code: def relative_position_bucket(
      relative_position,
      bidirectional: bool = True,
      num_buckets: int = 32,
      max_distance: int = 128,
  ):
      """Map the relative position to buckets. The implementation is consistent with that
      in [mesh_tensorflow](https://github.com/tensorflow/mesh/blob/c59988047e49b4d2af05603e3170724cdbadc467/mesh_tensorflow/transformer/transformer_layers.py#L595-L637)
      where relative position is defined as `mem_i - query_j`. Thus, a positive value indicates
      that the memory slot is in a later timestamp than the query slot.
  
      After handling the bidirectional case (see below), the implementation uses the first half
      of buckets to store exact differences and the second half to store the differences after
      a logrithmic transformation.
  
      Parameters
      ----------
      relative_position
          Shape (...,)
      bidirectional
          Whether we are dealing with bidirectional attention.
          If it's bidirectional, positive shifts are mapped to [0, num_buckets // 2),
          and negative shifts are mapped to [num_buckets // 2, num_buckets).
      num_buckets
          The number of buckets.
      max_distance
          Maximum distance. Positions that fall outside of 'max_distance' will be trimmed.
  
      Returns
      -------
      buckets
          Shape (...,).
          It has the same shape as the `relative_position`. It will have int32 type.
      """
      ret = 0
      relative_position = -relative_position
      if bidirectional:
          assert num_buckets % 2 == 0, (
              "When bidirectional is True, the number of buckets must be "
              "divisible by 2."
          )
          num_buckets //= 2
          ret = (
              ret
              + (relative_position < 0).astype(np.int32) * num_buckets
          )
          relative_position = np.abs(relative_position)
      else:
          # Clip all the negative values to 0
          relative_position = np.clip(
              relative_position, a_min=0, a_max=None
          )
      # Now, the relative_position is in the range [0, inf)
  
      # Half of the buckets deal with the exact increments,
      # i.e., 0, 1, 2, ..., max_exact - 1, where max_exact = num_buckets // 2
      max_exact = num_buckets // 2
      is_small = relative_position < max_exact
  
      # The other half of the buckets are for logarithmically bigger bins in positions up to
      # max_distance
      val_if_large = max_exact + (
          np.log(relative_position.astype(np.float32) / max_exact)
          / math.log(max_distance / max_exact)
          * (num_buckets - max_exact)
      ).astype(np.int32)
      val_if_large = np.minimum(val_if_large, num_buckets - 1)
      ret = ret + np.where(is_small, relative_position, val_if_large)
      return ret
  
file_path: gluon-nlp/src/gluonnlp/op.py
imports: import mxnet
  from mxnet import np, npx
  import math
  from mxnet import use_np
label_desc: Use image node_id 6 for calling a global function with example usage: relative_position_bucket(relative_position, bidirectional, num_buckets, max_distance) and returns: ret