





"""simple docstring"""




import math
from timeit import timeit





def 						UpperCAmelCase__		(					_UpperCAmelCase ):






  """simple docstring"""





  A_  :	Tuple    						=  0
  A_  :	Union[str, Any]    						=  abs(_UpperCAmelCase )
  while True:
    A_  :	str    						=  n // 10
    digits += 1
    if n == 0:
      break
  return digits





def 						UpperCAmelCase__		(					_UpperCAmelCase ):






  """simple docstring"""





  return 1 if n == 0 else math.floor(math.log(abs(_UpperCAmelCase )			, 10 ) + 1 )





def 						UpperCAmelCase__		(					_UpperCAmelCase ):






  """simple docstring"""





  return len(str(abs(_UpperCAmelCase ) ) )





def 						UpperCAmelCase__		(					):






  """simple docstring"""





  from collections.abc import Callable

  def benchmark_a_function(_UpperCAmelCase			, _UpperCAmelCase ) -> None:
    A_  :	List[str]    						=  f"""{func.__name__}({value})"""
    A_  :	Union[str, Any]    						=  timeit(f"""__main__.{call}"""			, setup='import __main__' )
    print(f"""{call}: {func(_UpperCAmelCase )} -- {timing} seconds""" )

  for value in (262144, 1125899906842624, 1267650600228229401496703205376):
    for func in (num_digits, num_digits_fast, num_digits_faster):
      benchmark_a_function(_UpperCAmelCase			, _UpperCAmelCase )
    print()


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   benchmark()






"""simple docstring"""




from functools import partial
from typing import Any, Callable, Dict, List, Type, TypeVar, Union, overload

import torch
import torch.nn as nn
import torch.types





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  if not inplace:
    A_  :	Optional[int]    						=  ma + ma
  else:
    ma += ma

  return ma





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  A_  :	Tuple    						=  -1 * len(_UpperCAmelCase )
  A_  :	List[str]    						=  list(range(len(tensor.shape[:zero_index] ) ) )
  return tensor.permute(first_inds + [zero_index + i for i in inds] )





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  return t.reshape(t.shape[:-no_dims] + (-1,) )





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase = 1E-4 ):






  """simple docstring"""





  A_  :	Optional[Any]    						=  mask.expand(*value.shape )
  return torch.sum(mask * value			, dim=_UpperCAmelCase ) / (eps + torch.sum(_UpperCAmelCase			, dim=_UpperCAmelCase ))





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase = 2.3_125			, _UpperCAmelCase = 21.6_875			, _UpperCAmelCase = 64 ):






  """simple docstring"""





  A_  :	List[str]    						=  torch.linspace(_UpperCAmelCase			, _UpperCAmelCase			, no_bins - 1			, device=pts.device )
  A_  :	Optional[Any]    						=  torch.sqrt(torch.sum((pts.unsqueeze(-2 ) - pts.unsqueeze(-3 )) ** 2			, dim=-1 ) )
  return torch.bucketize(_UpperCAmelCase			, _UpperCAmelCase )





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  A_  :	Any    						=  dicts[0]
  A_  :	int    						=  {}
  for k, v in first.items():
    A_  :	Dict    						=  [d[k] for d in dicts]
    if isinstance(_UpperCAmelCase			, _UpperCAmelCase ):
      A_  :	List[Any]    						=  dict_multimap(_UpperCAmelCase			, _UpperCAmelCase )
    else:
      A_  :	Union[str, Any]    						=  fn(_UpperCAmelCase )

  return new_dict





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  A_  :	Tuple    						=  v_bins.view(((1,) * len(x.shape )) + (len(_UpperCAmelCase ),) )
  A_  :	Any    						=  x[..., None] - reshaped_bins
  A_  :	List[str]    						=  torch.argmin(torch.abs(_UpperCAmelCase )			, dim=-1 )
  return nn.functional.one_hot(_UpperCAmelCase			, num_classes=len(_UpperCAmelCase ) ).float()





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase = 0			, _UpperCAmelCase = 0 ):






  """simple docstring"""





  A_  :	List[Union[slice, torch.Tensor]]    						=  []
  for i, s in enumerate(data.shape[:no_batch_dims] ):
    A_  :	List[Any]    						=  torch.arange(_UpperCAmelCase )
    A_  :	Dict    						=  r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape ) - i - 1))) )
    ranges.append(_UpperCAmelCase )

  A_  :	List[Union[slice, torch.Tensor]]    						=  [slice(_UpperCAmelCase ) for _ in range(len(data.shape ) - no_batch_dims )]
  A_  :	Optional[Any]    						=  inds
  ranges.extend(_UpperCAmelCase )
  # Matt note: Editing this to get around the behaviour of using a list as an array index changing
  # in recent Numpy versions
  return data[tuple(_UpperCAmelCase )]


lowerCamelCase_					:						Union[str, Any]      = TypeVar('T')





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  A_  :	Dict[Any, Union[dict, list, tuple, Any]]    						=  {}
  for k, v in dic.items():
    if isinstance(_UpperCAmelCase			, _UpperCAmelCase ):
      A_  :	int    						=  dict_map(_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase )
    else:
      A_  :	Any    						=  tree_map(_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase )

  return new_dict





@overload
def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  ...





@overload
def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  ...





@overload
def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  ...





@overload
def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  ...





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase ):






  """simple docstring"""





  if isinstance(_UpperCAmelCase			, _UpperCAmelCase ):
    return dict_map(_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase )
  elif isinstance(_UpperCAmelCase			, _UpperCAmelCase ):
    return [tree_map(_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase ) for x in tree]
  elif isinstance(_UpperCAmelCase			, _UpperCAmelCase ):
    return tuple(tree_map(_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase ) for x in tree )
  elif isinstance(_UpperCAmelCase			, _UpperCAmelCase ):
    return fn(_UpperCAmelCase )
  else:
    print(type(_UpperCAmelCase ) )
    raise ValueError('Not supported' )





lowerCamelCase_					:						Optional[int]      = partial(tree_map, leaf_type=torch.Tensor)