
"""simple docstring"""






from math import isclose, sqrt






def 						_snake_case       (	lowercase__		:  float      ,     lowercase__		:  float      ,     lowercase__		:  float		)  ->				tuple[float, float, float]:


			'''simple docstring'''





			lowerCAmelCase_    :Optional[int]			     =  point_y / 4 / point_x
			lowerCAmelCase_    :Dict			     =  2 * normal_gradient / (1 + normal_gradient * normal_gradient)
			lowerCAmelCase_    :Union[str, Any]			     =  (1 - normal_gradient * normal_gradient) / (
			    1 + normal_gradient * normal_gradient
			)
			lowerCAmelCase_    :str			     =  (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
			lowerCAmelCase_    :Tuple			     =  outgoing_gradient**2 + 4
			lowerCAmelCase_    :Tuple			     =  2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
			lowerCAmelCase_    :str			     =  (point_y - outgoing_gradient * point_x) ** 2 - 1_0_0

			lowerCAmelCase_    :Optional[Any]			     =  (
			    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term		)
			) / (2 * quadratic_term)
			lowerCAmelCase_    :Optional[int]			     =  (
			    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term		)
			) / (2 * quadratic_term)

			# two solutions, one of which is our input point
			lowerCAmelCase_    :List[Any]			     =  x_minus if isclose(lowercase__      ,     lowercase__		) else x_plus
			lowerCAmelCase_    :List[str]			     =  point_y + outgoing_gradient * (next_x - point_x)

			return next_x, next_y, outgoing_gradient






def 						_snake_case       (	lowercase__		:  float = 1.4      ,     lowercase__		:  float = -9.6		)  ->				int:


			'''simple docstring'''





			lowerCAmelCase_    :int			     =  0
			lowerCAmelCase_    :float			     =  first_x_coord
			lowerCAmelCase_    :float			     =  first_y_coord
			lowerCAmelCase_    :float			     =  (10.1 - point_y) / (0.0 - point_x)

			while not (-0.01 <= point_x <= 0.01 and point_y > 0):
						lowerCAmelCase_     ,       lowerCAmelCase_     ,       lowerCAmelCase_    :List[str]			     =  next_point(lowercase__      ,     lowercase__      ,     lowercase__		)
						num_reflections += 1

			return num_reflections


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













import json
import os
import unittest

from transformers.models.gptsan_japanese.tokenization_gptsan_japanese import (
    VOCAB_FILES_NAMES,
    GPTSanJapaneseTokenizer,
)
from transformers.testing_utils import require_tokenizers, slow

from ...test_tokenization_common import TokenizerTesterMixin







@require_tokenizers
class     __snake_case       (							__lowerCamelCase   ,			unittest.TestCase			):





       '''simple docstring'''







       lowerCAmelCase__      		=     GPTSanJapaneseTokenizer
       lowerCAmelCase__      		=     False
       lowerCAmelCase__      		=     {"""do_clean_text""": False, """add_prefix_space""": False}




       def 							UpperCAmelCase__ (  self :    Union[str, Any]		):
         super().setUp()

         # fmt: off
         __snake_case:						str   =						["""こん""", """こんに""", """にちは""", """ばんは""", """世界,㔺界""", """、""", """。""", """<BR>""", """<SP>""", """<TAB>""", """<URL>""", """<EMAIL>""", """<TEL>""", """<DATE>""", """<PRICE>""", """<BLOCK>""", """<KIGOU>""", """<U2000U2BFF>""", """<|emoji1|>""", """<unk>""", """<|bagoftoken|>""", """<|endoftext|>"""]
         # fmt: on
         __snake_case:						List[Any]   =						{"""emoji""": {"""\ud83d\ude00""": """<|emoji1|>"""}, """emoji_inv""": {"""<|emoji1|>""": """\ud83d\ude00"""}}  # 😀
         __snake_case:						Optional[int]   =						{"""unk_token""": """<unk>"""}

         __snake_case:						Any   =						os.path.join(self.tmpdirname							,				VOCAB_FILES_NAMES["""vocab_file"""]		)
         __snake_case:						int   =						os.path.join(self.tmpdirname							,				VOCAB_FILES_NAMES["""emoji_file"""]		)
         with open(self.vocab_file							,				"""w"""							,				encoding="""utf-8"""		) as vocab_writer:
           vocab_writer.write("""""".join([x + """\n""" for x in vocab_tokens]		)		)
         with open(self.emoji_file							,				"""w"""		) as emoji_writer:
           emoji_writer.write(json.dumps(A		)		)




       def 							UpperCAmelCase__ (  self :    Optional[int]							,				**A :    int		):
         kwargs.update(self.special_tokens_map		)
         return GPTSanJapaneseTokenizer.from_pretrained(self.tmpdirname							,				**A		)




       def 							UpperCAmelCase__ (  self :    Optional[Any]							,				A :    Dict		):
         __snake_case:						Tuple   =						"""こんにちは、世界。 \nこんばんは、㔺界。😀"""
         __snake_case:						str   =						"""こんにちは、世界。 \nこんばんは、世界。😀"""
         return input_text, output_text




       def 							UpperCAmelCase__ (  self :    Optional[int]							,				A :    Optional[int]		):
         __snake_case  ,   __snake_case:						Optional[int]   =						self.get_input_output_texts(A		)
         __snake_case:						Optional[Any]   =						tokenizer.encode(A							,				add_special_tokens=A		)
         __snake_case:						int   =						tokenizer.decode(A							,				clean_up_tokenization_spaces=A		)
         return text, ids




       def 							UpperCAmelCase__ (  self :    int		):
         pass  # TODO add if relevant




       def 							UpperCAmelCase__ (  self :    Dict		):
         pass  # TODO add if relevant




       def 							UpperCAmelCase__ (  self :    Optional[int]		):
         pass  # TODO add if relevant




       def 							UpperCAmelCase__ (  self :    Union[str, Any]		):
         __snake_case:						Dict   =						self.get_tokenizer()

         # Testing tokenization
         __snake_case:						List[str]   =						"""こんにちは、世界。　こんばんは、㔺界。"""
         __snake_case:						Optional[int]   =						["""こん""", """にちは""", """、""", """世界""", """。""", """<SP>""", """こん""", """ばんは""", """、""", """㔺界""", """。"""]
         __snake_case:						Any   =						tokenizer.tokenize(A		)
         self.assertListEqual(A							,				A		)

         # Testing conversion to ids without special tokens
         __snake_case:						str   =						[0, 2, 5, 4, 6, 8, 0, 3, 5, 4, 6]
         __snake_case:						str   =						tokenizer.convert_tokens_to_ids(A		)
         self.assertListEqual(A							,				A		)

         # Testing conversion to ids with special tokens
         __snake_case:						Optional[int]   =						tokens + [tokenizer.unk_token]
         __snake_case:						List[str]   =						[0, 2, 5, 4, 6, 8, 0, 3, 5, 4, 6, 19]
         __snake_case:						str   =						tokenizer.convert_tokens_to_ids(A		)
         self.assertListEqual(A							,				A		)




       def 							UpperCAmelCase__ (  self :    str		):
         __snake_case:						Union[str, Any]   =						self.get_tokenizer()

         # Testing tokenization
         __snake_case:						Optional[Any]   =						"""こんにちは、<|bagoftoken|>世界。こんばんは、<|bagoftoken|>㔺界。"""
         __snake_case:						Optional[Any]   =						"""こんにちは、、、、世界。こんばんは、、、、世界。"""
         __snake_case:						Union[str, Any]   =						tokenizer.encode(A		)
         __snake_case:						List[Any]   =						tokenizer.decode(A		)
         self.assertEqual(A							,				A		)




       @slow
       def 							UpperCAmelCase__ (  self :    Any		):
         __snake_case:						Dict   =						self.tokenizer_class.from_pretrained("""Tanrei/GPTSAN-japanese"""		)

         # Testing tokenization
         __snake_case:						Any   =						"""こんにちは、世界。"""
         __snake_case:						Tuple   =						"""こんばんは、㔺界。😀"""
         __snake_case:						Optional[Any]   =						"""こんにちは、世界。こんばんは、世界。😀"""
         __snake_case:						int   =						tokenizer.encode(prefix_text + input_text		)
         __snake_case:						Union[str, Any]   =						tokenizer.encode(""""""							,				prefix_text=prefix_text + input_text		)
         __snake_case:						Tuple   =						tokenizer.encode(A							,				prefix_text=A		)
         __snake_case:						Union[str, Any]   =						tokenizer.decode(A		)
         __snake_case:						Dict   =						tokenizer.decode(A		)
         __snake_case:						Optional[Any]   =						tokenizer.decode(A		)
         self.assertEqual(A							,				A		)
         self.assertEqual(A							,				A		)
         self.assertEqual(A							,				A		)




       @slow
       def 							UpperCAmelCase__ (  self :    List[str]		):
         __snake_case:						int   =						self.tokenizer_class.from_pretrained("""Tanrei/GPTSAN-japanese"""		)

         # Testing tokenization
         __snake_case:						Optional[int]   =						"""こんにちは、世界。"""
         __snake_case:						Any   =						"""こんばんは、㔺界。😀"""

         __snake_case:						Optional[int]   =						len(tokenizer.encode(A		)		) - 2
         __snake_case:						str   =						len(tokenizer.encode(A		)		) - 2

         __snake_case:						Dict   =						[1] + [0] * (len_prefix + len_text + 1)
         __snake_case:						str   =						[1] * (len_prefix + len_text + 1) + [0]
         __snake_case:						List[Any]   =						[1] + [1] * (len_prefix) + [0] * (len_text + 1)

         __snake_case:						int   =						tokenizer(prefix_text + input_text		).token_type_ids
         __snake_case:						Optional[int]   =						tokenizer(""""""							,				prefix_text=prefix_text + input_text		).token_type_ids
         __snake_case:						Tuple   =						tokenizer(A							,				prefix_text=A		).token_type_ids
         self.assertListEqual(A							,				A		)
         self.assertListEqual(A							,				A		)
         self.assertListEqual(A							,				A		)




       @slow
       def 							UpperCAmelCase__ (  self :    Dict		):
         __snake_case:						Dict   =						self.tokenizer_class.from_pretrained("""Tanrei/GPTSAN-japanese"""		)

         __snake_case:						int   =						tokenizer.encode("""あンいワ"""		)
         __snake_case:						Optional[int]   =						tokenizer.encode(""""""							,				prefix_text="""あンいワ"""		)
         __snake_case:						List[Any]   =						tokenizer.encode("""いワ"""							,				prefix_text="""あン"""		)

         self.assertEqual(tokenizer.decode(A		)							,				tokenizer.decode(A		)		)
         self.assertEqual(tokenizer.decode(A		)							,				tokenizer.decode(A		)		)
         self.assertNotEqual(A							,				A		)
         self.assertNotEqual(A							,				A		)
         self.assertEqual(x_token_a[1]							,				x_token_a[-1]		)  # SEG token
         self.assertEqual(x_token_a[1]							,				x_token_a[3]		)  # SEG token




       @slow
       def 							UpperCAmelCase__ (  self :    int		):
         __snake_case:						List[str]   =						self.tokenizer_class.from_pretrained("""Tanrei/GPTSAN-japanese"""		)

         __snake_case:						Union[str, Any]   =						[["""武田信玄""", """は、"""], ["""織田信長""", """の配下の、"""]]
         __snake_case:						Optional[int]   =						tokenizer(A							,				padding=A		)
         __snake_case:						int   =						tokenizer.batch_encode_plus(A							,				padding=A		)

         # fmt: off
         __snake_case:						List[str]   =						[[35_993, 8_640, 25_948, 35_998, 30_647, 35_675, 35_999, 35_999], [35_993, 10_382, 9_868, 35_998, 30_646, 9_459, 30_646, 35_675]]
         __snake_case:						int   =						[[1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0]]
         __snake_case:						Dict   =						[[1, 1, 1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1]]
         # fmt: on
         self.assertListEqual(x_token.input_ids							,				A		)
         self.assertListEqual(x_token.token_type_ids							,				A		)
         self.assertListEqual(x_token.attention_mask							,				A		)
         self.assertListEqual(x_token_a.input_ids							,				A		)
         self.assertListEqual(x_token_a.token_type_ids							,				A		)
         self.assertListEqual(x_token_a.attention_mask							,				A		)




       def 							UpperCAmelCase__ (  self :    Union[str, Any]		):
         # Intentionally convert some words to accommodate character fluctuations unique to Japanese
         pass






       def 							UpperCAmelCase__ (  self :    List[str]		):
         # tokenizer has no padding token
         pass






