


"""simple docstring"""




from dataclasses import dataclass
from enum import Enum
from typing import List, Optional, Union

import numpy as np
import PIL
from PIL import Image

from ...utils import BaseOutput, is_torch_available, is_transformers_available
@dataclass
class 					lowerCAmelCase	(					lowerCamelCase_    ):




		'''simple docstring'''







		SCREAMING_SNAKE_CASE_						:     Union[List[PIL.Image.Image], np.ndarray]
		SCREAMING_SNAKE_CASE_						:     Optional[List[bool]]


if is_transformers_available() and is_torch_available():
	from .pipeline_semantic_stable_diffusion import SemanticStableDiffusionPipeline






"""simple docstring"""




from math import isclose, sqrt


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float  )   ->						tuple[float, float, float]:
						SCREAMING_SNAKE_CASE													=					point_y / 4 / point_x
						SCREAMING_SNAKE_CASE													=					2 * normal_gradient / (1 + normal_gradient * normal_gradient)
						SCREAMING_SNAKE_CASE													=					(1 - normal_gradient * normal_gradient) / (
						    1 + normal_gradient * normal_gradient
						)
						SCREAMING_SNAKE_CASE													=					(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
						SCREAMING_SNAKE_CASE													=					outgoing_gradient**2 + 4
						SCREAMING_SNAKE_CASE													=					2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
						SCREAMING_SNAKE_CASE													=					(point_y - outgoing_gradient * point_x) ** 2 - 1_00

						SCREAMING_SNAKE_CASE													=					(
						    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term  )
						) / (2 * quadratic_term)
						SCREAMING_SNAKE_CASE													=					(
						    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term  )
						) / (2 * quadratic_term)

						# two solutions, one of which is our input point
						SCREAMING_SNAKE_CASE													=					x_minus if isclose(SCREAMING_SNAKE_CASE_ ,			SCREAMING_SNAKE_CASE_  ) else x_plus
						SCREAMING_SNAKE_CASE													=					point_y + outgoing_gradient * (next_x - point_x)

						return next_x, next_y, outgoing_gradient


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float = 1.4 ,			SCREAMING_SNAKE_CASE_		:				float = -9.6  )   ->						int:
						SCREAMING_SNAKE_CASE													=					0
						SCREAMING_SNAKE_CASE													=					first_x_coord
						SCREAMING_SNAKE_CASE													=					first_y_coord
						SCREAMING_SNAKE_CASE													=					(10.1 - point_y) / (0.0 - point_x)

						while not (-0.01 <= point_x <= 0.01 and point_y > 0):
												SCREAMING_SNAKE_CASE							,				SCREAMING_SNAKE_CASE							,				SCREAMING_SNAKE_CASE													=					next_point(SCREAMING_SNAKE_CASE_ ,			SCREAMING_SNAKE_CASE_ ,			SCREAMING_SNAKE_CASE_  )
												num_reflections += 1

						return num_reflections


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


