



'''simple docstring'''
from __future__ import annotations


def   lowercase_	(   lowerCAmelCase__	:  list[int] ):

			"""simple docstring"""





			if not list_of_ints:
						return []

			if min(lowerCAmelCase__ ) < 0:
						raise ValueError("""All numbers must be positive""" )

			__UpperCAmelCase   :      List[str]										=     max(len(bin(lowerCAmelCase__ )[2:] ) for x in list_of_ints )
			return _msd_radix_sort(lowerCAmelCase__			,							lowerCAmelCase__ )


def   lowercase_	(   lowerCAmelCase__	:  list[int]			,							lowerCAmelCase__	:  int ):

			"""simple docstring"""





			if bit_position == 0 or len(lowerCAmelCase__ ) in [0, 1]:
						return list_of_ints

			__UpperCAmelCase   :      Optional[int]										=     []
			__UpperCAmelCase   :      Optional[Any]										=     []
			# Split numbers based on bit at bit_position from the right
			for number in list_of_ints:
						if (number >> (bit_position - 1)) & 1:
									# number has a one at bit bit_position
									ones.append(lowerCAmelCase__ )
						else:
									# number has a zero at bit bit_position
									zeros.append(lowerCAmelCase__ )

    # recursively split both lists further
			__UpperCAmelCase   :      List[str]										=     _msd_radix_sort(lowerCAmelCase__			,							bit_position - 1 )
			__UpperCAmelCase   :      int										=     _msd_radix_sort(lowerCAmelCase__			,							bit_position - 1 )

			# recombine lists
			__UpperCAmelCase   :      List[str]										=     zeros
			res.extend(lowerCAmelCase__ )

			return res


def   lowercase_	(   lowerCAmelCase__	:  list[int] ):

			"""simple docstring"""





			__UpperCAmelCase   :      Dict										=     len(lowerCAmelCase__ )
			if not list_of_ints or length == 1:
						return

			if min(lowerCAmelCase__ ) < 0:
						raise ValueError("""All numbers must be positive""" )

			__UpperCAmelCase   :      Optional[Any]										=     max(len(bin(lowerCAmelCase__ )[2:] ) for x in list_of_ints )
			_msd_radix_sort_inplace(lowerCAmelCase__			,							lowerCAmelCase__			,							0			,							lowerCAmelCase__ )


def   lowercase_	(   lowerCAmelCase__	:  list[int]			,							lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  int ):

			"""simple docstring"""





			if bit_position == 0 or end_index - begin_index <= 1:
						return

			bit_position -= 1

			__UpperCAmelCase   :      Optional[int]										=     begin_index
			__UpperCAmelCase   :      Union[str, Any]										=     end_index - 1
			while i <= j:
						__UpperCAmelCase   :      Tuple										=     False
						if not (list_of_ints[i] >> bit_position) & 1:
									# found zero at the beginning
									i += 1
									__UpperCAmelCase   :      int										=     True
						if (list_of_ints[j] >> bit_position) & 1:
									# found one at the end
									j -= 1
									__UpperCAmelCase   :      Dict										=     True

						if changed:
									continue

						__UpperCAmelCase				,  __UpperCAmelCase   :      Optional[Any]										=     list_of_ints[j], list_of_ints[i]
						j -= 1
						if j != i:
									i += 1

			_msd_radix_sort_inplace(lowerCAmelCase__			,							lowerCAmelCase__			,							lowerCAmelCase__			,							lowerCAmelCase__ )
			_msd_radix_sort_inplace(lowerCAmelCase__			,							lowerCAmelCase__			,							lowerCAmelCase__			,							lowerCAmelCase__ )


if __name__ == "__main__":
					import doctest

					doctest.testmod()









'''simple docstring'''
from .chunk_utils import chunk_layer
from .data_transforms import make_atomaa_masks
from .feats import atomaa_to_atomaa, frames_and_literature_positions_to_atomaa_pos, torsion_angles_to_frames
from .loss import compute_predicted_aligned_error, compute_tm
from .protein import Protein as OFProtein
from .protein import to_pdb
from .rigid_utils import Rigid, Rotation
from .tensor_utils import dict_multimap, flatten_final_dims, permute_final_dims




