snake_case__						      =			[0.33, 0.44, 0.55, 0.44, 0.33]
snake_case__						      =			3
snake_case__						      =			5

# Buffer Space (with Parameters Space)
snake_case__						      =			[]
snake_case__						      =			[]

# Machine Time
snake_case__						      =			0
def    __magic_name__(	__UpperCAmelCase		)    ->     Optional[int]:



      '''simple docstring'''

      global buffer_space, params_space, machine_time, K, m, t

      # Choosing Dynamical Systems (All)
      for key, value in enumerate(UpperCAmelCase__		):
            # Evolution Parameter
            _lowerCamelCase           =					float(seed / value		)

            # Control Theory: Orbit Change
            _lowerCamelCase           =					(buffer_space[(key + 1) % m] + e) % 1

            # Control Theory: Trajectory Change
            _lowerCamelCase           =					(params_space[key] + e) % 1 + 3

            # Modification (Transition Function) - Jumps
            _lowerCamelCase           =					round(float(r * value * (1 - value)		)			,    10		)
            _lowerCamelCase           =					r  # Saving to Parameters Space

      # Logistic Map
      assert max(UpperCAmelCase__		) < 1
      assert max(UpperCAmelCase__		) < 4

      # Machine Time
      machine_time += 1
def    __magic_name__(	)    ->     List[Any]:



      '''simple docstring'''

      global buffer_space, params_space, machine_time, K, m, t

      # PRNG (Xorshift by George Marsaglia)
      def xorshift(__UpperCAmelCase			,    __UpperCAmelCase		):
            x ^= y >> 13
            y ^= x << 17
            x ^= y >> 5
            return x

      # Choosing Dynamical Systems (Increment)
      _lowerCamelCase           =					machine_time % m

      # Evolution (Time Length)
      for _ in range(0			,    UpperCAmelCase__		):
            # Variables (Position + Parameters)
            _lowerCamelCase           =					params_space[key]
            _lowerCamelCase           =					buffer_space[key]

            # Modification (Transition Function) - Flow
            _lowerCamelCase           =					round(float(r * value * (1 - value)		)			,    10		)
            _lowerCamelCase           =					(machine_time * 0.0_1 + r * 1.0_1) % 1 + 3

      # Choosing Chaotic Data
      _lowerCamelCase           =					int(buffer_space[(key + 2) % m] * (10**10)		)
      _lowerCamelCase           =					int(buffer_space[(key - 2) % m] * (10**10)		)

      # Machine Time
      machine_time += 1

      return xorshift(UpperCAmelCase__			,    UpperCAmelCase__		) % 0xffff_ffff
def    __magic_name__(	)    ->     str:



      '''simple docstring'''

      global buffer_space, params_space, machine_time, K, m, t

      _lowerCamelCase           =					K
      _lowerCamelCase           =					[0] * m
      _lowerCamelCase           =					0


if __name__ == "__main__":
     # Initialization
     reset()

     # Pushing Data (Input)
     import random

     snake_case__						      =			random.sample(range(0xff_ff_ff_ff), 100)
     for chunk in message:
          push(chunk)

     # for controlling
     snake_case__						      =			""

     # Pulling Data (Output)
     while inp in ("e", "E"):
          print(f'''{format(pull(), "#04x")}''')
          print(buffer_space)
          print(params_space)
          snake_case__						      =			input('(e)exit? ').strip()



"""simple docstring"""






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 	A_       :





  """simple docstring"""

  lowercase		:	CommonSchedulerState

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

  # running values
  lowercase		:	Optional[jnp.ndarray]   =						None
  @classmethod
  def 							lowercase_     (						cls  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase						)				->					Tuple:
     return cls(common=__UpperCAmelCase  ,					init_noise_sigma=__UpperCAmelCase  ,					timesteps=__UpperCAmelCase  ,					sigmas=__UpperCAmelCase						)



@dataclass
class 	A_       (     _UpperCAmelCase   ):





  """simple docstring"""

  lowercase		:	LMSDiscreteSchedulerState



class 	A_       (     _UpperCAmelCase      ,  _UpperCAmelCase   ):





  """simple docstring"""

  lowercase		:	int   =						[e.name for e in FlaxKarrasDiffusionSchedulers]

  lowercase		:	jnp.dtype
  @property
  def 							lowercase_     (						self						)				->					Union[str, Any]:
     return True
  @register_to_config
  def __init__(						self  ,					__UpperCAmelCase = 10_00  ,					__UpperCAmelCase = 0.0001  ,					__UpperCAmelCase = 0.02  ,					__UpperCAmelCase = "linear"  ,					__UpperCAmelCase = None  ,					__UpperCAmelCase = "epsilon"  ,					__UpperCAmelCase = jnp.floataa  ,					)				->					Union[str, Any]:
     a   :	Dict						=    dtype
  def 							lowercase_     (						self  ,					__UpperCAmelCase = None						)				->					LMSDiscreteSchedulerState:
     if common is None:
        a   :	Dict						=    CommonSchedulerState.create(self						)

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

     # standard deviation of the initial noise distribution
     a   :	Union[str, Any]						=    sigmas.max()

     return LMSDiscreteSchedulerState.create(
         common=__UpperCAmelCase  ,					init_noise_sigma=__UpperCAmelCase  ,					timesteps=__UpperCAmelCase  ,					sigmas=__UpperCAmelCase  ,					)
  def 							lowercase_     (						self  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase						)				->					jnp.ndarray:
     ((a)	, )   :	Optional[int]						=    jnp.where(state.timesteps == timestep  ,					size=1						)
     a   :	Optional[Any]						=    step_index[0]

     a   :	Union[str, Any]						=    state.sigmas[step_index]
     a   :	Optional[int]						=    sample / ((sigma**2 + 1) ** 0.5)
     return sample
  def 							lowercase_     (						self  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase						)				->					Optional[int]:

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

     a   :	Union[str, Any]						=    integrate.quad(__UpperCAmelCase  ,					state.sigmas[t]  ,					state.sigmas[t + 1]  ,					epsrel=1E-4						)[0]

     return integrated_coeff
  def 							lowercase_     (						self  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase = ()						)				->					LMSDiscreteSchedulerState:
     a   :	Optional[int]						=    jnp.linspace(self.config.num_train_timesteps - 1  ,					0  ,					__UpperCAmelCase  ,					dtype=self.dtype						)

     a   :	Dict						=    jnp.floor(__UpperCAmelCase						).astype(jnp.intaa						)
     a   :	str						=    jnp.ceil(__UpperCAmelCase						).astype(jnp.intaa						)

     a   :	List[Any]						=    jnp.mod(__UpperCAmelCase  ,					1.0						)

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

     a   :	Any						=    timesteps.astype(jnp.intaa						)

     # initial running values
     a   :	Optional[int]						=    jnp.zeros((0,) + shape  ,					dtype=self.dtype						)

     return state.replace(
         timesteps=__UpperCAmelCase  ,					sigmas=__UpperCAmelCase  ,					num_inference_steps=__UpperCAmelCase  ,					derivatives=__UpperCAmelCase  ,					)
  def 							lowercase_     (						self  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase = 4  ,					__UpperCAmelCase = True  ,					)				->					Union[FlaxLMSSchedulerOutput, Tuple]:
     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'						)

     a   :	Dict						=    state.sigmas[timestep]

     # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
     if self.config.prediction_type == "epsilon":
        a   :	Any						=    sample - sigma * model_output
     elif self.config.prediction_type == "v_prediction":
        # * c_out + input * c_skip
        a   :	str						=    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
     a   :	str						=    (sample - pred_original_sample) / sigma
     a   :	int						=    state.replace(derivatives=jnp.append(state.derivatives  ,					__UpperCAmelCase						)						)
     if len(state.derivatives						) > order:
        a   :	Any						=    state.replace(derivatives=jnp.delete(state.derivatives  ,					0						)						)

     # 3. Compute linear multistep coefficients
     a   :	Any						=    min(timestep + 1  ,					__UpperCAmelCase						)
     a   :	Dict						=    [self.get_lms_coefficient(__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase						) for curr_order in range(__UpperCAmelCase						)]

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

     if not return_dict:
        return (prev_sample, state)

     return FlaxLMSSchedulerOutput(prev_sample=__UpperCAmelCase  ,					state=__UpperCAmelCase						)
  def 							lowercase_     (						self  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase  ,					)				->					jnp.ndarray:
     a   :	Dict						=    state.sigmas[timesteps].flatten()
     a   :	Union[str, Any]						=    broadcast_to_shape_from_left(__UpperCAmelCase  ,					noise.shape						)

     a   :	List[Any]						=    original_samples + noise * sigma

     return noisy_samples






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





