

def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     int   ,      SCREAMING_SNAKE_CASE__      :     bool = 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 > 3317044064679887385961981 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
    A__   				=       [
        2047,
        1373653,
        25326001,
        3215031751,
        2152302898747,
        3474749660383,
        341550071728321,
        1,
        3825123056546413051,
        1,
        1,
        318665857834031151167461,
        3317044064679887385961981,
    ]

    A__   				=       [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
    for idx, _p in enumerate(SCREAMING_SNAKE_CASE__   ,      1				):
        if n < _p:
            # then we have our last prime to check
            A__   				=       primes[:idx]
            break
    A__				,						A__   				=       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:
        A__   				=       False
        for r in range(SCREAMING_SNAKE_CASE__				):
            A__   				=       pow(SCREAMING_SNAKE_CASE__   ,      d * 2**r   ,      SCREAMING_SNAKE_CASE__				)
            # see article for analysis explanation for m
            if (r == 0 and m == 1) or ((m + 1) % n == 0):
                A__   				=       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 						_snake_case(   )							->				None:





    '''simple docstring'''






    assert not miller_rabin(561				)
    assert miller_rabin(563				)
    # 2047

    assert not miller_rabin(838201				)
    assert miller_rabin(838207				)
    # 1_373_653

    assert not miller_rabin(17316001				)
    assert miller_rabin(17316017				)
    # 25_326_001

    assert not miller_rabin(3078386641				)
    assert miller_rabin(3078386653				)
    # 3_215_031_751

    assert not miller_rabin(1713045574801				)
    assert miller_rabin(1713045574819				)
    # 2_152_302_898_747

    assert not miller_rabin(2779799728307				)
    assert miller_rabin(2779799728327				)
    # 3_474_749_660_383

    assert not miller_rabin(113850023909441				)
    assert miller_rabin(113850023909527				)
    # 341_550_071_728_321

    assert not miller_rabin(1275041018848804351				)
    assert miller_rabin(1275041018848804391				)
    # 3_825_123_056_546_413_051

    assert not miller_rabin(79666464458507787791867				)
    assert miller_rabin(79666464458507787791951				)
    # 318_665_857_834_031_151_167_461

    assert not miller_rabin(552840677446647897660333				)
    assert miller_rabin(552840677446647897660359				)
    # 3_317_044_064_679_887_385_961_981
    # upper limit for probabilistic test


if __name__ == "__main__":
     test_miller_rabin()




import datasets

from .evaluate import evaluate


lowercase_			=  "\\n@inproceedings{Rajpurkar2016SQuAD10,\n  title={SQuAD: 100, 000+ Questions for Machine Comprehension of Text},\n  author={Pranav Rajpurkar and Jian Zhang and Konstantin Lopyrev and Percy Liang},\n  booktitle={EMNLP},\n  year={2016}\n}\n"

lowercase_			=  "\nThis metric wrap the official scoring script for version 1 of the Stanford Question Answering Dataset (SQuAD).\n\nStanford Question Answering Dataset (SQuAD) is a reading comprehension dataset, consisting of questions posed by\ncrowdworkers on a set of Wikipedia articles, where the answer to every question is a segment of text, or span,\nfrom the corresponding reading passage, or the question might be unanswerable.\n"

lowercase_			=  "\nComputes SQuAD scores (F1 and EM).\nArgs:\n    predictions: List of question-answers dictionaries with the following key-values:\n        - 'id': id of the question-answer pair as given in the references (see below)\n        - 'prediction_text': the text of the answer\n    references: List of question-answers dictionaries with the following key-values:\n        - 'id': id of the question-answer pair (see above),\n        - 'answers': a Dict in the SQuAD dataset format\n            {\n                'text': list of possible texts for the answer, as a list of strings\n                'answer_start': list of start positions for the answer, as a list of ints\n            }\n            Note that answer_start values are not taken into account to compute the metric.\nReturns:\n    'exact_match': Exact match (the normalized answer exactly match the gold answer)\n    'f1': The F-score of predicted tokens versus the gold answer\nExamples:\n\n    >>> predictions = [{'prediction_text': '1976', 'id': '56e10a3be3433e1400422b22'}]\n    >>> references = [{'answers': {'answer_start': [97], 'text': ['1976']}, 'id': '56e10a3be3433e1400422b22'}]\n    >>> squad_metric = datasets.load_metric(\"squad\")\n    >>> results = squad_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {'exact_match': 100.0, 'f1': 100.0}\n"


@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION   ,							_KWARGS_DESCRIPTION			)
class 			A						(							datasets.Metric			):







    """simple docstring"""





    def 						snake_case__					(				self			:	List[Any]		)->   Tuple:





        '''simple docstring'''







        return datasets.MetricInfo(
            description=_DESCRIPTION,citation=_CITATION,inputs_description=_KWARGS_DESCRIPTION,features=datasets.Features(
                {
                    'predictions': {'id': datasets.Value('string'		), 'prediction_text': datasets.Value('string'		)},
                    'references': {
                        'id': datasets.Value('string'		),
                        'answers': datasets.features.Sequence(
                            {
                                'text': datasets.Value('string'		),
                                'answer_start': datasets.Value('int32'		),
                            }		),
                    },
                }		),codebase_urls=['https://rajpurkar.github.io/SQuAD-explorer/'],reference_urls=['https://rajpurkar.github.io/SQuAD-explorer/'],)


    def 						snake_case__					(				self			:	str,lowercase_			:	List[Any],lowercase_			:	Dict		)->   List[str]:





        '''simple docstring'''







        A__   				=       {prediction['id']: prediction['prediction_text'] for prediction in predictions}
        A__   				=       [
            {
                'paragraphs': [
                    {
                        'qas': [
                            {
                                'answers': [{'text': answer_text} for answer_text in ref['answers']['text']],
                                'id': ref['id'],
                            }
                            for ref in references
                        ]
                    }
                ]
            }
        ]
        A__   				=       evaluate(dataset=lowercase_,predictions=lowercase_		)
        return score

