



# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

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

import flax
import jax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)
@flax.struct.dataclass
class    __UpperCamelCase			:

 """simple docstring"""



 _lowercase   :    CommonSchedulerState

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

 @classmethod
 def 						_UpperCAmelCase       (	cls		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE      ) ->			List[Any]:
  return cls(common=SCREAMING_SNAKE_CASE		,				init_noise_sigma=SCREAMING_SNAKE_CASE		,				timesteps=SCREAMING_SNAKE_CASE      )





@dataclass
class    __UpperCamelCase			(       _lowercase				):

 """simple docstring"""



 _lowercase   :    DDPMSchedulerState





class    __UpperCamelCase			(       _lowercase	,	_lowercase				):

 """simple docstring"""



 _lowercase   :    Optional[Any]      						=					[e.name for e in FlaxKarrasDiffusionSchedulers]

 _lowercase   :    jnp.dtype

 @property
 def 						_UpperCAmelCase       (	self      ) ->			Any:
  return True

 @register_to_config
 def __init__(	self		,				SCREAMING_SNAKE_CASE = 1_0_0_0		,				SCREAMING_SNAKE_CASE = 0.00_01		,				SCREAMING_SNAKE_CASE = 0.02		,				SCREAMING_SNAKE_CASE = "linear"		,				SCREAMING_SNAKE_CASE = None		,				SCREAMING_SNAKE_CASE = "fixed_small"		,				SCREAMING_SNAKE_CASE = True		,				SCREAMING_SNAKE_CASE = "epsilon"		,				SCREAMING_SNAKE_CASE = jnp.floataa		,				) ->			int:
  a__												= dtype

 def 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE = None      ) ->			DDPMSchedulerState:
  if common is None:
   a__												= CommonSchedulerState.create(self      )

  # standard deviation of the initial noise distribution
  a__												= jnp.array(1.0		,				dtype=self.dtype      )

  a__												= jnp.arange(0		,				self.config.num_train_timesteps      ).round()[::-1]

  return DDPMSchedulerState.create(
      common=SCREAMING_SNAKE_CASE		,				init_noise_sigma=SCREAMING_SNAKE_CASE		,				timesteps=SCREAMING_SNAKE_CASE		,				)

 def 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE = None      ) ->			jnp.ndarray:
  return sample

 def 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE = ()      ) ->			DDPMSchedulerState:
  a__												= self.config.num_train_timesteps // num_inference_steps
  # creates integer timesteps by multiplying by ratio
  # rounding to avoid issues when num_inference_step is power of 3
  a__												= (jnp.arange(0		,				SCREAMING_SNAKE_CASE      ) * step_ratio).round()[::-1]

  return state.replace(
      num_inference_steps=SCREAMING_SNAKE_CASE		,				timesteps=SCREAMING_SNAKE_CASE		,				)

 def 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE=None		,				SCREAMING_SNAKE_CASE=None      ) ->			Union[str, Any]:
  a__												= state.common.alphas_cumprod[t]
  a__												= jnp.where(t > 0		,				state.common.alphas_cumprod[t - 1]		,				jnp.array(1.0		,				dtype=self.dtype      )      )

  # 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
  a__												= (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

  if variance_type is None:
   a__												= self.config.variance_type

  # hacks - were probably added for training stability
  if variance_type == "fixed_small":
   a__												= jnp.clip(SCREAMING_SNAKE_CASE		,				a_min=1e-2_0      )
  # for rl-diffuser https://arxiv.org/abs/2205.09991
  elif variance_type == "fixed_small_log":
   a__												= jnp.log(jnp.clip(SCREAMING_SNAKE_CASE		,				a_min=1e-2_0      )      )
  elif variance_type == "fixed_large":
   a__												= state.common.betas[t]
  elif variance_type == "fixed_large_log":
   # Glide max_log
   a__												= jnp.log(state.common.betas[t]      )
  elif variance_type == "learned":
   return predicted_variance
  elif variance_type == "learned_range":
   a__												= variance
   a__												= state.common.betas[t]
   a__												= (predicted_variance + 1) / 2
   a__												= frac * max_log + (1 - frac) * min_log

  return variance

 def 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE = None		,				SCREAMING_SNAKE_CASE = True		,				) ->			Union[FlaxDDPMSchedulerOutput, Tuple]:
  a__												= timestep

  if key is None:
   a__												= jax.random.PRNGKey(0      )

  if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
   a__							,			a__												= jnp.split(SCREAMING_SNAKE_CASE		,				sample.shape[1]		,				axis=1      )
  else:
   a__												= None

  # 1. compute alphas, betas
  a__												= state.common.alphas_cumprod[t]
  a__												= jnp.where(t > 0		,				state.common.alphas_cumprod[t - 1]		,				jnp.array(1.0		,				dtype=self.dtype      )      )
  a__												= 1 - alpha_prod_t
  a__												= 1 - alpha_prod_t_prev

  # 2. compute predicted original sample from predicted noise also called
  # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
  if self.config.prediction_type == "epsilon":
   a__												= (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
  elif self.config.prediction_type == "sample":
   a__												= model_output
  elif self.config.prediction_type == "v_prediction":
   a__												= (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
  else:
   raise ValueError(
       f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` "
       ''' for the FlaxDDPMScheduler.'''      )

  # 3. Clip "predicted x_0"
  if self.config.clip_sample:
   a__												= jnp.clip(SCREAMING_SNAKE_CASE		,				-1		,				1      )

  # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
  # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
  a__												= (alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
  a__												= state.common.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

  # 5. Compute predicted previous sample µ_t
  # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
  a__												= pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

  # 6. Add noise
  def random_variance():
   a__												= jax.random.split(SCREAMING_SNAKE_CASE		,				num=1      )
   a__												= jax.random.normal(SCREAMING_SNAKE_CASE		,				shape=model_output.shape		,				dtype=self.dtype      )
   return (self._get_variance(SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				predicted_variance=SCREAMING_SNAKE_CASE      ) ** 0.5) * noise

  a__												= jnp.where(t > 0		,				random_variance()		,				jnp.zeros(model_output.shape		,				dtype=self.dtype      )      )

  a__												= pred_prev_sample + variance

  if not return_dict:
   return (pred_prev_sample, state)

  return FlaxDDPMSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE		,				state=SCREAMING_SNAKE_CASE      )

 def 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				) ->			jnp.ndarray:
  return add_noise_common(state.common		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE      )

 def 						_UpperCAmelCase       (	self		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				) ->			jnp.ndarray:
  return get_velocity_common(state.common		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE      )



 def __len__(	self      ) ->			List[Any]:
  return self.config.num_train_timesteps










import math
from collections.abc import Iterator
from itertools import takewhile






def     __a					(		__UpperCAmelCase       ):

 if 1 < number < 4:
  # 2 and 3 are primes
  return True
 elif number < 2 or number % 2 == 0 or number % 3 == 0:
  # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
  return False

 # All primes number are in format of 6k +/- 1
 for i in range(5							,  int(math.sqrt(__UpperCAmelCase       ) + 1       )							,  6       ):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True






def     __a					(		):
 a__												= 2
 while True:
  if is_prime(__UpperCAmelCase       ):
   yield num
  num += 1






def     __a					(		__UpperCAmelCase = 200_0000       ):
 return sum(takewhile(lambda __UpperCAmelCase       : x < n							,  prime_generator()       )       )


if __name__ == "__main__":
     print(f'{solution() = }')





