



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 						lowerCamelCase__			(		unittest.TestCase ):


						@slow
						@unittest.skip("Model is not available."      )
						def 	_lowerCamelCase      (			self    :	Any      ):
													a__:							int									="nvidia/megatron-gpt2-345m/"
													if "MYDIR" in os.environ:
																				a__:							Dict									=os.path.join(os.environ["MYDIR"]   ,							_lowerCAmelCase      )
													a__:							Dict									=GPTaLMHeadModel.from_pretrained(_lowerCAmelCase      )
													model.to(_lowerCAmelCase      )
													model.half()

													a__:							Dict									=torch.tensor(
													    [[1_0_1, 7_1_1_0, 1_0_0_5, 1_0_5_6, 2_0_2_3, 1_1_3_3_3, 1_7_4_1_3, 1_0_2_9, 1_0_2]]   ,							device=_lowerCAmelCase   ,							dtype=torch.long   ,							)

													with torch.no_grad():
																				a__:							Tuple									=model(_lowerCAmelCase      ).logits

													a__:							Any									=torch.Size((1, 9, 5_0_2_5_7)      )
													self.assertEqual(output.shape   ,							_lowerCAmelCase      )

													a__:							Dict									=torch.tensor(
													    [
													        4.9_4_1_4,
													        -0.2_9_2_0,
													        -1.2_1_4_8,
													        -4.0_2_7_3,
													        -0.5_1_6_1,
													        -5.2_1_0_9,
													        -1.2_4_1_2,
													        -1.8_3_0_1,
													        -1.7_7_3_4,
													        -4.7_1_4_8,
													        -0.2_3_1_7,
													        -1.0_8_1_1,
													        -2.1_7_7_7,
													        0.4_1_4_1,
													        -3.7_9_6_9,
													        -4.0_5_8_6,
													        -2.5_3_3_2,
													        -3.3_8_0_9,
													        4.3_8_6_7,
													    ]   ,							device=_lowerCAmelCase   ,							dtype=torch.half   ,							)

													for i in range(1_9      ):
																				a__				,      a__:							Optional[Any]									=8 * i // 1_7, 2_7_9_2 * i  # along the diagonal
																				a__				,      a__:							Tuple									=output[0, r, c], expected_diag[i]
																				a__:							Dict									=F"row={r} col={c} computed={computed} expected={expected}"
																				self.assertAlmostEqual(_lowerCAmelCase   ,							_lowerCAmelCase   ,							delta=1e-4   ,							msg=_lowerCAmelCase      )









from itertools import count
from math import asin, pi, sqrt
def 				UpperCamelCase_	(					__snake_case      :    float  )->   float:




						'''simple docstring'''
						return (
						    (1 - 2 * point) * sqrt(point - point**2  ) + 2 * point + asin(sqrt(1 - point  )  )
						) / 4
def 				UpperCamelCase_	(					__snake_case      :    int  )->   float:




						'''simple docstring'''
						__magic_name__					=      (circles_number + 1 - sqrt(2 * circles_number  )) / (
						    2 * (circles_number**2 + 1)
						)
						__magic_name__					=      circles_number * intersection_y

						__magic_name__					=      intersection_x * intersection_y / 2
						__magic_name__					=      circle_bottom_arc_integral(
						    1 / 2  ) - circle_bottom_arc_integral(__snake_case  )

						return triangle_area + concave_region_area
def 				UpperCamelCase_	(					__snake_case      :    float = 1 / 10_00  )->   int:




						'''simple docstring'''
						__magic_name__					=      (1 - pi / 4) / 4

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

						return -1


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

