

"""simple docstring"""





from math import isclose, sqrt




def   _A  (  UpperCamelCase_					:	float,      UpperCamelCase_					:	float,      UpperCamelCase_					:	float)     ->						tuple[float, float, float]:
   '''simple docstring'''


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

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

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

   return next_x, next_y, outgoing_gradient




def   _A  (  UpperCamelCase_					:	float = 1.4,      UpperCamelCase_					:	float = -9.6)     ->						int:
   '''simple docstring'''


   __lowercase								=						0
   __lowercase								=						first_x_coord
   __lowercase								=						first_y_coord
   __lowercase								=						(10.1 - point_y) / (0.0 - point_x)

   while not (-0.01 <= point_x <= 0.01 and point_y > 0):
      __lowercase		,__lowercase		,__lowercase								=						next_point(UpperCamelCase_,      UpperCamelCase_,      UpperCamelCase_)
      num_reflections += 1

   return num_reflections


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







"""simple docstring"""





import argparse
import os
import re


_a							=							'src/transformers/models/auto'


# re pattern that matches mapping introductions:
#    SUPER_MODEL_MAPPING_NAMES = OrderedDict or SUPER_MODEL_MAPPING = OrderedDict
_a							=							re.compile(r'[A-Z_]+_MAPPING(\s+|_[A-Z_]+\s+)=\s+OrderedDict')
# re pattern that matches identifiers in mappings
_a							=							re.compile(r'\s*\(\s*"(\S[^"]+)"')




def   _A  (  UpperCamelCase_					:	Any,      UpperCamelCase_					:	bool = False)     ->						Optional[Any]:
   '''simple docstring'''


   with open(UpperCamelCase_,      "r",      encoding="utf-8") as f:
      __lowercase								=						f.read()

   __lowercase								=						content.split("\n")
   __lowercase								=						[]
   __lowercase								=						0
   while line_idx < len(UpperCamelCase_):
      if _re_intro_mapping.search(lines[line_idx]) is not None:
         __lowercase								=						len(re.search(r"^(\s*)\S",      lines[line_idx]).groups()[0]) + 8
         # Start of a new mapping!
         while not lines[line_idx].startswith(" " * indent + "("):
            new_lines.append(lines[line_idx])
            line_idx += 1

         __lowercase								=						[]
         while lines[line_idx].strip() != "]":
            # Blocks either fit in one line or not
            if lines[line_idx].strip() == "(":
               __lowercase								=						line_idx
               while not lines[line_idx].startswith(" " * indent + ")"):
                  line_idx += 1
               blocks.append("\n".join(lines[start_idx : line_idx + 1]))
            else:
               blocks.append(lines[line_idx])
            line_idx += 1

         # Sort blocks by their identifiers
         __lowercase								=						sorted(UpperCamelCase_,      key=lambda UpperCamelCase_: _re_identifier.search(UpperCamelCase_).groups()[0])
         new_lines += blocks
      else:
         new_lines.append(lines[line_idx])
         line_idx += 1

   if overwrite:
      with open(UpperCamelCase_,      "w",      encoding="utf-8") as f:
         f.write("\n".join(UpperCamelCase_))
   elif "\n".join(UpperCamelCase_) != content:
      return True




def   _A  (  UpperCamelCase_					:	bool = False)     ->						Optional[Any]:
   '''simple docstring'''


   __lowercase								=						[os.path.join(UpperCamelCase_,      UpperCamelCase_) for f in os.listdir(UpperCamelCase_) if f.endswith(".py")]
   __lowercase								=						[sort_auto_mapping(UpperCamelCase_,      overwrite=UpperCamelCase_) for fname in fnames]

   if not overwrite and any(UpperCamelCase_):
      __lowercase								=						[f for f, d in zip(UpperCamelCase_,      UpperCamelCase_) if d]
      raise ValueError(
          F"""The following files have auto mappings that need sorting: {", ".join(UpperCamelCase_)}. Run `make style` to fix"""
          " this.")


if __name__ == "__main__":
   _a							=							argparse.ArgumentParser()
   parser.add_argument('--check_only', action='store_true', help='Whether to only check or fix style.')
   _a							=							parser.parse_args()

   sort_all_auto_mappings(not args.check_only)




