_			(       lowercase_ ):





					"""simple docstring"""


					A__								=     42

class SCREAMING_SNAKE_CASE_			(       lowercase_				,							lowercase_ ):





					"""simple docstring"""


					A__								=     [e.name for e in FlaxKarrasDiffusionSchedulers]

					A__								=     42





					@property
					def        __magic_name__			(			self						):
										return True





					@register_to_config
					def __init__(			self						,	_lowerCAmelCase = 1000						,	_lowerCAmelCase = 0.0_001						,	_lowerCAmelCase = 0.02						,	_lowerCAmelCase = "linear"						,	_lowerCAmelCase = None						,	_lowerCAmelCase = "epsilon"						,	_lowerCAmelCase = jnp.floataa						,	):
										lowerCamelCase__      =							dtype





					def        __magic_name__			(			self						,	_lowerCAmelCase = None						):
										if common is None:
															lowerCamelCase__      =							CommonSchedulerState.create(self						)

										lowerCamelCase__      =							jnp.arange(0						,	self.config.num_train_timesteps						).round()[::-1]
										lowerCamelCase__      =							((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

										# standard deviation of the initial noise distribution
										lowerCamelCase__      =							sigmas.max()

										return LMSDiscreteSchedulerState.create(
										    common=_lowerCAmelCase						,	init_noise_sigma=_lowerCAmelCase						,	timesteps=_lowerCAmelCase						,	sigmas=_lowerCAmelCase						,	)





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						):
										((lowerCamelCase__)     ,		)      =							jnp.where(state.timesteps == timestep						,	size=1						)
										lowerCamelCase__      =							step_index[0]

										lowerCamelCase__      =							state.sigmas[step_index]
										lowerCamelCase__      =							sample / ((sigma**2 + 1) ** 0.5)
										return sample





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						):

										def lms_derivative(_lowerCAmelCase						):
															lowerCamelCase__      =							1.0
															for k in range(_lowerCAmelCase						):
																				if current_order == k:
																									continue
																				prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
															return prod

										lowerCamelCase__      =							integrate.quad(_lowerCAmelCase						,	state.sigmas[t]						,	state.sigmas[t + 1]						,	epsrel=1E-4						)[0]

										return integrated_coeff





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase = ()						):
										lowerCamelCase__      =							jnp.linspace(self.config.num_train_timesteps - 1						,	0						,	_lowerCAmelCase						,	dtype=self.dtype						)

										lowerCamelCase__      =							jnp.floor(_lowerCAmelCase						).astype(jnp.intaa						)
										lowerCamelCase__      =							jnp.ceil(_lowerCAmelCase						).astype(jnp.intaa						)

										lowerCamelCase__      =							jnp.mod(_lowerCAmelCase						,	1.0						)

										lowerCamelCase__      =							((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
										lowerCamelCase__      =							(1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
										lowerCamelCase__      =							jnp.concatenate([sigmas, jnp.array([0.0]						,	dtype=self.dtype						)]						)

										lowerCamelCase__      =							timesteps.astype(jnp.intaa						)

										# initial running values
										lowerCamelCase__      =							jnp.zeros((0,) + shape						,	dtype=self.dtype						)

										return state.replace(
										    timesteps=_lowerCAmelCase						,	sigmas=_lowerCAmelCase						,	num_inference_steps=_lowerCAmelCase						,	derivatives=_lowerCAmelCase						,	)





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase = 4						,	_lowerCAmelCase = True						,	):
										if state.num_inference_steps is None:
															raise ValueError(
															    "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"						)

										lowerCamelCase__      =							state.sigmas[timestep]

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
															lowerCamelCase__      =							sample - sigma * model_output
										elif self.config.prediction_type == "v_prediction":
															# * c_out + input * c_skip
															lowerCamelCase__      =							model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
										else:
															raise ValueError(
															    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"						)

										# 2. Convert to an ODE derivative
										lowerCamelCase__      =							(sample - pred_original_sample) / sigma
										lowerCamelCase__      =							state.replace(derivatives=jnp.append(state.derivatives						,	_lowerCAmelCase						)						)
										if len(state.derivatives						) > order:
															lowerCamelCase__      =							state.replace(derivatives=jnp.delete(state.derivatives						,	0						)						)

										# 3. Compute linear multistep coefficients
										lowerCamelCase__      =							min(timestep + 1						,	_lowerCAmelCase						)
										lowerCamelCase__      =							[self.get_lms_coefficient(_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						) for curr_order in range(_lowerCAmelCase						)]

										# 4. Compute previous sample based on the derivatives path
										lowerCamelCase__      =							sample + sum(
										    coeff * derivative for coeff, derivative in zip(_lowerCAmelCase						,	reversed(state.derivatives						)						)						)

										if not return_dict:
															return (prev_sample, state)

										return FlaxLMSSchedulerOutput(prev_sample=_lowerCAmelCase						,	state=_lowerCAmelCase						)





					def        __magic_name__			(			self						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	):
										lowerCamelCase__      =							state.sigmas[timesteps].flatten()
										lowerCamelCase__      =							broadcast_to_shape_from_left(_lowerCAmelCase						,	noise.shape						)

										lowerCamelCase__      =							original_samples + noise * sigma

										return noisy_samples






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

