import math
from timeit import timeit







def 						UpperCAmelCase							(		lowerCAmelCase_							)						->						int:
     a	:     Any						      =    0
     a	:     Optional[Any]						      =    abs(lowerCAmelCase_							)
     while True:
          a	:     int						      =    n // 1_0
          digits += 1
          if n == 0:
               break
     return digits







def 						UpperCAmelCase							(		lowerCAmelCase_							)						->						int:
     return 1 if n == 0 else math.floor(math.log(abs(lowerCAmelCase_							)    ,   1_0							) + 1							)







def 						UpperCAmelCase							(		lowerCAmelCase_							)						->						int:
     return len(str(abs(lowerCAmelCase_							)							)							)







def 						UpperCAmelCase							(		)						->						None:
     from collections.abc import Callable

     def benchmark_a_function(lowerCAmelCase_    ,   lowerCAmelCase_							) -> None:
          a	:     Union[str, Any]						      =    f"""{func.__name__}({value})"""
          a	:     Optional[int]						      =    timeit(f"""__main__.{call}"""    ,   setup='''import __main__'''							)
          print(f"""{call}: {func(lowerCAmelCase_							)} -- {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(lowerCAmelCase_    ,   lowerCAmelCase_							)
          print()


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  benchmark()
import torch
from torch import autograd






class 				_SCREAMING_SNAKE_CASE( autograd.Function						):
   @staticmethod
   def _lowercase(     lowerCAmelCase_				,  lowerCAmelCase_				,  lowerCAmelCase_				,  lowerCAmelCase_     )						->List[str]:
        a	:     str						      =    inputs.numel()
        a	:     str						      =    int(0.0_05 * nb_elems     ) + 1
        if sigmoid:
             a	:     Optional[Any]						      =    (torch.sigmoid(lowerCAmelCase_     ) > threshold).type(inputs.type()     )
        else:
             a	:     Union[str, 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
             a	:     str						      =    inputs.flatten().kthvalue(max(nb_elems - nb_min				,  1     )     ).values
             a	:     Tuple						      =    (inputs > k_threshold).type(inputs.type()     )
        return mask


   @staticmethod
   def _lowercase(     lowerCAmelCase_				,  lowerCAmelCase_     )						->Union[str, Any]:
        return gradOutput, None, None






class 				_SCREAMING_SNAKE_CASE( autograd.Function						):
   @staticmethod
   def _lowercase(     lowerCAmelCase_				,  lowerCAmelCase_				,  lowerCAmelCase_     )						->List[Any]:
        a	:     List[Any]						      =    inputs.clone()
        a      ,				a	:     Optional[Any]						      =    inputs.flatten().sort(descending=lowerCAmelCase_     )
        a	:     Tuple						      =    int(threshold * inputs.numel()     )

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


   @staticmethod
   def _lowercase(     lowerCAmelCase_				,  lowerCAmelCase_     )						->Tuple:
        return gradOutput, None






class 				_SCREAMING_SNAKE_CASE( snake_case__						):
   @staticmethod
   def _lowercase(     lowerCAmelCase_				,  lowerCAmelCase_     )						->Tuple:
        a	:     Union[str, Any]						      =    inputs.clone()
        a      ,				a	:     List[Any]						      =    inputs.abs().flatten().sort(descending=lowerCAmelCase_     )
        a	:     Optional[int]						      =    int(threshold * inputs.numel()     )

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