






"""simple docstring"""






from ...configuration_utils import PretrainedConfig
from ...utils import logging


UpperCAmelCase_   : Optional[int]   			= logging.get_logger(__name__)

UpperCAmelCase_   : int   			= {
    """uw-madison/mra-base-512-4""": """https://huggingface.co/uw-madison/mra-base-512-4/resolve/main/config.json""",
}




class 							lowerCAmelCase__				(			UpperCAmelCase__ ):






      '''simple docstring'''

      __UpperCamelCase	 =  "mra"
      def __init__(						self     :  int						,	lowercase_     :  Union[str, Any]=50265						,	lowercase_     :  Tuple=768						,	lowercase_     :  Optional[Any]=12						,	lowercase_     :  Tuple=12						,	lowercase_     :  Optional[int]=3072						,	lowercase_     :  Optional[Any]="gelu"						,	lowercase_     :  Union[str, Any]=0.1						,	lowercase_     :  Optional[Any]=0.1						,	lowercase_     :  Optional[Any]=512						,	lowercase_     :  Union[str, Any]=1						,	lowercase_     :  Optional[int]=0.02						,	lowercase_     :  Optional[Any]=1e-5						,	lowercase_     :  int="absolute"						,	lowercase_     :  Tuple=4						,	lowercase_     :  Any="full"						,	lowercase_     :  int=0						,	lowercase_     :  List[Any]=0						,	lowercase_     :  List[Any]=1						,	lowercase_     :  Optional[int]=0						,	lowercase_     :  Optional[Any]=2						,	**lowercase_     :  Tuple						,	):




          '''simple docstring'''


          super().__init__(pad_token_id=lowercase_						,	bos_token_id=lowercase_						,	eos_token_id=lowercase_						,	**lowercase_)

          SCREAMING_SNAKE_CASE_      :  Tuple    						=		vocab_size
          SCREAMING_SNAKE_CASE_      :  Union[str, Any]    						=		max_position_embeddings
          SCREAMING_SNAKE_CASE_      :  Tuple    						=		hidden_size
          SCREAMING_SNAKE_CASE_      :  Union[str, Any]    						=		num_hidden_layers
          SCREAMING_SNAKE_CASE_      :  str    						=		num_attention_heads
          SCREAMING_SNAKE_CASE_      :  Any    						=		intermediate_size
          SCREAMING_SNAKE_CASE_      :  List[str]    						=		hidden_act
          SCREAMING_SNAKE_CASE_      :  List[Any]    						=		hidden_dropout_prob
          SCREAMING_SNAKE_CASE_      :  Union[str, Any]    						=		attention_probs_dropout_prob
          SCREAMING_SNAKE_CASE_      :  List[str]    						=		initializer_range
          SCREAMING_SNAKE_CASE_      :  List[str]    						=		type_vocab_size
          SCREAMING_SNAKE_CASE_      :  str    						=		layer_norm_eps
          SCREAMING_SNAKE_CASE_      :  str    						=		position_embedding_type
          SCREAMING_SNAKE_CASE_      :  List[Any]    						=		block_per_row
          SCREAMING_SNAKE_CASE_      :  Any    						=		approx_mode
          SCREAMING_SNAKE_CASE_      :  List[Any]    						=		initial_prior_first_n_blocks
          SCREAMING_SNAKE_CASE_      :  Union[str, Any]    						=		initial_prior_diagonal_n_blocks







'''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() = }")





