


"""simple docstring"""


from scipy.stats import spearmanr

import datasets


_snake_case          =							"\nThe Spearman rank-order correlation coefficient is a measure of the\nrelationship between two datasets. Like other correlation coefficients,\nthis one varies between -1 and +1 with 0 implying no correlation.\nPositive correlations imply that as data in dataset x increases, so\ndoes data in dataset y. Negative correlations imply that as x increases,\ny decreases. Correlations of -1 or +1 imply an exact monotonic relationship.\n\nUnlike the Pearson correlation, the Spearman correlation does not\nassume that both datasets are normally distributed.\n\nThe p-value roughly indicates the probability of an uncorrelated system\nproducing datasets that have a Spearman correlation at least as extreme\nas the one computed from these datasets. The p-values are not entirely\nreliable but are probably reasonable for datasets larger than 500 or so.\n"

_snake_case          =							"\nArgs:\n    predictions (`List[float]`): Predicted labels, as returned by a model.\n    references (`List[float]`): Ground truth labels.\n    return_pvalue (`bool`): If `True`, returns the p-value. If `False`, returns\n            only the spearmanr score. Defaults to `False`.\nReturns:\n    spearmanr (`float`): Spearman correlation coefficient.\n    p-value (`float`): p-value. **Note**: is only returned if `return_pvalue=True` is input.\nExamples:\n    Example 1:\n        >>> spearmanr_metric = datasets.load_metric(\"spearmanr\")\n        >>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5], predictions=[10, 9, 2.5, 6, 4])\n        >>> print(results)\n        {'spearmanr': -0.7}\n\n    Example 2:\n        >>> spearmanr_metric = datasets.load_metric(\"spearmanr\")\n        >>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5],\n        ...                                     predictions=[10, 9, 2.5, 6, 4],\n        ...                                     return_pvalue=True)\n        >>> print(results['spearmanr'])\n        -0.7\n        >>> print(round(results['spearmanr_pvalue'], 2))\n        0.19\n"

_snake_case          =							R"\\n@book{kokoska2000crc,\n  title={CRC standard probability and statistics tables and formulae},\n  author={Kokoska, Stephen and Zwillinger, Daniel},\n  year={2000},\n  publisher={Crc Press}\n}\n@article{2020SciPy-NMeth,\n  author  = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and\n            Haberland, Matt and Reddy, Tyler and Cournapeau, David and\n            Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and\n            Bright, Jonathan and {van der Walt}, St{\'e}fan J. and\n            Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and\n            Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and\n            Kern, Robert and Larson, Eric and Carey, C J and\n            Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and\n            {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and\n            Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and\n            Harris, Charles R. and Archibald, Anne M. and\n            Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and\n            {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},\n  title   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific\n            Computing in Python}},\n  journal = {Nature Methods},\n  year    = {2020},\n  volume  = {17},\n  pages   = {261--272},\n  adsurl  = {https://rdcu.be/b08Wh},\n  doi     = {10.1038/s41592-019-0686-2},\n}\n"



@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION		,		_KWARGS_DESCRIPTION )
class   _a      (      datasets.Metric ):
    def      _UpperCamelCase       ( self							:					List[str]				):
          return datasets.MetricInfo(
              description=_DESCRIPTION							,					citation=_CITATION							,					inputs_description=_KWARGS_DESCRIPTION							,					features=datasets.Features(
                  {
                      'predictions': datasets.Value('float'				),
                      'references': datasets.Value('float'				),
                  }				)							,					reference_urls=['https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html']							,					)


    def      _UpperCamelCase       ( self							:					List[Any]							,					SCREAMING_SNAKE_CASE__							:					Dict							,					SCREAMING_SNAKE_CASE__							:					Optional[Any]							,					SCREAMING_SNAKE_CASE__							:					Any=False				):
          lowerCamelCase__           =		spearmanr(SCREAMING_SNAKE_CASE__							,					SCREAMING_SNAKE_CASE__				)
          if return_pvalue:
                return {"spearmanr": results[0], "spearmanr_pvalue": results[1]}
          else:
                return {"spearmanr": results[0]}







"""simple docstring"""


from __future__ import annotations

from math import gcd



def   snake_case						(				_a:     int		,   _a:     int = 2		,   _a:     int = 1		,   _a:     int = 3		,   )->		int | None:
      '''simple docstring'''


      if num < 2:
            raise ValueError('The input value cannot be less than 2'							)

      # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
      # algorithm struggles to find factors that are divisible by two.
      # As a workaround, we specifically check for two and even inputs.
      #   See: https://math.stackexchange.com/a/2856214/165820
      if num > 2 and num % 2 == 0:
            return 2

      # Pollard's Rho algorithm requires a function that returns pseudorandom
      # values between 0 <= X < ``num``.  It doesn't need to be random in the
      # sense that the output value is cryptographically secure or difficult
      # to calculate, it only needs to be random in the sense that all output
      # values should be equally likely to appear.
      # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
      # However, the success of Pollard's algorithm isn't guaranteed and is
      # determined in part by the initial seed and the chosen random function.
      # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
      # where ``C`` is a value that we can modify between each attempt.
      def rand_fn(_a:     int		,   _a:     int		,   _a:     int							) -> int:
            return (pow(_a		,   2							) + step) % modulus

      for _ in range(_a							):
            # These track the position within the cycle detection logic.
            lowerCamelCase__           =		seed
            lowerCamelCase__           =		seed

            while True:
                  # At each iteration, the tortoise moves one step and the hare moves two.
                  lowerCamelCase__           =		rand_fn(_a		,   _a		,   _a							)
                  lowerCamelCase__           =		rand_fn(_a		,   _a		,   _a							)
                  lowerCamelCase__           =		rand_fn(_a		,   _a		,   _a							)

                  # At some point both the tortoise and the hare will enter a cycle whose
                  # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
                  # the tortoise and hare will end up on the same value modulo ``p``.
                  # We can detect when this happens because the position difference between
                  # the tortoise and the hare will share a common divisor with ``num``.
                  lowerCamelCase__           =		gcd(hare - tortoise		,   _a							)

                  if divisor == 1:
                        # No common divisor yet, just keep searching.
                        continue
                  else:
                        # We found a common divisor!
                        if divisor == num:
                              # Unfortunately, the divisor is ``num`` itself and is useless.
                              break
                        else:
                              # The divisor is a nontrivial factor of ``num``!
                              return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
            lowerCamelCase__           =		hare

            # The new step value for the random function can just be incremented.
            # At first the results will be similar to what the old function would
            # have produced, but the value will quickly diverge after a bit.
            step += 1

      # We haven't found a divisor within the requested number of attempts.
      # We were unlucky or ``num`` itself is actually prime.
      return None


if __name__ == "__main__":
   import argparse

   _snake_case          =							argparse.ArgumentParser()
   parser.add_argument(
       "num",
       type=int,
       help="The value to find a divisor of",
   )
   parser.add_argument(
       "--attempts",
       type=int,
       default=3,
       help="The number of attempts before giving up",
   )
   _snake_case          =							parser.parse_args()

   _snake_case          =							pollard_rho(args.num, attempts=args.attempts)
   if divisor is None:
      print(f"""{args.num} is probably prime""")
   else:
      _snake_case          =							args.num // divisor
      print(f"""{args.num} = {divisor} * {quotient}""")



