

'''simple docstring'''

import math

def 			__magic_name__				(       A							)	->						Union[str, Any]:
	snake_case							       = math.log(2    ,      1_0							) * number
	snake_case							       = round((log_number - int(_lowercase							))    ,      1_5							)

	return difference

def 			__magic_name__				(       A = 6_7_8_9_1_0							)	->						int:
	snake_case							       = 9_0
	snake_case							       = 0

	snake_case							       = math.log(1.23    ,      1_0							)
	snake_case							       = math.log(1.24    ,      1_0							)
	snake_case							       = 0

	while position < number:
		snake_case							       = log_difference(_lowercase							)

		if difference >= upper_limit:
			power_iterator += 9_3

		elif difference < lower_limit:
			power_iterator += 1_9_6

		else:
			snake_case							       = power_iterator
			power_iterator += 1_9_6
			position += 1

	return previous_power


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						print(f"{solution() = }")












"""simple docstring"""




import torch
from torch import autograd




class  _a						(      autograd.Function				):






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    str, lowerCAmelCase__		:    torch.tensor, lowerCAmelCase__		:    float, lowerCAmelCase__		:    bool							)	->      List[Any]:




										'''simple docstring'''



										_UpperCamelCase			:					Optional[Any]     =    inputs.numel()
										_UpperCamelCase			:					int     =    int(0.005 * nb_elems							) + 1
										if sigmoid:
																_UpperCamelCase			:					Dict     =    (torch.sigmoid(lowerCAmelCase__							) > threshold).type(inputs.type()							)
										else:
																_UpperCamelCase			:					Optional[int]     =    (inputs > threshold).type(inputs.type()							)
										if mask.sum() < nb_min:
																# We limit the pruning so that at least 0.5% (half a percent) of the weights are remaining
																_UpperCamelCase			:					int     =    inputs.flatten().kthvalue(max(nb_elems - nb_min, 1							)							).values
																_UpperCamelCase			:					List[str]     =    (inputs > k_threshold).type(inputs.type()							)
										return mask






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    str, lowerCAmelCase__		:    Optional[int]							)	->      Union[str, Any]:




										'''simple docstring'''



										return gradOutput, None, None




class  _a						(      autograd.Function				):






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    Any, lowerCAmelCase__		:    torch.tensor, lowerCAmelCase__		:    float							)	->      Dict:




										'''simple docstring'''



										_UpperCamelCase			:					str     =    inputs.clone()
										_UpperCamelCase   ,							_UpperCamelCase			:					Union[str, Any]     =    inputs.flatten().sort(descending=lowerCAmelCase__							)
										_UpperCamelCase			:					Optional[Any]     =    int(threshold * inputs.numel()							)

										# flat_out and mask access the same memory.
										_UpperCamelCase			:					Tuple     =    mask.flatten()
										_UpperCamelCase			:					int     =    0
										_UpperCamelCase			:					Tuple     =    1
										return mask






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    Any, lowerCAmelCase__		:    Union[str, Any]							)	->      int:




										'''simple docstring'''



										return gradOutput, None




class  _a						(      _lowerCAmelCase				):






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    torch.tensor, lowerCAmelCase__		:    float							)	->      Dict:




										'''simple docstring'''



										_UpperCamelCase			:					List[Any]     =    inputs.clone()
										_UpperCamelCase   ,							_UpperCamelCase			:					Optional[int]     =    inputs.abs().flatten().sort(descending=lowerCAmelCase__							)
										_UpperCamelCase			:					List[Any]     =    int(threshold * inputs.numel()							)

										# flat_out and mask access the same memory.
										_UpperCamelCase			:					List[str]     =    mask.flatten()
										_UpperCamelCase			:					List[Any]     =    0
										_UpperCamelCase			:					str     =    1
										return mask



