code: def associative_scan(
      x: Union[ivy.Array, ivy.NativeArray],
      fn: Callable,
      /,
      *,
      reverse: bool = False,
      axis: int = 0,
  ) -> ivy.Array:
      """Perform an associative scan over the given array.
  
      Parameters
      ----------
      x
          The array to scan over.
      fn
          The associative function to apply.
      reverse
          Whether to scan in reverse with respect to the given axis.
      axis
          The axis to scan over.
  
      Returns
      -------
      ret
          The result of the scan.
      """
      elems = [x]
  
      if reverse:
          elems = [ivy.flip(elem, axis=[axis]) for elem in elems]
  
      def _combine(a, b):
          a = a[0]
          b = b[0]
          if a.shape[axis] == 0:
              return [a]
          c = fn(a, b)
          return [c]
  
      def _scan(elems):
          num_elems = elems[0].shape[axis]
  
          if num_elems < 2:
              return elems
  
          reduced_elems = _combine(
              [
                  _slice_along_axis(elem, 0, -1, stride=2, axis=axis)
                  for elem in elems
              ],
              [
                  _slice_along_axis(elem, 1, None, stride=2, axis=axis)
                  for elem in elems
              ],
          )
  
          odd_elems = _scan(reduced_elems)
  
          if num_elems % 2 == 0:
              even_elems = _combine(
                  [
                      _slice_along_axis(e, 0, -1, axis=axis)
                      for e in odd_elems
                  ],
                  [
                      _slice_along_axis(e, 2, None, stride=2, axis=axis)
                      for e in elems
                  ],
              )
          else:
              even_elems = _combine(
                  odd_elems,
                  [
                      _slice_along_axis(e, 2, None, stride=2, axis=axis)
                      for e in elems
                  ],
              )
          even_elems = [
              ivy.concat(
                  [_slice_along_axis(elem, 0, 1, axis=axis), result],
                  axis=axis,
              )
              for (elem, result) in zip(elems, even_elems)
          ]
          return list(
              map(
                  partial(_interleave, axis=axis), even_elems, odd_elems
              )
          )
  
      scans = _scan(elems)
  
      if reverse:
          scans = [ivy.flip(scanned, axis=[axis]) for scanned in scans]
  
      return ivy.reshape(ivy.asarray(scans), elems[0].shape)
  
imports: from typing import Optional, Union, Tuple, Iterable, Sequence, Callable, Any, Literal, List
  from numbers import Number
  from functools import partial
  import math
  import ivy
  from ivy.func_wrapper import handle_out_argument, handle_partial_mixed_function, to_native_arrays_and_back, inputs_to_native_shapes, handle_nestable, handle_array_like_without_promotion, handle_view, inputs_to_ivy_arrays, handle_array_function, handle_device, handle_backend_invalid
  from ivy.functional.ivy.general import _numel
  from ivy.utils.backend import current_backend
  from ivy.utils.exceptions import handle_exceptions
label_desc: Use image node_id 45 for calling a global function with example usage: associative_scan() and returns: ivy, list, list, list, elems