
"""simple docstring"""


import collections
from typing import List, Optional, Union

from ...tokenization_utils_base import BatchEncoding
from ...utils import TensorType, add_end_docstrings, add_start_docstrings, logging
from ..bert.tokenization_bert import BertTokenizer


SCREAMING_SNAKE_CASE      =     logging.get_logger(__name__)

SCREAMING_SNAKE_CASE      =     {"""vocab_file""": """vocab.txt""", """tokenizer_file""": """tokenizer.json"""}

SCREAMING_SNAKE_CASE      =     {
    """vocab_file""": {
        """facebook/dpr-ctx_encoder-single-nq-base""": (
            """https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/vocab.txt"""
        ),
        """facebook/dpr-ctx_encoder-multiset-base""": (
            """https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/vocab.txt"""
        ),
    },
    """tokenizer_file""": {
        """facebook/dpr-ctx_encoder-single-nq-base""": (
            """https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/tokenizer.json"""
        ),
        """facebook/dpr-ctx_encoder-multiset-base""": (
            """https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/tokenizer.json"""
        ),
    },
}
SCREAMING_SNAKE_CASE      =     {
    """vocab_file""": {
        """facebook/dpr-question_encoder-single-nq-base""": (
            """https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/vocab.txt"""
        ),
        """facebook/dpr-question_encoder-multiset-base""": (
            """https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/vocab.txt"""
        ),
    },
    """tokenizer_file""": {
        """facebook/dpr-question_encoder-single-nq-base""": (
            """https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/tokenizer.json"""
        ),
        """facebook/dpr-question_encoder-multiset-base""": (
            """https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/tokenizer.json"""
        ),
    },
}
SCREAMING_SNAKE_CASE      =     {
    """vocab_file""": {
        """facebook/dpr-reader-single-nq-base""": (
            """https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/vocab.txt"""
        ),
        """facebook/dpr-reader-multiset-base""": (
            """https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/vocab.txt"""
        ),
    },
    """tokenizer_file""": {
        """facebook/dpr-reader-single-nq-base""": (
            """https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/tokenizer.json"""
        ),
        """facebook/dpr-reader-multiset-base""": (
            """https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/tokenizer.json"""
        ),
    },
}

SCREAMING_SNAKE_CASE      =     {
    """facebook/dpr-ctx_encoder-single-nq-base""": 512,
    """facebook/dpr-ctx_encoder-multiset-base""": 512,
}
SCREAMING_SNAKE_CASE      =     {
    """facebook/dpr-question_encoder-single-nq-base""": 512,
    """facebook/dpr-question_encoder-multiset-base""": 512,
}
SCREAMING_SNAKE_CASE      =     {
    """facebook/dpr-reader-single-nq-base""": 512,
    """facebook/dpr-reader-multiset-base""": 512,
}


SCREAMING_SNAKE_CASE      =     {
    """facebook/dpr-ctx_encoder-single-nq-base""": {"""do_lower_case""": True},
    """facebook/dpr-ctx_encoder-multiset-base""": {"""do_lower_case""": True},
}
SCREAMING_SNAKE_CASE      =     {
    """facebook/dpr-question_encoder-single-nq-base""": {"""do_lower_case""": True},
    """facebook/dpr-question_encoder-multiset-base""": {"""do_lower_case""": True},
}
SCREAMING_SNAKE_CASE      =     {
    """facebook/dpr-reader-single-nq-base""": {"""do_lower_case""": True},
    """facebook/dpr-reader-multiset-base""": {"""do_lower_case""": True},
}



class   __a  (      _lowerCAmelCase	):
       UpperCamelCase_		:					Optional[Any]   =			VOCAB_FILES_NAMES
       UpperCamelCase_		:					Optional[Any]   =			CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
       UpperCamelCase_		:					List[str]   =			CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
       UpperCamelCase_		:					List[Any]   =			CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION





class   __a  (      _lowerCAmelCase	):
       UpperCamelCase_		:					List[Any]   =			VOCAB_FILES_NAMES
       UpperCamelCase_		:					Optional[int]   =			QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
       UpperCamelCase_		:					Optional[int]   =			QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
       UpperCamelCase_		:					Any   =			QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION





SCREAMING_SNAKE_CASE      =     collections.namedtuple(
    """DPRSpanPrediction""", ["""span_score""", """relevance_score""", """doc_id""", """start_index""", """end_index""", """text"""]
)

SCREAMING_SNAKE_CASE      =     collections.namedtuple("""DPRReaderOutput""", ["""start_logits""", """end_logits""", """relevance_logits"""])


SCREAMING_SNAKE_CASE      =     R"""
    Return a dictionary with the token ids of the input strings and other information to give to `.decode_best_spans`.
    It converts the strings of a question and different passages (title and text) in a sequence of IDs (integers),
    using the tokenizer and vocabulary. The resulting `input_ids` is a matrix of size `(n_passages, sequence_length)`
    with the format:

    ```
    [CLS] <question token ids> [SEP] <titles ids> [SEP] <texts ids>
    ```

    Args:
        questions (`str` or `List[str]`):
            The questions to be encoded. You can specify one question for many passages. In this case, the question
            will be duplicated like `[questions] * n_passages`. Otherwise you have to specify as many questions as in
            `titles` or `texts`.
        titles (`str` or `List[str]`):
            The passages titles to be encoded. This can be a string or a list of strings if there are several passages.
        texts (`str` or `List[str]`):
            The passages texts to be encoded. This can be a string or a list of strings if there are several passages.
        padding (`bool`, `str` or [`~utils.PaddingStrategy`], *optional*, defaults to `False`):
            Activates and controls padding. Accepts the following values:

            - `True` or `'longest'`: Pad to the longest sequence in the batch (or no padding if only a single sequence
              if provided).
            - `'max_length'`: Pad to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided.
            - `False` or `'do_not_pad'` (default): No padding (i.e., can output a batch with sequences of different
              lengths).
        truncation (`bool`, `str` or [`~tokenization_utils_base.TruncationStrategy`], *optional*, defaults to `False`):
            Activates and controls truncation. Accepts the following values:

            - `True` or `'longest_first'`: Truncate to a maximum length specified with the argument `max_length` or to
              the maximum acceptable input length for the model if that argument is not provided. This will truncate
              token by token, removing a token from the longest sequence in the pair if a pair of sequences (or a batch
              of pairs) is provided.
            - `'only_first'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided. This will only truncate the first
              sequence of a pair if a pair of sequences (or a batch of pairs) is provided.
            - `'only_second'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided. This will only truncate the
              second sequence of a pair if a pair of sequences (or a batch of pairs) is provided.
            - `False` or `'do_not_truncate'` (default): No truncation (i.e., can output batch with sequence lengths
              greater than the model maximum admissible input size).
        max_length (`int`, *optional*):
                Controls the maximum length to use by one of the truncation/padding parameters.

                If left unset or set to `None`, this will use the predefined model maximum length if a maximum length
                is required by one of the truncation/padding parameters. If the model has no specific maximum input
                length (like XLNet) truncation/padding to a maximum length will be deactivated.
        return_tensors (`str` or [`~utils.TensorType`], *optional*):
                If set, will return tensors instead of list of python integers. Acceptable values are:

                - `'tf'`: Return TensorFlow `tf.constant` objects.
                - `'pt'`: Return PyTorch `torch.Tensor` objects.
                - `'np'`: Return Numpy `np.ndarray` objects.
        return_attention_mask (`bool`, *optional*):
            Whether or not to return the attention mask. If not set, will return the attention mask according to the
            specific tokenizer's default, defined by the `return_outputs` attribute.

            [What are attention masks?](../glossary#attention-mask)

    Returns:
        `Dict[str, List[List[int]]]`: A dictionary with the following keys:

        - `input_ids`: List of token ids to be fed to a model.
        - `attention_mask`: List of indices specifying which tokens should be attended to by the model.
    """



@add_start_docstrings(_lowerCAmelCase	)
class   __a  :






       def __call__(  self :							List[Any]       ,      UpperCAmelCase_ :							Tuple       ,      UpperCAmelCase_ :							Optional[str] = None       ,      UpperCAmelCase_ :							Optional[str] = None       ,      UpperCAmelCase_ :							Union[bool, str] = False       ,      UpperCAmelCase_ :							Union[bool, str] = False       ,      UpperCAmelCase_ :							Optional[int] = None       ,      UpperCAmelCase_ :							Optional[Union[str, TensorType]] = None       ,      UpperCAmelCase_ :							Optional[bool] = None       ,      **UpperCAmelCase_ :							Tuple       ,      )->  BatchEncoding:







              """simple docstring"""
              if titles is None and texts is None:
                     return super().__call__(
                         UpperCAmelCase_       ,      padding=UpperCAmelCase_       ,      truncation=UpperCAmelCase_       ,      max_length=UpperCAmelCase_       ,      return_tensors=UpperCAmelCase_       ,      return_attention_mask=UpperCAmelCase_       ,      **UpperCAmelCase_       ,      )
              elif titles is None or texts is None:
                     UpperCamelCase					 =		titles if texts is None else texts
                     return super().__call__(
                         UpperCAmelCase_       ,      UpperCAmelCase_       ,      padding=UpperCAmelCase_       ,      truncation=UpperCAmelCase_       ,      max_length=UpperCAmelCase_       ,      return_tensors=UpperCAmelCase_       ,      return_attention_mask=UpperCAmelCase_       ,      **UpperCAmelCase_       ,      )
              UpperCamelCase					 =		titles if not isinstance(UpperCAmelCase_       ,      UpperCAmelCase_			) else [titles]
              UpperCamelCase					 =		texts if not isinstance(UpperCAmelCase_       ,      UpperCAmelCase_			) else [texts]
              UpperCamelCase					 =		len(UpperCAmelCase_			)
              UpperCamelCase					 =		questions if not isinstance(UpperCAmelCase_       ,      UpperCAmelCase_			) else [questions] * n_passages
              if len(UpperCAmelCase_			) != len(UpperCAmelCase_			):
                     raise ValueError(
                         f"There should be as many titles than texts but got {len(UpperCAmelCase_			)} titles and {len(UpperCAmelCase_			)} texts."			)
              UpperCamelCase					 =		super().__call__(UpperCAmelCase_       ,      UpperCAmelCase_       ,      padding=UpperCAmelCase_       ,      truncation=UpperCAmelCase_			)["input_ids"]
              UpperCamelCase					 =		super().__call__(UpperCAmelCase_       ,      add_special_tokens=UpperCAmelCase_       ,      padding=UpperCAmelCase_       ,      truncation=UpperCAmelCase_			)["input_ids"]
              UpperCamelCase					 =		{
                  "input_ids": [
                      (encoded_question_and_title + encoded_text)[:max_length]
                      if max_length is not None and truncation
                      else encoded_question_and_title + encoded_text
                      for encoded_question_and_title, encoded_text in zip(UpperCAmelCase_       ,      UpperCAmelCase_			)
                  ]
              }
              if return_attention_mask is not False:
                     UpperCamelCase					 =		[]
                     for input_ids in encoded_inputs["input_ids"]:
                            attention_mask.append([int(input_id != self.pad_token_id			) for input_id in input_ids]			)
                     UpperCamelCase					 =		attention_mask
              return self.pad(UpperCAmelCase_       ,      padding=UpperCAmelCase_       ,      max_length=UpperCAmelCase_       ,      return_tensors=UpperCAmelCase_			)






       def 	_SCREAMING_SNAKE_CASE       (  self :							Any       ,      UpperCAmelCase_ :							BatchEncoding       ,      UpperCAmelCase_ :							DPRReaderOutput       ,      UpperCAmelCase_ :							int = 16       ,      UpperCAmelCase_ :							int = 64       ,      UpperCAmelCase_ :							int = 4       ,      )->  List[DPRSpanPrediction]:







              """simple docstring"""
              UpperCamelCase					 =		reader_input["input_ids"]
              UpperCamelCase ,       UpperCamelCase ,       UpperCamelCase					 =		reader_output[:3]
              UpperCamelCase					 =		len(UpperCAmelCase_			)
              UpperCamelCase					 =		sorted(range(UpperCAmelCase_			)       ,      reverse=UpperCAmelCase_       ,      key=relevance_logits.__getitem__			)
              UpperCamelCase					 =		[]
              for doc_id in sorted_docs:
                     UpperCamelCase					 =		list(input_ids[doc_id]			)
                     # assuming question & title information is at the beginning of the sequence
                     UpperCamelCase					 =		sequence_ids.index(self.sep_token_id       ,      2			) + 1  # second sep id
                     if sequence_ids[-1] == self.pad_token_id:
                            UpperCamelCase					 =		sequence_ids.index(self.pad_token_id			)
                     else:
                            UpperCamelCase					 =		len(UpperCAmelCase_			)

                     UpperCamelCase					 =		self._get_best_spans(
                         start_logits=start_logits[doc_id][passage_offset:sequence_len]       ,      end_logits=end_logits[doc_id][passage_offset:sequence_len]       ,      max_answer_length=UpperCAmelCase_       ,      top_spans=UpperCAmelCase_       ,      )
                     for start_index, end_index in best_spans:
                            start_index += passage_offset
                            end_index += passage_offset
                            nbest_spans_predictions.append(
                                DPRSpanPrediction(
                                    span_score=start_logits[doc_id][start_index] + end_logits[doc_id][end_index]       ,      relevance_score=relevance_logits[doc_id]       ,      doc_id=UpperCAmelCase_       ,      start_index=UpperCAmelCase_       ,      end_index=UpperCAmelCase_       ,      text=self.decode(sequence_ids[start_index : end_index + 1]			)       ,      )			)
                     if len(UpperCAmelCase_			) >= num_spans:
                            break
              return nbest_spans_predictions[:num_spans]






       def 	_SCREAMING_SNAKE_CASE       (  self :							str       ,      UpperCAmelCase_ :							List[int]       ,      UpperCAmelCase_ :							List[int]       ,      UpperCAmelCase_ :							int       ,      UpperCAmelCase_ :							int       ,      )->  List[DPRSpanPrediction]:







              """simple docstring"""
              UpperCamelCase					 =		[]
              for start_index, start_score in enumerate(UpperCAmelCase_			):
                     for answer_length, end_score in enumerate(end_logits[start_index : start_index + max_answer_length]			):
                            scores.append(((start_index, start_index + answer_length), start_score + end_score)			)
              UpperCamelCase					 =		sorted(UpperCAmelCase_       ,      key=lambda UpperCAmelCase_			: x[1]       ,      reverse=UpperCAmelCase_			)
              UpperCamelCase					 =		[]
              for (start_index, end_index), score in scores:
                     if start_index > end_index:
                            raise ValueError(f"Wrong span indices: [{start_index}:{end_index}]"			)
                     UpperCamelCase					 =		end_index - start_index + 1
                     if length > max_answer_length:
                            raise ValueError(f"Span is too long: {length} > {max_answer_length}"			)
                     if any(
                         start_index <= prev_start_index <= prev_end_index <= end_index
                         or prev_start_index <= start_index <= end_index <= prev_end_index
                         for (prev_start_index, prev_end_index) in chosen_span_intervals			):
                            continue
                     chosen_span_intervals.append((start_index, end_index)			)

                     if len(UpperCAmelCase_			) == top_spans:
                            break
              return chosen_span_intervals





@add_end_docstrings(_lowerCAmelCase	)
class   __a  (      _lowerCAmelCase    ,     _lowerCAmelCase	):
       UpperCamelCase_		:					str   =			VOCAB_FILES_NAMES
       UpperCamelCase_		:					Tuple   =			READER_PRETRAINED_VOCAB_FILES_MAP
       UpperCamelCase_		:					List[str]   =			READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
       UpperCamelCase_		:					Tuple   =			READER_PRETRAINED_INIT_CONFIGURATION
       UpperCamelCase_		:					Any   =			['''input_ids''', '''attention_mask''']







"""simple docstring"""


def 	lowerCamelCase__			(							UpperCAmelCase_		,      UpperCAmelCase_ = False				)->							bool:







       """simple docstring"""
       if n == 2:
              return True
       if not n % 2 or n < 2:
              return False
       if n > 5 and n % 10 not in (1, 3, 7, 9):  # can quickly check last digit
              return False
       if n > 3_31_70_44_06_46_79_88_73_85_96_19_81 and not allow_probable:
              raise ValueError(
                  "Warning: upper bound of deterministic test is exceeded. "
                  "Pass allow_probable=True to allow probabilistic test. "
                  "A return value of True indicates a probable prime."				)
       # array bounds provided by analysis
       UpperCamelCase					 =		[
           20_47,
           1_37_36_53,
           25_32_60_01,
           32_15_03_17_51,
           2_15_23_02_89_87_47,
           3_47_47_49_66_03_83,
           3_41_55_00_71_72_83_21,
           1,
           3_82_51_23_05_65_46_41_30_51,
           1,
           1,
           31_86_65_85_78_34_03_11_51_16_74_61,
           3_31_70_44_06_46_79_88_73_85_96_19_81,
       ]

       UpperCamelCase					 =		[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
       for idx, _p in enumerate(UpperCAmelCase_		,      1				):
              if n < _p:
                     # then we have our last prime to check
                     UpperCamelCase					 =		primes[:idx]
                     break
       UpperCamelCase ,       UpperCamelCase					 =		n - 1, 0
       # break up n -1 into a power of 2 (s) and
       # remaining odd component
       # essentially, solve for d * 2 ** s == n - 1
       while d % 2 == 0:
              d //= 2
              s += 1
       for prime in plist:
              UpperCamelCase					 =		False
              for r in range(UpperCAmelCase_				):
                     UpperCamelCase					 =		pow(UpperCAmelCase_		,      d * 2**r		,      UpperCAmelCase_				)
                     # see article for analysis explanation for m
                     if (r == 0 and m == 1) or ((m + 1) % n == 0):
                            UpperCamelCase					 =		True
                            # this loop will not determine compositeness
                            break
              if pr:
                     continue
              # if pr is False, then the above loop never evaluated to true,
              # and the n MUST be composite
              return False
       return True



def 	lowerCamelCase__			(							)->							None:







       """simple docstring"""
       assert not miller_rabin(5_61				)
       assert miller_rabin(5_63				)
       # 2047

       assert not miller_rabin(83_82_01				)
       assert miller_rabin(83_82_07				)
       # 1_373_653

       assert not miller_rabin(17_31_60_01				)
       assert miller_rabin(17_31_60_17				)
       # 25_326_001

       assert not miller_rabin(30_78_38_66_41				)
       assert miller_rabin(30_78_38_66_53				)
       # 3_215_031_751

       assert not miller_rabin(1_71_30_45_57_48_01				)
       assert miller_rabin(1_71_30_45_57_48_19				)
       # 2_152_302_898_747

       assert not miller_rabin(2_77_97_99_72_83_07				)
       assert miller_rabin(2_77_97_99_72_83_27				)
       # 3_474_749_660_383

       assert not miller_rabin(1_13_85_00_23_90_94_41				)
       assert miller_rabin(1_13_85_00_23_90_95_27				)
       # 341_550_071_728_321

       assert not miller_rabin(1_27_50_41_01_88_48_80_43_51				)
       assert miller_rabin(1_27_50_41_01_88_48_80_43_91				)
       # 3_825_123_056_546_413_051

       assert not miller_rabin(7_96_66_46_44_58_50_77_87_79_18_67				)
       assert miller_rabin(7_96_66_46_44_58_50_77_87_79_19_51				)
       # 318_665_857_834_031_151_167_461

       assert not miller_rabin(55_28_40_67_74_46_64_78_97_66_03_33				)
       assert miller_rabin(55_28_40_67_74_46_64_78_97_66_03_59				)
       # 3_317_044_064_679_887_385_961_981
       # upper limit for probabilistic test


if __name__ == "__main__":
      test_miller_rabin()





