






def 				A	(			a_				,a_ = 1_000   )	->		Tuple:


					if (not isinstance(_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE   )) or (digit_position <= 0):
										raise ValueError('Digit position must be a positive integer'   )
					elif (not isinstance(_SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE   )) or (precision < 0):
										raise ValueError('Precision must be a nonnegative integer'   )

					# compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
					# accurate
					__UpperCamelCase :   Dict									=(
					    4 * _subsum(_SCREAMING_SNAKE_CASE				,1				,_SCREAMING_SNAKE_CASE   )
					    - 2 * _subsum(_SCREAMING_SNAKE_CASE				,4				,_SCREAMING_SNAKE_CASE   )
					    - _subsum(_SCREAMING_SNAKE_CASE				,5				,_SCREAMING_SNAKE_CASE   )
					    - _subsum(_SCREAMING_SNAKE_CASE				,6				,_SCREAMING_SNAKE_CASE   )
					)

					# return the first hex digit of the fractional part of the result
					return hex(int((sum_result % 1) * 16   )   )[2:]






def 				A	(			a_				,a_				,a_   )	->		str:
					__UpperCamelCase :   str									=0.0
					for sum_index in range(digit_pos_to_extract + precision   ):
										__UpperCamelCase :   Tuple									=8 * sum_index + denominator_addend
										if sum_index < digit_pos_to_extract:
															# if the exponential term is an integer and we mod it by the denominator
															# before dividing, only the integer part of the sum will change;
															# the fractional part will not
															__UpperCamelCase :   str									=pow(
															    16				,digit_pos_to_extract - 1 - sum_index				,_SCREAMING_SNAKE_CASE   )
										else:
															__UpperCamelCase :   List[Any]									=pow(16				,digit_pos_to_extract - 1 - sum_index   )
										total += exponential_term / denominator
					return total


if __name__ == "__main__":
							import doctest

							doctest.testmod()








"""simple docstring"""





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCAmelCase__        =      {
    '''configuration_deberta_v2''': ['''DEBERTA_V2_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''DebertaV2Config''', '''DebertaV2OnnxConfig'''],
    '''tokenization_deberta_v2''': ['''DebertaV2Tokenizer'''],
}

try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__        =      ['''DebertaV2TokenizerFast''']

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__        =      [
						    '''TF_DEBERTA_V2_PRETRAINED_MODEL_ARCHIVE_LIST''',
						    '''TFDebertaV2ForMaskedLM''',
						    '''TFDebertaV2ForQuestionAnswering''',
						    '''TFDebertaV2ForSequenceClassification''',
						    '''TFDebertaV2ForTokenClassification''',
						    '''TFDebertaV2Model''',
						    '''TFDebertaV2PreTrainedModel''',
						]

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__        =      [
						    '''DEBERTA_V2_PRETRAINED_MODEL_ARCHIVE_LIST''',
						    '''DebertaV2ForMaskedLM''',
						    '''DebertaV2ForMultipleChoice''',
						    '''DebertaV2ForQuestionAnswering''',
						    '''DebertaV2ForSequenceClassification''',
						    '''DebertaV2ForTokenClassification''',
						    '''DebertaV2Model''',
						    '''DebertaV2PreTrainedModel''',
						]


if TYPE_CHECKING:
						from .configuration_deberta_va import (
						    DEBERTA_V2_PRETRAINED_CONFIG_ARCHIVE_MAP,
						    DebertaVaConfig,
						    DebertaVaOnnxConfig,
						)
						from .tokenization_deberta_va import DebertaVaTokenizer

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_deberta_va_fast import DebertaVaTokenizerFast

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_deberta_va import (
												    TF_DEBERTA_V2_PRETRAINED_MODEL_ARCHIVE_LIST,
												    TFDebertaVaForMaskedLM,
												    TFDebertaVaForQuestionAnswering,
												    TFDebertaVaForSequenceClassification,
												    TFDebertaVaForTokenClassification,
												    TFDebertaVaModel,
												    TFDebertaVaPreTrainedModel,
												)

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_deberta_va import (
												    DEBERTA_V2_PRETRAINED_MODEL_ARCHIVE_LIST,
												    DebertaVaForMaskedLM,
												    DebertaVaForMultipleChoice,
												    DebertaVaForQuestionAnswering,
												    DebertaVaForSequenceClassification,
												    DebertaVaForTokenClassification,
												    DebertaVaModel,
												    DebertaVaPreTrainedModel,
												)

else:
						import sys

						lowerCAmelCase__        =      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)






