






from math import isclose, sqrt





def 				snake_case  (     lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase					):




	'''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(lowerCamelCase				,  lowerCamelCase					) else x_plus
	__lowercase             =  point_y + outgoing_gradient * (next_x - point_x)

	return next_x, next_y, outgoing_gradient





def 				snake_case  (     lowerCamelCase = 1.4				,  lowerCamelCase = -9.6					):




	'''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(lowerCamelCase				,  lowerCamelCase				,  lowerCamelCase					)
		num_reflections += 1

	return num_reflections


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









import argparse

import torch
from huggingface_hub import hf_hub_download

from transformers import AutoTokenizer, RobertaPreLayerNormConfig, RobertaPreLayerNormForMaskedLM
from transformers.utils import logging


logging.set_verbosity_info()
__UpperCamelCase      :      str     						=						logging.get_logger(__name__)





def 				snake_case  (     lowerCamelCase				,  lowerCamelCase					):




	'''simple docstring'''







	__lowercase             =  RobertaPreLayerNormConfig.from_pretrained(
	    lowerCamelCase				,  architectures=["""RobertaPreLayerNormForMaskedLM"""]					)

	# convert state_dict
	__lowercase             =  torch.load(hf_hub_download(repo_id=lowerCamelCase				,  filename="""pytorch_model.bin"""					)					)
	__lowercase             =  {}
	for tensor_key, tensor_value in original_state_dict.items():
		# The transformer implementation gives the model a unique name, rather than overwiriting 'roberta'
		if tensor_key.startswith("""roberta."""					):
			__lowercase             =  """roberta_prelayernorm.""" + tensor_key[len("""roberta."""					) :]

		# The original implementation contains weights which are not used, remove them from the state_dict
		if tensor_key.endswith(""".self.LayerNorm.weight"""					) or tensor_key.endswith(""".self.LayerNorm.bias"""					):
			continue

		__lowercase             =  tensor_value

	__lowercase             =  RobertaPreLayerNormForMaskedLM.from_pretrained(
	    pretrained_model_name_or_path=lowerCamelCase				,  config=lowerCamelCase				,  state_dict=lowerCamelCase					)
	model.save_pretrained(lowerCamelCase					)

	# convert tokenizer
	__lowercase             =  AutoTokenizer.from_pretrained(lowerCamelCase					)
	tokenizer.save_pretrained(lowerCamelCase					)


if __name__ == "__main__":
						__UpperCamelCase      :      List[Any]     						=						argparse.ArgumentParser()
						# Required parameters
						parser.add_argument(
						    """--checkpoint-repo""",
						    default=None,
						    type=str,
						    required=True,
						    help="""Path the official PyTorch dump, e.g. 'andreasmadsen/efficient_mlm_m0.40'.""",
						)
						parser.add_argument(
						    """--pytorch_dump_folder_path""", default=None, type=str, required=True, help="""Path to the output PyTorch model."""
						)
						__UpperCamelCase      :      Dict     						=						parser.parse_args()
						convert_roberta_prelayernorm_checkpoint_to_pytorch(args.checkpoint_repo, args.pytorch_dump_folder_path)

