

'''simple docstring'''





from math import factorial





class 		__SCREAMING_SNAKE_CASE       :







				def __init__(					self    :		List[Any]		,				UpperCAmelCase__    :		Dict		,				UpperCAmelCase__    :		List[str]      ):
										'''simple docstring'''
										lowercase   :       Any								=real
										if isinstance(UpperCAmelCase__		,				UpperCAmelCase__      ):
																lowercase   :       int								=[1] * rank
										else:
																lowercase   :       Optional[int]								=rank







				def __repr__(					self    :		List[Any]      ):
										'''simple docstring'''
										return (
										    F'''{self.real}+'''
										    F'''{"+".join(str(UpperCAmelCase__      )+"E"+str(n+1      )for n,dual in enumerate(self.duals      )      )}'''
										)







				def    lowerCamelCase_  (					self    :		List[Any]      ):
										'''simple docstring'''
										lowercase   :       List[str]								=self.duals.copy()
										while cur[-1] == 0:
																cur.pop(-1      )
										return Dual(self.real		,				UpperCAmelCase__      )







				def __add__(					self    :		Any		,				UpperCAmelCase__    :		Union[str, Any]      ):
										'''simple docstring'''
										if not isinstance(UpperCAmelCase__		,				UpperCAmelCase__      ):
																return Dual(self.real + other		,				self.duals      )
										lowercase   :       Tuple								=self.duals.copy()
										lowercase   :       str								=other.duals.copy()
										if len(UpperCAmelCase__      ) > len(UpperCAmelCase__      ):
																o_dual.extend([1] * (len(UpperCAmelCase__      ) - len(UpperCAmelCase__      ))      )
										elif len(UpperCAmelCase__      ) < len(UpperCAmelCase__      ):
																s_dual.extend([1] * (len(UpperCAmelCase__      ) - len(UpperCAmelCase__      ))      )
										lowercase   :       Optional[Any]								=[]
										for i in range(len(UpperCAmelCase__      )      ):
																new_duals.append(s_dual[i] + o_dual[i]      )
										return Dual(self.real + other.real		,				UpperCAmelCase__      )

				lowerCamelCase_							=						__add__







				def __sub__(					self    :		List[str]		,				UpperCAmelCase__    :		Tuple      ):
										'''simple docstring'''
										return self + other * -1







				def __mul__(					self    :		Union[str, Any]		,				UpperCAmelCase__    :		Tuple      ):
										'''simple docstring'''
										if not isinstance(UpperCAmelCase__		,				UpperCAmelCase__      ):
																lowercase   :       str								=[]
																for i in self.duals:
																						new_duals.append(i * other      )
																return Dual(self.real * other		,				UpperCAmelCase__      )
										lowercase   :       Any								=[0] * (len(self.duals      ) + len(other.duals      ) + 1)
										for i, item in enumerate(self.duals      ):
																for j, jtem in enumerate(other.duals      ):
																						new_duals[i + j + 1] += item * jtem
										for k in range(len(self.duals      )      ):
																new_duals[k] += self.duals[k] * other.real
										for index in range(len(other.duals      )      ):
																new_duals[index] += other.duals[index] * self.real
										return Dual(self.real * other.real		,				UpperCAmelCase__      )

				lowerCamelCase_							=						__mul__







				def __truediv__(					self    :		int		,				UpperCAmelCase__    :		Optional[int]      ):
										'''simple docstring'''
										if not isinstance(UpperCAmelCase__		,				UpperCAmelCase__      ):
																lowercase   :       Any								=[]
																for i in self.duals:
																						new_duals.append(i / other      )
																return Dual(self.real / other		,				UpperCAmelCase__      )
										raise ValueError







				def __floordiv__(					self    :		Optional[int]		,				UpperCAmelCase__    :		int      ):
										'''simple docstring'''
										if not isinstance(UpperCAmelCase__		,				UpperCAmelCase__      ):
																lowercase   :       Dict								=[]
																for i in self.duals:
																						new_duals.append(i // other      )
																return Dual(self.real // other		,				UpperCAmelCase__      )
										raise ValueError







				def __pow__(					self    :		Any		,				UpperCAmelCase__    :		Union[str, Any]      ):
										'''simple docstring'''
										if n < 0 or isinstance(UpperCAmelCase__		,				UpperCAmelCase__      ):
																raise ValueError('''power must be a positive integer'''      )
										if n == 0:
																return 1
										if n == 1:
																return self
										lowercase   :       Optional[int]								=self
										for _ in range(n - 1      ):
																x *= self
										return x






def 							_lowerCAmelCase (      __magic_name__	:    int      ,   __magic_name__	:    List[str]      ,   __magic_name__	:    Optional[int]	)							->     Any:
						if not callable(__magic_name__	):
												raise ValueError('''differentiate() requires a function as input for func'''	)
						if not isinstance(__magic_name__      ,   (float, int)	):
												raise ValueError('''differentiate() requires a float as input for position'''	)
						if not isinstance(__magic_name__      ,   __magic_name__	):
												raise ValueError('''differentiate() requires an int as input for order'''	)
						lowercase   :       Optional[int]								=Dual(__magic_name__      ,   1	)
						lowercase   :       Tuple								=func(__magic_name__	)
						if order == 0:
												return result.real
						return result.duals[order - 1] * factorial(__magic_name__	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()






							def 							_lowerCAmelCase (      __magic_name__	:    Union[str, Any]	)							->     str:
													return y**2 * y**4







							print(differentiate(f, 9, 2))








'''simple docstring'''





import unittest

from datasets import load_dataset

from transformers import BloomTokenizerFast
from transformers.testing_utils import require_tokenizers

from ...test_tokenization_common import TokenizerTesterMixin





@require_tokenizers
class 		__SCREAMING_SNAKE_CASE       ( lowercase__	,       unittest.TestCase			):
				lowerCamelCase_							=						None
				lowerCamelCase_							=						BloomTokenizerFast
				lowerCamelCase_							=						BloomTokenizerFast
				lowerCamelCase_							=						True
				lowerCamelCase_							=						False
				lowerCamelCase_							=						'tokenizer_file'
				lowerCamelCase_							=						{'bos_token': '<s>', 'eos_token': '</s>', 'unk_token': '<unk>', 'pad_token': '<pad>'}







				def    lowerCamelCase_  (					self    :		List[str]      ):
										'''simple docstring'''
										super().setUp()
										lowercase   :       Union[str, Any]								=BloomTokenizerFast.from_pretrained('''bigscience/tokenizer'''      )
										tokenizer.save_pretrained(self.tmpdirname      )







				def    lowerCamelCase_  (					self    :		Union[str, Any]		,				**UpperCAmelCase__    :		Any      ):
										'''simple docstring'''
										kwargs.update(self.special_tokens_map      )
										return BloomTokenizerFast.from_pretrained(self.tmpdirname		,				**UpperCAmelCase__      )







				def    lowerCamelCase_  (					self    :		Any      ):
										'''simple docstring'''
										lowercase   :       str								=self.get_rust_tokenizer()

										lowercase   :       List[str]								=['''The quick brown fox</s>''', '''jumps over the lazy dog</s>''']
										lowercase   :       Any								=[[2175, 23714, 73173, 144252, 2], [77, 132619, 3478, 368, 109586, 35433, 2]]

										lowercase   :       Any								=tokenizer.batch_encode_plus(UpperCAmelCase__      )['''input_ids''']
										self.assertListEqual(UpperCAmelCase__		,				UpperCAmelCase__      )

										lowercase   :       int								=tokenizer.batch_decode(UpperCAmelCase__      )
										self.assertListEqual(UpperCAmelCase__		,				UpperCAmelCase__      )







				def    lowerCamelCase_  (					self    :		Tuple		,				UpperCAmelCase__    :		Any=6      ):
										'''simple docstring'''
										for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
																with self.subTest(F'''{tokenizer.__class__.__name__} ({pretrained_name})'''      ):
																						lowercase   :       Optional[int]								=self.rust_tokenizer_class.from_pretrained(UpperCAmelCase__		,				**UpperCAmelCase__      )
																						# tokenizer_r.pad_token = None # Hotfixing padding = None
																						# Simple input
																						lowercase   :       Tuple								='''This is a simple input'''
																						lowercase   :       int								=['''This is a simple input 1''', '''This is a simple input 2''']
																						lowercase   :       Optional[Any]								=('''This is a simple input''', '''This is a pair''')
																						lowercase   :       int								=[
																						    ('''This is a simple input 1''', '''This is a simple input 2'''),
																						    ('''This is a simple pair 1''', '''This is a simple pair 2'''),
																						]

																						# Simple input tests
																						try:
																												tokenizer_r.encode(UpperCAmelCase__		,				max_length=UpperCAmelCase__      )
																												tokenizer_r.encode_plus(UpperCAmelCase__		,				max_length=UpperCAmelCase__      )

																												tokenizer_r.batch_encode_plus(UpperCAmelCase__		,				max_length=UpperCAmelCase__      )
																												tokenizer_r.encode(UpperCAmelCase__		,				max_length=UpperCAmelCase__      )
																												tokenizer_r.batch_encode_plus(UpperCAmelCase__		,				max_length=UpperCAmelCase__      )
																						except ValueError:
																												self.fail('''Bloom Tokenizer should be able to deal with padding'''      )

																						lowercase   :       Optional[int]								=None  # Hotfixing padding = None
																						self.assertRaises(UpperCAmelCase__		,				tokenizer_r.encode		,				UpperCAmelCase__		,				max_length=UpperCAmelCase__		,				padding='''max_length'''      )

																						# Simple input
																						self.assertRaises(UpperCAmelCase__		,				tokenizer_r.encode_plus		,				UpperCAmelCase__		,				max_length=UpperCAmelCase__		,				padding='''max_length'''      )

																						# Simple input
																						self.assertRaises(
																						    UpperCAmelCase__		,				tokenizer_r.batch_encode_plus		,				UpperCAmelCase__		,				max_length=UpperCAmelCase__		,				padding='''max_length'''		,				)

																						# Pair input
																						self.assertRaises(UpperCAmelCase__		,				tokenizer_r.encode		,				UpperCAmelCase__		,				max_length=UpperCAmelCase__		,				padding='''max_length'''      )

																						# Pair input
																						self.assertRaises(UpperCAmelCase__		,				tokenizer_r.encode_plus		,				UpperCAmelCase__		,				max_length=UpperCAmelCase__		,				padding='''max_length'''      )

																						# Pair input
																						self.assertRaises(
																						    UpperCAmelCase__		,				tokenizer_r.batch_encode_plus		,				UpperCAmelCase__		,				max_length=UpperCAmelCase__		,				padding='''max_length'''		,				)







				def    lowerCamelCase_  (					self    :		Union[str, Any]      ):
										'''simple docstring'''
										lowercase   :       Union[str, Any]								=self.get_rust_tokenizer()
										lowercase   :       Dict								=load_dataset('''xnli'''		,				'''all_languages'''		,				split='''test'''		,				streaming=UpperCAmelCase__      )

										lowercase   :       Union[str, Any]								=next(iter(UpperCAmelCase__      )      )['''premise''']  # pick up one data
										lowercase   :       int								=list(sample_data.values()      )

										lowercase   :       Any								=list(map(tokenizer.encode		,				UpperCAmelCase__      )      )
										lowercase   :       List[str]								=[tokenizer.decode(UpperCAmelCase__		,				clean_up_tokenization_spaces=UpperCAmelCase__      ) for x in output_tokens]
										self.assertListEqual(UpperCAmelCase__		,				UpperCAmelCase__      )







				def    lowerCamelCase_  (					self    :		List[Any]      ):
										'''simple docstring'''
										# The test has to be overriden because BLOOM uses ALiBi positional embeddings that does not have
										# any sequence length constraints. This test of the parent class will fail since it relies on the
										# maximum sequence length of the positoonal embeddings.
										self.assertGreaterEqual(len(self.tokenizer_class.pretrained_vocab_files_map      )		,				1      )
										self.assertGreaterEqual(len(list(self.tokenizer_class.pretrained_vocab_files_map.values()      )[0]      )		,				1      )





