
import math
from timeit import timeit



def      __UpperCAmelCase    (  snake_case_							:		int				):



	'''simple docstring'''



	UpperCAmelCase:					Tuple 						=     0
	UpperCAmelCase:					str 						=     abs(snake_case_				)
	while True:
		UpperCAmelCase:					Union[str, Any] 						=     n // 1_0
		digits += 1
		if n == 0:
			break
	return digits



def      __UpperCAmelCase    (  snake_case_							:		int				):



	'''simple docstring'''



	return 1 if n == 0 else math.floor(math.log(abs(snake_case_				)				,					1_0				) + 1				)



def      __UpperCAmelCase    (  snake_case_							:		int				):



	'''simple docstring'''



	return len(str(abs(snake_case_				)				)				)



def      __UpperCAmelCase    (  ):



	'''simple docstring'''



	from collections.abc import Callable

	def benchmark_a_function(snake_case_							:		Callable				,					snake_case_							:		int				) -> None:
		UpperCAmelCase:					Tuple 						=     F'{func.__name__}({value})'
		UpperCAmelCase:					Optional[int] 						=     timeit(F'__main__.{call}'				,					setup="import __main__"				)
		print(F'{call}: {func(snake_case_				)} -- {timing} seconds'				)

	for value in (2_6_2_1_4_4, 1_1_2_5_8_9_9_9_0_6_8_4_2_6_2_4, 1_2_6_7_6_5_0_6_0_0_2_2_8_2_2_9_4_0_1_4_9_6_7_0_3_2_0_5_3_7_6):
		for func in (num_digits, num_digits_fast, num_digits_faster):
			benchmark_a_function(snake_case_				,					snake_case_				)
		print()


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	benchmark()


import torch
from torch import autograd





class 		__lowerCamelCase     (   autograd.Function		):



							@staticmethod
							def     A__ (     __snake_case	,				__snake_case	,				__snake_case	,				__snake_case							)						->     Dict:






								"""simple docstring"""



								UpperCAmelCase:					Optional[Any] 						=     inputs.numel()
								UpperCAmelCase:					Tuple 						=     int(0.0_05 * nb_elems							) + 1
								if sigmoid:
									UpperCAmelCase:					int 						=     (torch.sigmoid(__snake_case							) > threshold).type(inputs.type()							)
								else:
									UpperCAmelCase:					List[Any] 						=     (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:					List[Any] 						=     inputs.flatten().kthvalue(max(nb_elems - nb_min	,				1							)							).values
									UpperCAmelCase:					Optional[int] 						=     (inputs > k_threshold).type(inputs.type()							)
								return mask




							@staticmethod
							def     A__ (     __snake_case	,				__snake_case							)						->     Any:






								"""simple docstring"""



								return gradOutput, None, None





class 		__lowerCamelCase     (   autograd.Function		):



							@staticmethod
							def     A__ (     __snake_case	,				__snake_case	,				__snake_case							)						->     Any:






								"""simple docstring"""



								UpperCAmelCase:					Tuple 						=     inputs.clone()
								UpperCAmelCase						,   UpperCAmelCase:					List[Any] 						=     inputs.flatten().sort(descending=__snake_case							)
								UpperCAmelCase:					Optional[Any] 						=     int(threshold * inputs.numel()							)

								# flat_out and mask access the same memory.
								UpperCAmelCase:					Optional[int] 						=     mask.flatten()
								UpperCAmelCase:					Union[str, Any] 						=     0
								UpperCAmelCase:					int 						=     1
								return mask




							@staticmethod
							def     A__ (     __snake_case	,				__snake_case							)						->     Optional[Any]:






								"""simple docstring"""



								return gradOutput, None





class 		__lowerCamelCase     (   lowercase		):



							@staticmethod
							def     A__ (     __snake_case	,				__snake_case							)						->     str:






								"""simple docstring"""



								UpperCAmelCase:					Union[str, Any] 						=     inputs.clone()
								UpperCAmelCase						,   UpperCAmelCase:					Any 						=     inputs.abs().flatten().sort(descending=__snake_case							)
								UpperCAmelCase:					str 						=     int(threshold * inputs.numel()							)

								# flat_out and mask access the same memory.
								UpperCAmelCase:					Optional[int] 						=     mask.flatten()
								UpperCAmelCase:					Union[str, Any] 						=     0
								UpperCAmelCase:					List[str] 						=     1
								return mask
