

def  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ ,	SCREAMING_SNAKE_CASE_ = 1_0_0_0 )->	List[Any]:



    """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
    UpperCamelCase_      =	(
        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) * 1_6 ) )[2:]




def  lowerCAmelCase(			SCREAMING_SNAKE_CASE_ ,	SCREAMING_SNAKE_CASE_ ,	SCREAMING_SNAKE_CASE_ )->	List[str]:



    """simple docstring"""






    UpperCamelCase_      =	0.0
    for sum_index in range(digit_pos_to_extract + precision ):
        UpperCamelCase_      =	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
            UpperCamelCase_      =	pow(
                1_6 ,	digit_pos_to_extract - 1 - sum_index ,	__A )
        else:
            UpperCamelCase_      =	pow(1_6 ,	digit_pos_to_extract - 1 - sum_index )
        total += exponential_term / denominator
    return total


if __name__ == "__main__":
 import doctest

 doctest.testmod()



import unittest

from transformers.image_processing_utils import get_size_dict






class 	__magic_name__				(       unittest.TestCase							):






     def   UpperCAmelCase_							(							self  )->    int:
         # Test a dict with the wrong keys raises an error
         UpperCamelCase_      =	{"wrong_key": 224}
         with self.assertRaises(_lowercase  ):
             get_size_dict(_lowercase  )

         UpperCamelCase_      =	{"height": 224}
         with self.assertRaises(_lowercase  ):
             get_size_dict(_lowercase  )

         UpperCamelCase_      =	{"width": 224, "shortest_edge": 224}
         with self.assertRaises(_lowercase  ):
             get_size_dict(_lowercase  )

         # Test a dict with the correct keys is returned as is
         UpperCamelCase_      =	{"height": 224, "width": 224}
         UpperCamelCase_      =	get_size_dict(_lowercase  )
         self.assertEqual(_lowercase		,	_lowercase  )

         UpperCamelCase_      =	{"shortest_edge": 224}
         UpperCamelCase_      =	get_size_dict(_lowercase  )
         self.assertEqual(_lowercase		,	{"shortest_edge": 224}  )

         UpperCamelCase_      =	{"longest_edge": 224, "shortest_edge": 224}
         UpperCamelCase_      =	get_size_dict(_lowercase  )
         self.assertEqual(_lowercase		,	{"longest_edge": 224, "shortest_edge": 224}  )

         # Test a single int value which  represents (size, size)
         UpperCamelCase_      =	get_size_dict(224  )
         self.assertEqual(_lowercase		,	{"height": 224, "width": 224}  )

         # Test a single int value which represents the shortest edge
         UpperCamelCase_      =	get_size_dict(224		,	default_to_square=_lowercase  )
         self.assertEqual(_lowercase		,	{"shortest_edge": 224}  )

         # Test a tuple of ints which represents (height, width)
         UpperCamelCase_      =	get_size_dict((150, 200)  )
         self.assertEqual(_lowercase		,	{"height": 150, "width": 200}  )

         # Test a tuple of ints which represents (width, height)
         UpperCamelCase_      =	get_size_dict((150, 200)		,	height_width_order=_lowercase  )
         self.assertEqual(_lowercase		,	{"height": 200, "width": 150}  )

         # Test an int representing the shortest edge and max_size which represents the longest edge
         UpperCamelCase_      =	get_size_dict(224		,	max_size=256		,	default_to_square=_lowercase  )
         self.assertEqual(_lowercase		,	{"shortest_edge": 224, "longest_edge": 256}  )

         # Test int with default_to_square=True and max_size fails
         with self.assertRaises(_lowercase  ):
             get_size_dict(224		,	max_size=256		,	default_to_square=_lowercase  )
