



def 						a__	(						_UpperCamelCase	:       int       ,_UpperCamelCase	:       int							):
   return abs(snake_case_							) if a == 0 else greatest_common_divisor(b % a       ,snake_case_							)





def 						a__	(						_UpperCamelCase	:       int       ,_UpperCamelCase	:       int							):







   while y:  # --> when y=0 then loop will terminate and return x as final GCD.
      __lowerCamelCase  							=			y, x % y
   return abs(snake_case_							)





def 						a__	(						):







   try:
      __lowerCamelCase  							=			input('''Enter two integers separated by comma (,): '''							).split(''','''							)
      __lowerCamelCase  							=			int(nums[0]							)
      __lowerCamelCase  							=			int(nums[1]							)
      print(
          F"""greatest_common_divisor({num_a}, {num_a}) = """
          F"""{greatest_common_divisor(snake_case_       ,snake_case_							)}"""							)
      print(F"""By iterative gcd({num_a}, {num_a}) = {gcd_by_iterative(snake_case_       ,snake_case_							)}"""							)
   except (IndexError, UnboundLocalError, ValueError):
      print('''Wrong input'''							)


if __name__ == "__main__":
  main()













"""simple docstring"""



# 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 		__snake_case					:





 """simple docstring"""


 _lowerCamelCase        =     42

 # setable values
 _lowerCamelCase        =     42
 _lowerCamelCase        =     42
 _lowerCamelCase        =     None

 @classmethod
 def 					UpperCamelCase__(    cls					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase  ):



     '''simple docstring'''




     return cls(common=__lowerCamelCase					,						init_noise_sigma=__lowerCamelCase					,						timesteps=__lowerCamelCase  )






@dataclass
class 		__snake_case					(		SCREAMING_SNAKE_CASE__     ):





 """simple docstring"""


 _lowerCamelCase        =     42






class 		__snake_case					(		SCREAMING_SNAKE_CASE__							,							SCREAMING_SNAKE_CASE__     ):





 """simple docstring"""


 _lowerCamelCase        =     [e.name for e in FlaxKarrasDiffusionSchedulers]

 _lowerCamelCase        =     42

 @property
 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     return True

 @register_to_config
 def __init__(    self					,						__lowerCamelCase = 1000					,						__lowerCamelCase = 0.0_0_0_1					,						__lowerCamelCase = 0.0_2					,						__lowerCamelCase = "linear"					,						__lowerCamelCase = None					,						__lowerCamelCase = "fixed_small"					,						__lowerCamelCase = True					,						__lowerCamelCase = "epsilon"					,						__lowerCamelCase = jnp.floataa					,						):



     '''simple docstring'''




     __A    :						Tuple						 =     dtype

 def 					UpperCamelCase__(    self					,						__lowerCamelCase = None  ):



     '''simple docstring'''




     if common is None:
         __A    :						Tuple						 =     CommonSchedulerState.create(self  )

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

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

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

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase = None  ):



     '''simple docstring'''




     return sample

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase = ()  ):



     '''simple docstring'''




     __A    :						Optional[Any]						 =     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    :						Optional[Any]						 =     (jnp.arange(0					,						__lowerCamelCase  ) * step_ratio).round()[::-1]

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

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase=None					,						__lowerCamelCase=None  ):



     '''simple docstring'''




     __A    :						int						 =     state.common.alphas_cumprod[t]
     __A    :						List[str]						 =     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    :						str						 =     (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

     if variance_type is None:
         __A    :						Dict						 =     self.config.variance_type

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

     return variance

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase = None					,						__lowerCamelCase = True					,						):



     '''simple docstring'''




     __A    :						Optional[int]						 =     timestep

     if key is None:
         __A    :						List[Any]						 =     jax.random.PRNGKey(0  )

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

     # 1. compute alphas, betas
     __A    :						Dict						 =     state.common.alphas_cumprod[t]
     __A    :						int						 =     jnp.where(t > 0					,						state.common.alphas_cumprod[t - 1]					,						jnp.array(1.0					,						dtype=self.dtype  )  )
     __A    :						Tuple						 =     1 - alpha_prod_t
     __A    :						Optional[int]						 =     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    :						Optional[Any]						 =     (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
     elif self.config.prediction_type == "sample":
         __A    :						Any						 =     model_output
     elif self.config.prediction_type == "v_prediction":
         __A    :						str						 =     (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    :						str						 =     jnp.clip(__lowerCamelCase					,						-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    :						Optional[Any]						 =     (alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
     __A    :						Union[str, Any]						 =     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    :						Optional[Any]						 =     pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

     # 6. Add noise
     def random_variance():
         __A    :						List[Any]						 =     jax.random.split(__lowerCamelCase					,						num=1  )
         __A    :						List[str]						 =     jax.random.normal(__lowerCamelCase					,						shape=model_output.shape					,						dtype=self.dtype  )
         return (self._get_variance(__lowerCamelCase					,						__lowerCamelCase					,						predicted_variance=__lowerCamelCase  ) ** 0.5) * noise

     __A    :						Optional[Any]						 =     jnp.where(t > 0					,						random_variance()					,						jnp.zeros(model_output.shape					,						dtype=self.dtype  )  )

     __A    :						Any						 =     pred_prev_sample + variance

     if not return_dict:
         return (pred_prev_sample, state)

     return FlaxDDPMSchedulerOutput(prev_sample=__lowerCamelCase					,						state=__lowerCamelCase  )

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase					,						):



     '''simple docstring'''




     return add_noise_common(state.common					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase  )

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase					,						):



     '''simple docstring'''




     return get_velocity_common(state.common					,						__lowerCamelCase					,						__lowerCamelCase					,						__lowerCamelCase  )







 def __len__(    self  ):



     '''simple docstring'''




     return self.config.num_train_timesteps




