


'''simple docstring'''






from math import isclose, sqrt






def 	_A				(lowerCAmelCase__  :float				,						lowerCAmelCase__  :float				,						lowerCAmelCase__  :float		)   ->  tuple[float, float, float]:




     '''simple docstring'''



     _a			      =							point_y / 4 / point_x
     _a			      =							2 * normal_gradient / (1 + normal_gradient * normal_gradient)
     _a			      =							(1 - normal_gradient * normal_gradient) / (
         1 + normal_gradient * normal_gradient
     )
     _a			      =							(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

     # to find the next point, solve the simultaeneous equations:
     # y^2 + 4x^2 = 100
     # y - b = m * (x - a)
     # ==> A x^2 + B x + C = 0
     _a			      =							outgoing_gradient**2 + 4
     _a			      =							2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
     _a			      =							(point_y - outgoing_gradient * point_x) ** 2 - 1_00

     _a			      =							(
         -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term		)
     ) / (2 * quadratic_term)
     _a			      =							(
         -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term		)
     ) / (2 * quadratic_term)

     # two solutions, one of which is our input point
     _a			      =							x_minus if isclose(lowerCAmelCase__				,						lowerCAmelCase__		) else x_plus
     _a			      =							point_y + outgoing_gradient * (next_x - point_x)

     return next_x, next_y, outgoing_gradient






def 	_A				(lowerCAmelCase__  :float = 1.4				,						lowerCAmelCase__  :float = -9.6		)   ->  int:




     '''simple docstring'''



     _a			      =							0
     _a			      =							first_x_coord
     _a			      =							first_y_coord
     _a			      =							(1_0.1 - point_y) / (0.0 - point_x)

     while not (-0.0_1 <= point_x <= 0.0_1 and point_y > 0):
          _a      ,   _a      ,   _a			      =							next_point(lowerCAmelCase__				,						lowerCAmelCase__				,						lowerCAmelCase__		)
          num_reflections += 1

     return num_reflections


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





'''simple docstring'''






from typing import List, Optional

import numpy as np

from ...processing_utils import ProcessorMixin
from ...utils import to_numpy




class  a     (     _SCREAMING_SNAKE_CASE       ):
 _lowerCAmelCase 					=	"""EncodecFeatureExtractor"""
 _lowerCAmelCase 					=	("""T5Tokenizer""", """T5TokenizerFast""")
 def __init__( self      ,				__magic_name__      ,				__magic_name__						)					->							Optional[Any]:
      super().__init__(__magic_name__      ,				__magic_name__						)
      _a			      =							self.feature_extractor
      _a			      =							False
 def 							__UpperCAmelCase		( self      ,				__magic_name__=None      ,				__magic_name__=None      ,				__magic_name__=True						)					->							Tuple:
      return self.tokenizer.get_decoder_prompt_ids(task=__magic_name__      ,				language=__magic_name__      ,				no_timestamps=__magic_name__						)
 def __call__( self      ,				*__magic_name__      ,				**__magic_name__						)					->							List[str]:
      # For backward compatibility
      if self._in_target_context_manager:
           return self.current_processor(*__magic_name__      ,				**__magic_name__						)

      _a			      =							kwargs.pop('audio'      ,				__magic_name__						)
      _a			      =							kwargs.pop('sampling_rate'      ,				__magic_name__						)
      _a			      =							kwargs.pop('text'      ,				__magic_name__						)
      if len(__magic_name__						) > 0:
           _a			      =							args[0]
           _a			      =							args[1:]

      if audio is None and text is None:
           raise ValueError('You need to specify either an `audio` or `text` input to process.'						)

      if text is not None:
           _a			      =							self.tokenizer(__magic_name__      ,				**__magic_name__						)

      if audio is not None:
           _a			      =							self.feature_extractor(__magic_name__      ,				*__magic_name__      ,				sampling_rate=__magic_name__      ,				**__magic_name__						)

      if audio is None:
           return inputs

      elif text is None:
           return audio_inputs

      else:
           _a			      =							audio_inputs['input_values']
           if "padding_mask" in audio_inputs:
                _a			      =							audio_inputs['padding_mask']
           return inputs
 def 							__UpperCAmelCase		( self      ,				*__magic_name__      ,				**__magic_name__						)					->							Tuple:
      _a			      =							kwargs.pop('audio'      ,				__magic_name__						)
      _a			      =							kwargs.pop('padding_mask'      ,				__magic_name__						)

      if len(__magic_name__						) > 0:
           _a			      =							args[0]
           _a			      =							args[1:]

      if audio_values is not None:
           return self._decode_audio(__magic_name__      ,				padding_mask=__magic_name__						)
      else:
           return self.tokenizer.batch_decode(*__magic_name__      ,				**__magic_name__						)
 def 							__UpperCAmelCase		( self      ,				*__magic_name__      ,				**__magic_name__						)					->							List[Any]:
      return self.tokenizer.decode(*__magic_name__      ,				**__magic_name__						)




 def 							__UpperCAmelCase		( self      ,				__magic_name__      ,				__magic_name__ = None						)					->							List[np.ndarray]:
      _a			      =							to_numpy(__magic_name__						)
      _a      ,   _a      ,   _a			      =							audio_values.shape

      if padding_mask is None:
           return list(__magic_name__						)

      _a			      =							to_numpy(__magic_name__						)

      # match the sequence length of the padding mask to the generated audio arrays by padding with the **non-padding**
      # token (so that the generated audio values are **not** treated as padded tokens)
      _a			      =							seq_len - padding_mask.shape[-1]
      _a			      =							1 - self.feature_extractor.padding_value
      _a			      =							np.pad(__magic_name__      ,				((0, 0), (0, difference))      ,				'constant'      ,				constant_values=__magic_name__						)

      _a			      =							audio_values.tolist()
      for i in range(__magic_name__						):
           _a			      =							np.asarray(audio_values[i]						)[
               padding_mask[i][None, :] != self.feature_extractor.padding_value
           ]
           _a			      =							sliced_audio.reshape(__magic_name__      ,				-1						)

      return audio_values

