


import os
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
		import torch

		from transformers import GPTaLMHeadModel





@require_torch
@require_sentencepiece
@require_tokenizers
class       _a							(       unittest.TestCase):




	@slow
	@unittest.skip('''Model is not available.'''	)
	def 							UpperCAmelCase__(      self		:	Dict	)-> Union[str, Any]:
			lowerCAmelCase__     :    Optional[Any]					  =      '''nvidia/megatron-gpt2-345m/'''
			if "MYDIR" in os.environ:
					lowerCAmelCase__     :    Optional[Any]					  =      os.path.join(os.environ['''MYDIR''']	,      _SCREAMING_SNAKE_CASE	)
			lowerCAmelCase__     :    Any					  =      GPTaLMHeadModel.from_pretrained(_SCREAMING_SNAKE_CASE	)
			model.to(_SCREAMING_SNAKE_CASE	)
			model.half()

			lowerCAmelCase__     :    int					  =      torch.tensor(
			    [[101, 7110, 1005, 1056, 2023, 1_1333, 1_7413, 1029, 102]]	,      device=_SCREAMING_SNAKE_CASE	,      dtype=torch.long	,      )

			with torch.no_grad():
					lowerCAmelCase__     :    Optional[int]					  =      model(_SCREAMING_SNAKE_CASE	).logits

			lowerCAmelCase__     :    Tuple					  =      torch.Size((1, 9, 5_0257)	)
			self.assertEqual(output.shape	,      _SCREAMING_SNAKE_CASE	)

			lowerCAmelCase__     :    Optional[int]					  =      torch.tensor(
			    [
			        4.9414,
			        -0.2920,
			        -1.2148,
			        -4.0273,
			        -0.5161,
			        -5.2109,
			        -1.2412,
			        -1.8301,
			        -1.7734,
			        -4.7148,
			        -0.2317,
			        -1.0811,
			        -2.1777,
			        0.4141,
			        -3.7969,
			        -4.0586,
			        -2.5332,
			        -3.3809,
			        4.3867,
			    ]	,      device=_SCREAMING_SNAKE_CASE	,      dtype=torch.half	,      )

			for i in range(19	):
					lowerCAmelCase__  ,			lowerCAmelCase__     :    Optional[Any]					  =      8 * i // 17, 2792 * i  # along the diagonal
					lowerCAmelCase__  ,			lowerCAmelCase__     :    Union[str, Any]					  =      output[0, r, c], expected_diag[i]
					lowerCAmelCase__     :    List[Any]					  =      F'row={r} col={c} computed={computed} expected={expected}'
					self.assertAlmostEqual(_SCREAMING_SNAKE_CASE	,      _SCREAMING_SNAKE_CASE	,      delta=1E-4	,      msg=_SCREAMING_SNAKE_CASE	)








from itertools import count
from math import asin, pi, sqrt






def   lowerCamelCase_					( _a ):




		"""simple docstring"""






		return (
		    (1 - 2 * point) * sqrt(point - point**2 ) + 2 * point + asin(sqrt(1 - point ) )
		) / 4






def   lowerCamelCase_					( _a ):




		"""simple docstring"""






		lowerCAmelCase__     :    Union[str, Any]					  =      (circles_number + 1 - sqrt(2 * circles_number )) / (
		    2 * (circles_number**2 + 1)
		)
		lowerCAmelCase__     :    Tuple					  =      circles_number * intersection_y

		lowerCAmelCase__     :    Any					  =      intersection_x * intersection_y / 2
		lowerCAmelCase__     :    Optional[Any]					  =      circle_bottom_arc_integral(
		    1 / 2 ) - circle_bottom_arc_integral(_a )

		return triangle_area + concave_region_area






def   lowerCamelCase_					( _a = 1 / 1_000 ):




		"""simple docstring"""






		lowerCAmelCase__     :    Any					  =      (1 - pi / 4) / 4

		for n in count(1 ):
				if concave_triangle_area(_a ) / l_section_area < fraction:
						return n

		return -1


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




