

from math import isclose, sqrt



def     lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							float		,				SCREAMING_SNAKE_CASE_:							float		,				SCREAMING_SNAKE_CASE_:							float					)	->					Tuple:




				'''simple docstring'''





				A__						=	point_y / 4 / point_x
				A__						=	2 * normal_gradient / (1 + normal_gradient * normal_gradient)
				A__						=	(1 - normal_gradient * normal_gradient) / (
				    1 + normal_gradient * normal_gradient
				)
				A__						=	(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
				A__						=	outgoing_gradient**2 + 4
				A__						=	2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
				A__						=	(point_y - outgoing_gradient * point_x) ** 2 - 1_0_0

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

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

				return next_x, next_y, outgoing_gradient



def     lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							float = 1.4		,				SCREAMING_SNAKE_CASE_:							float = -9.6					)	->					str:




				'''simple docstring'''





				A__						=	0
				A__						=	first_x_coord
				A__						=	first_y_coord
				A__						=	(10.1 - point_y) / (0.0 - point_x)

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

				return num_reflections


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








"""simple docstring"""





from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch
import torch.nn as nn

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, apply_forward_hook
from .modeling_utils import ModelMixin
from .vae import Decoder, DecoderOutput, Encoder, VectorQuantizer

@dataclass
class 		lowercase					(					_UpperCAmelCase					):
      _SCREAMING_SNAKE_CASE					=      42







class 		lowercase					(					_UpperCAmelCase     ,  _UpperCAmelCase					):





      @register_to_config
      def __init__(       self      ,						lowercase = 3      ,						lowercase = 3      ,						lowercase = ("DownEncoderBlock2D",)      ,						lowercase = ("UpDecoderBlock2D",)      ,						lowercase = (64,)      ,						lowercase = 1      ,						lowercase = "silu"      ,						lowercase = 3      ,						lowercase = 32      ,						lowercase = 256      ,						lowercase = 32      ,						lowercase = None      ,						lowercase = 0.18_215      ,						lowercase = "group"      ,						)		->     Union[str, Any]:
            super().__init__()

            # pass init params to Encoder
            lowerCAmelCase  						=       Encoder(
                in_channels=lowercase      ,						out_channels=lowercase      ,						down_block_types=lowercase      ,						block_out_channels=lowercase      ,						layers_per_block=lowercase      ,						act_fn=lowercase      ,						norm_num_groups=lowercase      ,						double_z=lowercase      ,						)

            lowerCAmelCase  						=       vq_embed_dim if vq_embed_dim is not None else latent_channels

            lowerCAmelCase  						=       nn.Convad(lowercase      ,						lowercase      ,						1 )
            lowerCAmelCase  						=       VectorQuantizer(lowercase      ,						lowercase      ,						beta=0.25      ,						remap=lowercase      ,						sane_index_shape=lowercase )
            lowerCAmelCase  						=       nn.Convad(lowercase      ,						lowercase      ,						1 )

            # pass init params to Decoder
            lowerCAmelCase  						=       Decoder(
                in_channels=lowercase      ,						out_channels=lowercase      ,						up_block_types=lowercase      ,						block_out_channels=lowercase      ,						layers_per_block=lowercase      ,						act_fn=lowercase      ,						norm_num_groups=lowercase      ,						norm_type=lowercase      ,						)





      @apply_forward_hook
      def     _snake_case			(       self      ,						lowercase      ,						lowercase = True )		->     VQEncoderOutput:
            lowerCAmelCase  						=       self.encoder(lowercase )
            lowerCAmelCase  						=       self.quant_conv(lowercase )

            if not return_dict:
                  return (h,)

            return VQEncoderOutput(latents=lowercase )





      @apply_forward_hook
      def     _snake_case			(       self      ,						lowercase      ,						lowercase = False      ,						lowercase = True )		->     Union[DecoderOutput, torch.FloatTensor]:
            # also go through quantization layer
            if not force_not_quantize:
                  lowerCAmelCase						,		lowerCAmelCase						,		lowerCAmelCase  						=       self.quantize(lowercase )
            else:
                  lowerCAmelCase  						=       h
            lowerCAmelCase  						=       self.post_quant_conv(lowercase )
            lowerCAmelCase  						=       self.decoder(lowercase      ,						quant if self.config.norm_type == """spatial""" else None )

            if not return_dict:
                  return (dec,)

            return DecoderOutput(sample=lowercase )





      def     _snake_case			(       self      ,						lowercase      ,						lowercase = True )		->     Union[DecoderOutput, torch.FloatTensor]:
            lowerCAmelCase  						=       sample
            lowerCAmelCase  						=       self.encode(lowercase ).latents
            lowerCAmelCase  						=       self.decode(lowercase ).sample

            if not return_dict:
                  return (dec,)

            return DecoderOutput(sample=lowercase )






