from math import factorial

def 							UpperCamelCase				(    lowerCAmelCase_       ,					lowerCAmelCase_       ,					lowerCAmelCase_   )		->						float:




       '''simple docstring'''






       if successes > trials:
              raise ValueError('successes must be lower or equal to trials'   )
       if trials < 0 or successes < 0:
              raise ValueError('the function is defined for non-negative integers'   )
       if not isinstance(lowerCAmelCase_       ,					lowerCAmelCase_   ) or not isinstance(lowerCAmelCase_       ,					lowerCAmelCase_   ):
              raise ValueError('the function is defined for non-negative integers'   )
       if not 0 < prob < 1:
              raise ValueError('prob has to be in range of 1 - 0'   )
       _A=	(prob**successes) * ((1 - prob) ** (trials - successes))
       # Calculate the binomial coefficient: n! / k!(n-k)!
       _A=	float(factorial(lowerCAmelCase_   )   )
       coefficient /= factorial(lowerCAmelCase_   ) * factorial(trials - successes   )
       return probability * coefficient


if __name__ == "__main__":
      from doctest import testmod

      testmod()
      print('''Probability of 2 successes out of 4 trails''')
      print('''with probability of 0.75 is:''', end=''' ''')
      print(binomial_distribution(2, 4, 0.75))
import time
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch, torch_device

from ..test_modeling_common import ids_tensor


if is_torch_available():
      import torch

      from transformers.generation import (
          MaxLengthCriteria,
          MaxNewTokensCriteria,
          MaxTimeCriteria,
          StoppingCriteriaList,
          validate_stopping_criteria,
      )





@require_torch
class      lowerCAmelCase						(					unittest.TestCase			):



     def 			a__  (					self				,      lowerCAmelCase__       ):
            _A=	3
            _A=	250

            _A=	ids_tensor((batch_size, length)				,      lowerCAmelCase__       )
            _A=	torch.ones((batch_size, length)				,      device=lowerCAmelCase__				,      dtype=torch.float       ) / length
            return input_ids, scores



     def 			a__  (					self       ):
            _A,			_A=	self._get_tensors(5       )

            _A=	StoppingCriteriaList(
                [
                    MaxLengthCriteria(max_length=10       ),
                    MaxTimeCriteria(max_time=0.1       ),
                ]       )

            self.assertFalse(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )

            _A,			_A=	self._get_tensors(9       )
            self.assertFalse(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )

            _A,			_A=	self._get_tensors(10       )
            self.assertTrue(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )



     def 			a__  (					self       ):
            _A=	MaxLengthCriteria(max_length=10       )

            _A,			_A=	self._get_tensors(5       )
            self.assertFalse(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )

            _A,			_A=	self._get_tensors(9       )
            self.assertFalse(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )

            _A,			_A=	self._get_tensors(10       )
            self.assertTrue(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )



     def 			a__  (					self       ):
            _A=	MaxNewTokensCriteria(start_length=5				,      max_new_tokens=5       )

            _A,			_A=	self._get_tensors(5       )
            self.assertFalse(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )

            _A,			_A=	self._get_tensors(9       )
            self.assertFalse(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )

            _A,			_A=	self._get_tensors(10       )
            self.assertTrue(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )

            _A=	StoppingCriteriaList([criteria]       )
            self.assertEqual(criteria_list.max_length				,      10       )



     def 			a__  (					self       ):
            _A,			_A=	self._get_tensors(5       )

            _A=	MaxTimeCriteria(max_time=0.1       )
            self.assertFalse(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )

            _A=	MaxTimeCriteria(max_time=0.1				,      initial_timestamp=time.time() - 0.2       )
            self.assertTrue(criteria(lowerCAmelCase__				,      lowerCAmelCase__       )       )





     def 			a__  (					self       ):
            validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10       )]       )				,      10       )

            with self.assertWarns(lowerCAmelCase__       ):
                   validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10       )]       )				,      11       )

            _A=	validate_stopping_criteria(StoppingCriteriaList()				,      11       )

            self.assertEqual(len(lowerCAmelCase__       )				,      1       )