





'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowercase__						:      List[Any]	=    {
    "configuration_nllb_moe": [
        "NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "NllbMoeConfig",
    ]
}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowercase__						:      Dict	=    [
       "NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST",
       "NllbMoeForConditionalGeneration",
       "NllbMoeModel",
       "NllbMoePreTrainedModel",
       "NllbMoeTop2Router",
       "NllbMoeSparseMLP",
   ]


if TYPE_CHECKING:
   from .configuration_nllb_moe import (
       NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP,
       NllbMoeConfig,
   )

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_nllb_moe import (
          NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST,
          NllbMoeForConditionalGeneration,
          NllbMoeModel,
          NllbMoePreTrainedModel,
          NllbMoeSparseMLP,
          NllbMoeTopaRouter,
      )


else:
   import sys

   lowercase__						:      List[str]	=    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)









'''simple docstring'''

from math import isclose, sqrt







def  a__    (    lowercase :					float, lowercase :					float, lowercase :					float				)		->		tuple[float, float, float]:





     """simple docstring"""

     _UpperCamelCase       =	point_y / 4 / point_x
     _UpperCamelCase       =	2 * normal_gradient / (1 + normal_gradient * normal_gradient)
     _UpperCamelCase       =	(1 - normal_gradient * normal_gradient) / (
         1 + normal_gradient * normal_gradient
     )
     _UpperCamelCase       =	(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
     _UpperCamelCase       =	outgoing_gradient**2 + 4
     _UpperCamelCase       =	2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
     _UpperCamelCase       =	(point_y - outgoing_gradient * point_x) ** 2 - 100

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

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

     return next_x, next_y, outgoing_gradient







def  a__    (    lowercase :					float = 1.4, lowercase :					float = -9.6				)		->		int:





     """simple docstring"""

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

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

     return num_reflections


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



