



'''simple docstring'''






from math import isclose, sqrt


def  snake_case_     (					_lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float  )      ->   tuple[float, float, float]:
							UpperCAmelCase :       Optional[int] 							=		point_y / 4 / point_x
							UpperCAmelCase :       str 							=		2 * normal_gradient / (1 + normal_gradient * normal_gradient)
							UpperCAmelCase :       Any 							=		(1 - normal_gradient * normal_gradient) / (
							    1 + normal_gradient * normal_gradient
							)
							UpperCAmelCase :       Union[str, Any] 							=		(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 :       Union[str, Any] 							=		outgoing_gradient**2 + 4
							UpperCAmelCase :       Dict 							=		2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
							UpperCAmelCase :       List[Any] 							=		(point_y - outgoing_gradient * point_x) ** 2 - 100

							UpperCAmelCase :       List[str] 							=		(
							    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term  )
							) / (2 * quadratic_term)
							UpperCAmelCase :       Optional[int] 							=		(
							    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term  )
							) / (2 * quadratic_term)

							# two solutions, one of which is our input point
							UpperCAmelCase :       Optional[Any] 							=		x_minus if isclose(_lowerCAmelCase   ,      _lowerCAmelCase  ) else x_plus
							UpperCAmelCase :       Union[str, Any] 							=		point_y + outgoing_gradient * (next_x - point_x)

							return next_x, next_y, outgoing_gradient


def  snake_case_     (					_lowerCAmelCase  :						float = 1.4   ,      _lowerCAmelCase  :						float = -9.6  )      ->   int:
							UpperCAmelCase :       int 							=		0
							UpperCAmelCase :       float 							=		first_x_coord
							UpperCAmelCase :       float 							=		first_y_coord
							UpperCAmelCase :       float 							=		(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 :       str 							=		next_point(_lowerCAmelCase   ,      _lowerCAmelCase   ,      _lowerCAmelCase  )
														num_reflections += 1

							return num_reflections


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












import unittest

from transformers import AutoConfig, AutoTokenizer, BertConfig, TensorType, is_flax_available
from transformers.testing_utils import DUMMY_UNKNOWN_IDENTIFIER, require_flax, slow


if is_flax_available():
       import jax

       from transformers.models.auto.modeling_flax_auto import FlaxAutoModel
       from transformers.models.bert.modeling_flax_bert import FlaxBertModel
       from transformers.models.roberta.modeling_flax_roberta import FlaxRobertaModel




@require_flax
class     SCREAMING_SNAKE_CASE__ (						unittest.TestCase      ):



 @slow
 def 				UpperCamelCase			(							self ):
        for model_name in ["bert-base-cased", "bert-large-uncased"]:
               with self.subTest(__lowerCamelCase ):
                      A__											=						AutoConfig.from_pretrained(__lowerCamelCase )
                      self.assertIsNotNone(__lowerCamelCase )
                      self.assertIsInstance(__lowerCamelCase,__lowerCamelCase )

                      A__											=						FlaxAutoModel.from_pretrained(__lowerCamelCase )
                      self.assertIsNotNone(__lowerCamelCase )
                      self.assertIsInstance(__lowerCamelCase,__lowerCamelCase )



 @slow
 def 				UpperCamelCase			(							self ):
        for model_name in ["roberta-base", "roberta-large"]:
               with self.subTest(__lowerCamelCase ):
                      A__											=						AutoConfig.from_pretrained(__lowerCamelCase )
                      self.assertIsNotNone(__lowerCamelCase )
                      self.assertIsInstance(__lowerCamelCase,__lowerCamelCase )

                      A__											=						FlaxAutoModel.from_pretrained(__lowerCamelCase )
                      self.assertIsNotNone(__lowerCamelCase )
                      self.assertIsInstance(__lowerCamelCase,__lowerCamelCase )



 @slow
 def 				UpperCamelCase			(							self ):
        for model_name in ["bert-base-cased", "bert-large-uncased"]:
               A__											=						AutoTokenizer.from_pretrained(__lowerCamelCase )
               A__											=						FlaxBertModel.from_pretrained(__lowerCamelCase )
               A__											=						tokenizer('''Do you support jax jitted function?''',return_tensors=TensorType.JAX )

               @jax.jit
               def eval(**__lowerCamelCase ):
                      return model(**__lowerCamelCase )

               eval(**__lowerCamelCase ).block_until_ready()



 @slow
 def 				UpperCamelCase			(							self ):
        for model_name in ["roberta-base", "roberta-large"]:
               A__											=						AutoTokenizer.from_pretrained(__lowerCamelCase )
               A__											=						FlaxRobertaModel.from_pretrained(__lowerCamelCase )
               A__											=						tokenizer('''Do you support jax jitted function?''',return_tensors=TensorType.JAX )

               @jax.jit
               def eval(**__lowerCamelCase ):
                      return model(**__lowerCamelCase )

               eval(**__lowerCamelCase ).block_until_ready()



 def 				UpperCamelCase			(							self ):
        with self.assertRaisesRegex(
            __lowerCamelCase,'''bert-base is not a local folder and is not a valid model identifier''' ):
               A__											=						FlaxAutoModel.from_pretrained('''bert-base''' )



 def 				UpperCamelCase			(							self ):
        with self.assertRaisesRegex(
            __lowerCamelCase,r'''aaaaaa is not a valid git identifier \(branch name, tag name or commit id\)''' ):
               A__											=						FlaxAutoModel.from_pretrained(__lowerCamelCase,revision='''aaaaaa''' )



 def 				UpperCamelCase			(							self ):
        with self.assertRaisesRegex(
            __lowerCamelCase,'''hf-internal-testing/config-no-model does not appear to have a file named flax_model.msgpack''',):
               A__											=						FlaxAutoModel.from_pretrained('''hf-internal-testing/config-no-model''' )




 def 				UpperCamelCase			(							self ):
        with self.assertRaisesRegex(__lowerCamelCase,'''Use `from_pt=True` to load this model''' ):
               A__											=						FlaxAutoModel.from_pretrained('''hf-internal-testing/tiny-bert-pt-only''' )





