





"""simple docstring"""




from __future__ import annotations





def        a_				(							_lowercase       ,						_lowercase       ,						_lowercase   ):
						assert n > 1 and a > 0 and greatest_common_divisor(_lowercase       ,						_lowercase   ) == 1
						((_UpperCamelCase)   ,							(_UpperCamelCase)   ,							(_UpperCamelCase))			:					Union[str, Any]     =    extended_gcd(_lowercase       ,						_lowercase   )  # Implemented below
						_UpperCamelCase			:					Optional[Any]     =    (b * s) % n
						return x





def        a_				(							_lowercase       ,						_lowercase   ):
						((_UpperCamelCase)   ,							(_UpperCamelCase))			:					int     =    extended_euclid(_lowercase       ,						_lowercase   )  # Implemented below
						if b < 0:
												_UpperCamelCase			:					Any     =    (b % n + n) % n
						return b





def        a_				(							_lowercase       ,						_lowercase       ,						_lowercase   ):
						_UpperCamelCase			:					Optional[Any]     =    invert_modulo(_lowercase       ,						_lowercase   )
						_UpperCamelCase			:					int     =    (b * s) % n
						return x





def        a_				(							_lowercase       ,						_lowercase   ):
						assert a >= 0 and b >= 0

						if b == 0:
												_UpperCamelCase   ,							_UpperCamelCase   ,							_UpperCamelCase			:					int     =    a, 1, 0
						else:
												((_UpperCamelCase)   ,							(_UpperCamelCase)   ,							(_UpperCamelCase))			:					Any     =    extended_gcd(_lowercase       ,						a % b   )
												_UpperCamelCase			:					List[Any]     =    q
												_UpperCamelCase			:					Tuple     =    p - q * (a // b)

						assert a % d == 0 and b % d == 0
						assert d == a * x + b * y

						return (d, x, y)





def        a_				(							_lowercase       ,						_lowercase   ):
						if b == 0:
												return (1, 0)
						((_UpperCamelCase)   ,							(_UpperCamelCase))			:					int     =    extended_euclid(_lowercase       ,						a % b   )
						_UpperCamelCase			:					Any     =    a // b
						return (y, x - k * y)





def        a_				(							_lowercase       ,						_lowercase   ):
						if a < b:
												_UpperCamelCase   ,							_UpperCamelCase			:					Tuple     =    b, a

						while a % b != 0:
												_UpperCamelCase   ,							_UpperCamelCase			:					Any     =    b, a % b

						return b


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

						testmod(name="""modular_division""", verbose=True)
						testmod(name="""modular_division2""", verbose=True)
						testmod(name="""invert_modulo""", verbose=True)
						testmod(name="""extended_gcd""", verbose=True)
						testmod(name="""extended_euclid""", verbose=True)
						testmod(name="""greatest_common_divisor""", verbose=True)










"""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



