



"""simple docstring"""






from typing import TYPE_CHECKING

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


__UpperCAmelCase      :      List[Any]   					=					{
    'configuration_gpt2': ['GPT2_PRETRAINED_CONFIG_ARCHIVE_MAP', 'GPT2Config', 'GPT2OnnxConfig'],
    'tokenization_gpt2': ['GPT2Tokenizer'],
}

try:
				if not is_tokenizers_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__UpperCAmelCase      :      Any   					=					['GPT2TokenizerFast']

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__UpperCAmelCase      :      List[Any]   					=					[
				    'GPT2_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'GPT2DoubleHeadsModel',
				    'GPT2ForQuestionAnswering',
				    'GPT2ForSequenceClassification',
				    'GPT2ForTokenClassification',
				    'GPT2LMHeadModel',
				    'GPT2Model',
				    'GPT2PreTrainedModel',
				    'load_tf_weights_in_gpt2',
				]

try:
				if not is_tf_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__UpperCAmelCase      :      Dict   					=					[
				    'TF_GPT2_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'TFGPT2DoubleHeadsModel',
				    'TFGPT2ForSequenceClassification',
				    'TFGPT2LMHeadModel',
				    'TFGPT2MainLayer',
				    'TFGPT2Model',
				    'TFGPT2PreTrainedModel',
				]

try:
				if not is_keras_nlp_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__UpperCAmelCase      :      str   					=					['TFGPT2Tokenizer']

try:
				if not is_flax_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__UpperCAmelCase      :      Tuple   					=					['FlaxGPT2LMHeadModel', 'FlaxGPT2Model', 'FlaxGPT2PreTrainedModel']

if TYPE_CHECKING:
				from .configuration_gpta import GPT2_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTaConfig, GPTaOnnxConfig
				from .tokenization_gpta import GPTaTokenizer

				try:
								if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_gpta_fast import GPTaTokenizerFast

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_gpta import (
								    GPT2_PRETRAINED_MODEL_ARCHIVE_LIST,
								    GPTaDoubleHeadsModel,
								    GPTaForQuestionAnswering,
								    GPTaForSequenceClassification,
								    GPTaForTokenClassification,
								    GPTaLMHeadModel,
								    GPTaModel,
								    GPTaPreTrainedModel,
								    load_tf_weights_in_gpta,
								)

				try:
								if not is_tf_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_tf_gpta import (
								    TF_GPT2_PRETRAINED_MODEL_ARCHIVE_LIST,
								    TFGPTaDoubleHeadsModel,
								    TFGPTaForSequenceClassification,
								    TFGPTaLMHeadModel,
								    TFGPTaMainLayer,
								    TFGPTaModel,
								    TFGPTaPreTrainedModel,
								)

				try:
								if not is_keras_nlp_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_gpta_tf import TFGPTaTokenizer

				try:
								if not is_flax_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_flax_gpta import FlaxGPTaLMHeadModel, FlaxGPTaModel, FlaxGPTaPreTrainedModel

else:
				import sys

				__UpperCAmelCase      :      int   					=					_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)






"""simple docstring"""






def      A      (			_A,     _A = 1_000							):




					"""simple docstring"""
					if (not isinstance(_A,     _A							)) or (digit_position <= 0):
										raise ValueError("Digit position must be a positive integer"							)
					elif (not isinstance(_A,     _A							)) 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
					snake_case_						:List[Any]								=						(
					    4 * _subsum(_A,     1,     _A							)
					    - 2 * _subsum(_A,     4,     _A							)
					    - _subsum(_A,     5,     _A							)
					    - _subsum(_A,     6,     _A							)
					)

					# 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							):




					"""simple docstring"""
					snake_case_						:int								=						0.0
					for sum_index in range(digit_pos_to_extract + precision							):
										snake_case_						:Optional[Any]								=						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
															snake_case_						:List[Any]								=						pow(
															    16,     digit_pos_to_extract - 1 - sum_index,     _A							)
										else:
															snake_case_						:Optional[Any]								=						pow(16,     digit_pos_to_extract - 1 - sum_index							)
										total += exponential_term / denominator
					return total


if __name__ == "__main__":
				import doctest

				doctest.testmod()

