text: import warnings
  from operator import getitem
  from itertools import product
  from numbers import Integral
  from tlz import merge, pipe, concat, partial, get
  from tlz.curried import map
  
  from . import chunk
  from .core import (
      Array,
      map_blocks,
      concatenate,
      concatenate3,
      reshapelist,
      unify_chunks,
  )
  from .creation import empty_like, full_like
  from ..highlevelgraph import HighLevelGraph
  from ..base import tokenize
  from ..core import flatten
  from ..utils import concrete
  
  
  def fractional_slice(task, axes):
      """
  
      >>> fractional_slice(('x', 5.1), {0: 2})  # doctest: +SKIP
      (getitem, ('x', 6), (slice(0, 2),))
  
      >>> fractional_slice(('x', 3, 5.1), {0: 2, 1: 3})  # doctest: +SKIP
      (getitem, ('x', 3, 5), (slice(None, None, None), slice(-3, None)))
  
      >>> fractional_slice(('x', 2.9, 5.1), {0: 2, 1: 3})  # doctest: +SKIP
      (getitem, ('x', 3, 5), (slice(0, 2), slice(-3, None)))
      """
      rounded = (task[0],) + tuple(int(round(i)) for i in task[1:])
  
      index = []
      for i, (t, r) in enumerate(zip(task[1:], rounded[1:])):
          depth = axes.get(i, 0)
          if isinstance(depth, tuple):
              left_depth = depth[0]
              right_depth = depth[1]
          else:
              left_depth = depth
              right_depth = depth
  
          if t == r:
              index.append(slice(None, None, None))
          elif t < r and right_depth:
              index.append(slice(0, right_depth))
          elif t > r and left_depth:
              index.append(slice(-left_depth, None))
          else:
              index.append(slice(0, 0))
      index = tuple(index)
  
      if all(ind == slice(None, None, None) for ind in index):
          return task
      else:
          return (getitem, rounded, index)
  
  
  def expand_key(k, dims, name=None, axes=None):
      """Get all neighboring keys around center
  
      Parameters
      ----------
      k: tuple
          They key around which to generate new keys
      dims: Sequence[int]
          The number of chunks in each dimension
      name: Option[str]
          The name to include in the output keys, or none to include no name
      axes: Dict[int, int]
          The axes active in the expansion.  We don't expand on non-active axes
  
      Examples
      --------
      >>> expand_key(('x', 2, 3), dims=[5, 5], name='y', axes={0: 1, 1: 1})  # doctest: +NORMALIZE_WHITESPACE
      [[('y', 1.1, 2.1), ('y', 1.1, 3), ('y', 1.1, 3.9)],
       [('y',   2, 2.1), ('y',   2, 3), ('y',   2, 3.9)],
       [('y', 2.9, 2.1), ('y', 2.9, 3), ('y', 2.9, 3.9)]]
  
      >>> expand_key(('x', 0, 4), dims=[5, 5], name='y', axes={0: 1, 1: 1})  # doctest: +NORMALIZE_WHITESPACE
      [[('y',   0, 3.1), ('y',   0,   4)],
       [('y', 0.9, 3.1), ('y', 0.9,   4)]]
      """
  
      def inds(i, ind):
          rv = []
          if ind - 0.9 > 0:
              rv.append(ind - 0.9)
          rv.append(ind)
          if ind + 0.9 < dims[i] - 1:
              rv.append(ind + 0.9)
          return rv
  
      shape = []
      for i, ind in enumerate(k[1:]):
          num = 1
          if ind > 0:
              num += 1
          if ind < dims[i] - 1:
              num += 1
          shape.append(num)
  
      args = [
          inds(i, ind) if any((axes.get(i, 0),)) else [ind] for i, ind in enumerate(k[1:])
      ]
      if name is not None:
          args = [[name]] + args
      seq = list(product(*args))
      shape2 = [d if any((axes.get(i, 0),)) else 1 for i, d in enumerate(shape)]
      result = reshapelist(shape2, seq)
      return result
  
  
  def overlap_internal(x, axes):
      """Share boundaries between neighboring blocks
  
      Parameters
      ----------
  
      x: da.Array
          A dask array
      axes: dict
          The size of the shared boundary per axis
  
      The axes input informs how many cells to overlap between neighboring blocks
      {0: 2, 2: 5} means share two cells in 0 axis, 5 cells in 2 axis
      """
      dims = list(map(len, x.chunks))
      expand_key2 = partial(expand_key, dims=dims, axes=axes)
  
      # Make keys for each of the surrounding sub-arrays
      interior_keys = pipe(
          x.__dask_keys__(), flatten, map(expand_key2), map(flatten), concat, list
      )
  
      name = "overlap-" + tokenize(x, axes)
      getitem_name = "getitem-" + tokenize(x, axes)
      interior_slices = {}
      overlap_blocks = {}
      for k in interior_keys:
          frac_slice = fractional_slice((x.name,) + k, axes)
          if (x.name,) + k != frac_slice:
              interior_slices[(getitem_name,) + k] = frac_slice
          else:
              interior_slices[(getitem_name,) + k] = (x.name,) + k
              overlap_blocks[(name,) + k] = (
                  concatenate3,
                  (concrete, expand_key2((None,) + k, name=getitem_name)),
              )
  
      chunks = []
      for i, bds in enumerate(x.chunks):
          depth = axes.get(i, 0)
          if isinstance(depth, tuple):
              left_depth = depth[0]
              right_depth = depth[1]
          else:
              left_depth = depth
              right_depth = depth
  
          if len(bds) == 1:
              chunks.append(bds)
          else:
              left = [bds[0] + right_depth]
              right = [bds[-1] + left_depth]
              mid = []
              for bd in bds[1:-1]:
                  mid.append(bd + left_depth + right_depth)
              chunks.append(left + mid + right)
  
      dsk = merge(interior_slices, overlap_blocks)
      graph = HighLevelGraph.from_collections(name, dsk, dependencies=[x])
  
      return Array(graph, name, chunks, meta=x)
  
  
  def trim_overlap(x, depth, boundary=None):
      """Trim sides from each block.
  
      This couples well with the ``map_overlap`` operation which may leave
      excess data on each block.
  
      See also
      --------
      dask.array.overlap.map_overlap
  
      """
  
      # parameter to be passed to trim_internal
      axes = coerce_depth(x.ndim, depth)
      boundary2 = coerce_boundary(x.ndim, boundary)
      return trim_internal(x, axes=axes, boundary=boundary2)
  
  
  def trim_internal(x, axes, boundary=None):
      """Trim sides from each block
  
      This couples well with the overlap operation, which may leave excess data on
      each block
  
      See also
      --------
      dask.array.chunk.trim
      dask.array.map_blocks
      """
      boundary = coerce_boundary(x.ndim, boundary)
  
      olist = []
      for i, bd in enumerate(x.chunks):
          bdy = boundary.get(i, "none")
          overlap = axes.get(i, 0)
          ilist = []
          for j, d in enumerate(bd):
              if bdy != "none":
                  if isinstance(overlap, tuple):
                      d = d - sum(overlap)
                  else:
                      d = d - overlap * 2
  
              else:
                  if isinstance(overlap, tuple):
                      d = d - overlap[0] if j != 0 else d
                      d = d - overlap[1] if j != len(bd) - 1 else d
                  else:
                      d = d - overlap if j != 0 else d
                      d = d - overlap if j != len(bd) - 1 else d
  
              ilist.append(d)
          olist.append(tuple(ilist))
      chunks = tuple(olist)
  
      return map_blocks(
          partial(_trim, axes=axes, boundary=boundary),
          x,
          chunks=chunks,
          dtype=x.dtype,
          meta=x._meta,
      )
  
  
  def _trim(x, axes, boundary, block_info):
      """Similar to dask.array.chunk.trim but requires one to specificy the
      boundary condition.
  
      ``axes``, and ``boundary`` are assumed to have been coerced.
  
      """
      axes = [axes.get(i, 0) for i in range(x.ndim)]
      axes_front = (ax[0] if isinstance(ax, tuple) else ax for ax in axes)
      axes_back = (
          -ax[1]
          if isinstance(ax, tuple) and ax[1]
          else -ax
          if isinstance(ax, Integral) and ax
          else None
          for ax in axes
      )
  
      trim_front = (
          0 if (chunk_location == 0 and boundary.get(i, "none") == "none") else ax
          for i, (chunk_location, ax) in enumerate(
              zip(block_info[0]["chunk-location"], axes_front)
          )
      )
      trim_back = (
          None
          if (chunk_location == chunks - 1 and boundary.get(i, "none") == "none")
          else ax
          for i, (chunks, chunk_location, ax) in enumerate(
              zip(block_info[0]["num-chunks"], block_info[0]["chunk-location"], axes_back)
          )
      )
      ind = tuple(slice(front, back) for front, back in zip(trim_front, trim_back))
      return x[ind]
  
  
  def periodic(x, axis, depth):
      """Copy a slice of an array around to its other side
  
      Useful to create periodic boundary conditions for overlap
      """
  
      left = (
          (slice(None, None, None),) * axis
          + (slice(0, depth),)
          + (slice(None, None, None),) * (x.ndim - axis - 1)
      )
      right = (
          (slice(None, None, None),) * axis
          + (slice(-depth, None),)
          + (slice(None, None, None),) * (x.ndim - axis - 1)
      )
      l = x[left]
      r = x[right]
  
      l, r = _remove_overlap_boundaries(l, r, axis, depth)
  
      return concatenate([r, x, l], axis=axis)
  
  
  def reflect(x, axis, depth):
      """Reflect boundaries of array on the same side
  
      This is the converse of ``periodic``
      """
      if depth == 1:
          left = (
              (slice(None, None, None),) * axis
              + (slice(0, 1),)
              + (slice(None, None, None),) * (x.ndim - axis - 1)
          )
      else:
          left = (
              (slice(None, None, None),) * axis
              + (slice(depth - 1, None, -1),)
              + (slice(None, None, None),) * (x.ndim - axis - 1)
          )
      right = (
          (slice(None, None, None),) * axis
          + (slice(-1, -depth - 1, -1),)
          + (slice(None, None, None),) * (x.ndim - axis - 1)
      )
      l = x[left]
      r = x[right]
  
      l, r = _remove_overlap_boundaries(l, r, axis, depth)
  
      return concatenate([l, x, r], axis=axis)
  
  
  def nearest(x, axis, depth):
      """Each reflect each boundary value outwards
  
      This mimics what the skimage.filters.gaussian_filter(... mode="nearest")
      does.
      """
      left = (
          (slice(None, None, None),) * axis
          + (slice(0, 1),)
          + (slice(None, None, None),) * (x.ndim - axis - 1)
      )
      right = (
          (slice(None, None, None),) * axis
          + (slice(-1, -2, -1),)
          + (slice(None, None, None),) * (x.ndim - axis - 1)
      )
  
      l = concatenate([x[left]] * depth, axis=axis)
      r = concatenate([x[right]] * depth, axis=axis)
  
      l, r = _remove_overlap_boundaries(l, r, axis, depth)
  
      return concatenate([l, x, r], axis=axis)
  
  
  def constant(x, axis, depth, value):
      """ Add constant slice to either side of array """
      chunks = list(x.chunks)
      chunks[axis] = (depth,)
  
      c = full_like(
          x,
          value,
          shape=tuple(map(sum, chunks)),
          chunks=tuple(chunks),
          dtype=x.dtype,
      )
  
      return concatenate([c, x, c], axis=axis)
  
  
  def _remove_overlap_boundaries(l, r, axis, depth):
      lchunks = list(l.chunks)
      lchunks[axis] = (depth,)
      rchunks = list(r.chunks)
      rchunks[axis] = (depth,)
  
      l = l.rechunk(tuple(lchunks))
      r = r.rechunk(tuple(rchunks))
      return l, r
  
  
  def boundaries(x, depth=None, kind=None):
      """Add boundary conditions to an array before overlaping
  
      See Also
      --------
      periodic
      constant
      """
      if not isinstance(kind, dict):
          kind = dict((i, kind) for i in range(x.ndim))
      if not isinstance(depth, dict):
          depth = dict((i, depth) for i in range(x.ndim))
  
      for i in range(x.ndim):
          d = depth.get(i, 0)
          if d == 0:
              continue
  
          this_kind = kind.get(i, "none")
          if this_kind == "none":
              continue
          elif this_kind == "periodic":
              x = periodic(x, i, d)
          elif this_kind == "reflect":
              x = reflect(x, i, d)
          elif this_kind == "nearest":
              x = nearest(x, i, d)
          elif i in kind:
              x = constant(x, i, d, kind[i])
  
      return x
  
  
  def ensure_minimum_chunksize(size, chunks):
      """Determine new chunks to ensure that every chunk >= size
  
      Parameters
      ----------
      size: int
          The maximum size of any chunk.
      chunks: tuple
          Chunks along one axis, e.g. ``(3, 3, 2)``
  
      Examples
      --------
      >>> ensure_minimum_chunksize(10, (20, 20, 1))
      (20, 11, 10)
      >>> ensure_minimum_chunksize(3, (1, 1, 3))
      (5,)
  
      See Also
      --------
      overlap
      """
      if size <= min(chunks):
          return chunks
  
      # add too-small chunks to chunks before them
      output = []
      new = 0
      for c in chunks:
          if c < size:
              if new > size + (size - c):
                  output.append(new - (size - c))
                  new = size
              else:
                  new += c
          if new >= size:
              output.append(new)
              new = 0
          if c >= size:
              new += c
      if new >= size:
          output.append(new)
      elif len(output) >= 1:
          output[-1] += new
      else:
          raise ValueError(
              f"The overlapping depth {size} is larger than your " f"array {sum(chunks)}."
          )
  
      return tuple(output)
  
  
  def overlap(x, depth, boundary):
      """Share boundaries between neighboring blocks
  
      Parameters
      ----------
  
      x: da.Array
          A dask array
      depth: dict
          The size of the shared boundary per axis
      boundary: dict
          The boundary condition on each axis. Options are 'reflect', 'periodic',
          'nearest', 'none', or an array value.  Such a value will fill the
          boundary with that value.
  
      The depth input informs how many cells to overlap between neighboring
      blocks ``{0: 2, 2: 5}`` means share two cells in 0 axis, 5 cells in 2 axis.
      Axes missing from this input will not be overlapped.
  
      Any axis containing chunks smaller than depth will be rechunked if
      possible.
  
      Examples
      --------
      >>> import numpy as np
      >>> import dask.array as da
  
      >>> x = np.arange(64).reshape((8, 8))
      >>> d = da.from_array(x, chunks=(4, 4))
      >>> d.chunks
      ((4, 4), (4, 4))
  
      >>> g = da.overlap.overlap(d, depth={0: 2, 1: 1},
      ...                       boundary={0: 100, 1: 'reflect'})
      >>> g.chunks
      ((8, 8), (6, 6))
  
      >>> np.array(g)
      array([[100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],
             [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],
             [  0,   0,   1,   2,   3,   4,   3,   4,   5,   6,   7,   7],
             [  8,   8,   9,  10,  11,  12,  11,  12,  13,  14,  15,  15],
             [ 16,  16,  17,  18,  19,  20,  19,  20,  21,  22,  23,  23],
             [ 24,  24,  25,  26,  27,  28,  27,  28,  29,  30,  31,  31],
             [ 32,  32,  33,  34,  35,  36,  35,  36,  37,  38,  39,  39],
             [ 40,  40,  41,  42,  43,  44,  43,  44,  45,  46,  47,  47],
             [ 16,  16,  17,  18,  19,  20,  19,  20,  21,  22,  23,  23],
             [ 24,  24,  25,  26,  27,  28,  27,  28,  29,  30,  31,  31],
             [ 32,  32,  33,  34,  35,  36,  35,  36,  37,  38,  39,  39],
             [ 40,  40,  41,  42,  43,  44,  43,  44,  45,  46,  47,  47],
             [ 48,  48,  49,  50,  51,  52,  51,  52,  53,  54,  55,  55],
             [ 56,  56,  57,  58,  59,  60,  59,  60,  61,  62,  63,  63],
             [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],
             [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]])
      """
      depth2 = coerce_depth(x.ndim, depth)
      boundary2 = coerce_boundary(x.ndim, boundary)
  
      # rechunk if new chunks are needed to fit depth in every chunk
      depths = [max(d) if isinstance(d, tuple) else d for d in depth2.values()]
      new_chunks = tuple(
          ensure_minimum_chunksize(size, c) for size, c in zip(depths, x.chunks)
      )
      x1 = x.rechunk(new_chunks)
  
      x2 = boundaries(x1, depth2, boundary2)
      x3 = overlap_internal(x2, depth2)
      trim = dict(
          (k, v * 2 if boundary2.get(k, "none") != "none" else 0)
          for k, v in depth2.items()
      )
      x4 = chunk.trim(x3, trim)
      return x4
  
  
  def add_dummy_padding(x, depth, boundary):
      """
      Pads an array which has 'none' as the boundary type.
      Used to simplify trimming arrays which use 'none'.
  
      >>> import dask.array as da
      >>> x = da.arange(6, chunks=3)
      >>> add_dummy_padding(x, {0: 1}, {0: 'none'}).compute()  # doctest: +NORMALIZE_WHITESPACE
      array([..., 0, 1, 2, 3, 4, 5, ...])
      """
      for k, v in boundary.items():
          d = depth.get(k, 0)
          if v == "none" and d > 0:
              empty_shape = list(x.shape)
              empty_shape[k] = d
  
              empty_chunks = list(x.chunks)
              empty_chunks[k] = (d,)
  
              empty = empty_like(
                  getattr(x, "_meta", x),
                  shape=empty_shape,
                  chunks=empty_chunks,
                  dtype=x.dtype,
              )
  
              out_chunks = list(x.chunks)
              ax_chunks = list(out_chunks[k])
              ax_chunks[0] += d
              ax_chunks[-1] += d
              out_chunks[k] = tuple(ax_chunks)
  
              x = concatenate([empty, x, empty], axis=k)
              x = x.rechunk(out_chunks)
      return x
  
  
  def map_overlap(
      func, *args, depth=None, boundary=None, trim=True, align_arrays=True, **kwargs
  ):
      """Map a function over blocks of arrays with some overlap
  
      We share neighboring zones between blocks of the array, map a
      function, and then trim away the neighboring strips. If depth is
      larger than any chunk along a particular axis, then the array is
      rechunked.
  
      Note that this function will attempt to automatically determine the output
      array type before computing it, please refer to the ``meta`` keyword argument
      in ``map_blocks`` if you expect that the function will not succeed when
      operating on 0-d arrays.
  
      Parameters
      ----------
      func: function
          The function to apply to each extended block.
          If multiple arrays are provided, then the function should expect to
          receive chunks of each array in the same order.
      args : dask arrays
      depth: int, tuple, dict or list
          The number of elements that each block should share with its neighbors
          If a tuple or dict then this can be different per axis.
          If a list then each element of that list must be an int, tuple or dict
          defining depth for the corresponding array in `args`.
          Asymmetric depths may be specified using a dict value of (-/+) tuples.
          Note that asymmetric depths are currently only supported when
          ``boundary`` is 'none'.
          The default value is 0.
      boundary: str, tuple, dict or list
          How to handle the boundaries.
          Values include 'reflect', 'periodic', 'nearest', 'none',
          or any constant value like 0 or np.nan.
          If a list then each element must be a str, tuple or dict defining the
          boundary for the corresponding array in `args`.
          The default value is 'reflect'.
      trim: bool
          Whether or not to trim ``depth`` elements from each block after
          calling the map function.
          Set this to False if your mapping function already does this for you
      align_arrays: bool
          Whether or not to align chunks along equally sized dimensions when
          multiple arrays are provided.  This allows for larger chunks in some
          arrays to be broken into smaller ones that match chunk sizes in other
          arrays such that they are compatible for block function mapping. If
          this is false, then an error will be thrown if arrays do not already
          have the same number of blocks in each dimension.
      **kwargs:
          Other keyword arguments valid in ``map_blocks``
  
      Examples
      --------
      >>> import numpy as np
      >>> import dask.array as da
  
      >>> x = np.array([1, 1, 2, 3, 3, 3, 2, 1, 1])
      >>> x = da.from_array(x, chunks=5)
      >>> def derivative(x):
      ...     return x - np.roll(x, 1)
  
      >>> y = x.map_overlap(derivative, depth=1, boundary=0)
      >>> y.compute()
      array([ 1,  0,  1,  1,  0,  0, -1, -1,  0])
  
      >>> x = np.arange(16).reshape((4, 4))
      >>> d = da.from_array(x, chunks=(2, 2))
      >>> d.map_overlap(lambda x: x + x.size, depth=1).compute()
      array([[16, 17, 18, 19],
             [20, 21, 22, 23],
             [24, 25, 26, 27],
             [28, 29, 30, 31]])
  
      >>> func = lambda x: x + x.size
      >>> depth = {0: 1, 1: 1}
      >>> boundary = {0: 'reflect', 1: 'none'}
      >>> d.map_overlap(func, depth, boundary).compute()  # doctest: +NORMALIZE_WHITESPACE
      array([[12,  13,  14,  15],
             [16,  17,  18,  19],
             [20,  21,  22,  23],
             [24,  25,  26,  27]])
  
      The ``da.map_overlap`` function can also accept multiple arrays.
  
      >>> func = lambda x, y: x + y
      >>> x = da.arange(8).reshape(2, 4).rechunk((1, 2))
      >>> y = da.arange(4).rechunk(2)
      >>> da.map_overlap(func, x, y, depth=1).compute() # doctest: +NORMALIZE_WHITESPACE
      array([[ 0,  2,  4,  6],
             [ 4,  6,  8,  10]])
  
      When multiple arrays are given, they do not need to have the
      same number of dimensions but they must broadcast together.
      Arrays are aligned block by block (just as in ``da.map_blocks``)
      so the blocks must have a common chunk size.  This common chunking
      is determined automatically as long as ``align_arrays`` is True.
  
      >>> x = da.arange(8, chunks=4)
      >>> y = da.arange(8, chunks=2)
      >>> r = da.map_overlap(func, x, y, depth=1, align_arrays=True)
      >>> len(r.to_delayed())
      4
  
      >>> da.map_overlap(func, x, y, depth=1, align_arrays=False).compute()
      Traceback (most recent call last):
          ...
      ValueError: Shapes do not align {'.0': {2, 4}}
  
      Note also that this function is equivalent to ``map_blocks``
      by default.  A non-zero ``depth`` must be defined for any
      overlap to appear in the arrays provided to ``func``.
  
      >>> func = lambda x: x.sum()
      >>> x = da.ones(10, dtype='int')
      >>> block_args = dict(chunks=(), drop_axis=0)
      >>> da.map_blocks(func, x, **block_args).compute()
      10
      >>> da.map_overlap(func, x, **block_args).compute()
      10
      >>> da.map_overlap(func, x, **block_args, depth=1).compute()
      12
  
      For functions that may not handle 0-d arrays, it's also possible to specify
      ``meta`` with an empty array matching the type of the expected result. In
      the example below, ``func`` will result in an ``IndexError`` when computing
      ``meta``:
  
      >>> x = np.arange(16).reshape((4, 4))
      >>> d = da.from_array(x, chunks=(2, 2))
      >>> y = d.map_overlap(lambda x: x + x[2], depth=1, meta=np.array(()))
      >>> y
      dask.array<_trim, shape=(4, 4), dtype=float64, chunksize=(2, 2), chunktype=numpy.ndarray>
      >>> y.compute()
      array([[ 4,  6,  8, 10],
             [ 8, 10, 12, 14],
             [20, 22, 24, 26],
             [24, 26, 28, 30]])
  
      Similarly, it's possible to specify a non-NumPy array to ``meta``:
  
      >>> import cupy  # doctest: +SKIP
      >>> x = cupy.arange(16).reshape((4, 4))  # doctest: +SKIP
      >>> d = da.from_array(x, chunks=(2, 2))  # doctest: +SKIP
      >>> y = d.map_overlap(lambda x: x + x[2], depth=1, meta=cupy.array(()))  # doctest: +SKIP
      >>> y  # doctest: +SKIP
      dask.array<_trim, shape=(4, 4), dtype=float64, chunksize=(2, 2), chunktype=cupy.ndarray>
      >>> y.compute()  # doctest: +SKIP
      array([[ 4,  6,  8, 10],
             [ 8, 10, 12, 14],
             [20, 22, 24, 26],
             [24, 26, 28, 30]])
      """
      # Look for invocation using deprecated single-array signature
      # map_overlap(x, func, depth, boundary=None, trim=True, **kwargs)
      if isinstance(func, Array) and callable(args[0]):
          warnings.warn(
              "The use of map_overlap(array, func, **kwargs) is deprecated since dask 2.17.0 "
              "and will be an error in a future release. To silence this warning, use the syntax "
              "map_overlap(func, array0,[ array1, ...,] **kwargs) instead.",
              FutureWarning,
          )
          sig = ["func", "depth", "boundary", "trim"]
          depth = get(sig.index("depth"), args, depth)
          boundary = get(sig.index("boundary"), args, boundary)
          trim = get(sig.index("trim"), args, trim)
          func, args = args[0], [func]
  
      if not callable(func):
          raise TypeError(
              "First argument must be callable function, not {}\n"
              "Usage:   da.map_overlap(function, x)\n"
              "   or:   da.map_overlap(function, x, y, z)".format(type(func).__name__)
          )
      if not all(isinstance(x, Array) for x in args):
          raise TypeError(
              "All variadic arguments must be arrays, not {}\n"
              "Usage:   da.map_overlap(function, x)\n"
              "   or:   da.map_overlap(function, x, y, z)".format(
                  [type(x).__name__ for x in args]
              )
          )
  
      # Coerce depth and boundary arguments to lists of individual
      # specifications for each array argument
      def coerce(xs, arg, fn):
          if not isinstance(arg, list):
              arg = [arg] * len(xs)
          return [fn(x.ndim, a) for x, a in zip(xs, arg)]
  
      depth = coerce(args, depth, coerce_depth)
      boundary = coerce(args, boundary, coerce_boundary)
  
      # Align chunks in each array to a common size
      if align_arrays:
          # Reverse unification order to allow block broadcasting
          inds = [list(reversed(range(x.ndim))) for x in args]
          _, args = unify_chunks(*list(concat(zip(args, inds))), warn=False)
  
      for i, x in enumerate(args):
          for j in range(x.ndim):
              if isinstance(depth[i][j], tuple) and boundary[i][j] != "none":
                  raise NotImplementedError(
                      "Asymmetric overlap is currently only implemented "
                      "for boundary='none', however boundary for dimension "
                      "{} in array argument {} is {}".format(j, i, boundary[i][j])
                  )
  
      def assert_int_chunksize(xs):
          assert all(type(c) is int for x in xs for cc in x.chunks for c in cc)
  
      assert_int_chunksize(args)
      if not trim and "chunks" not in kwargs:
          kwargs["chunks"] = args[0].chunks
      args = [overlap(x, depth=d, boundary=b) for x, d, b in zip(args, depth, boundary)]
      assert_int_chunksize(args)
      x = map_blocks(func, *args, **kwargs)
      assert_int_chunksize([x])
      if trim:
          # Find index of array argument with maximum rank and break ties by choosing first provided
          i = sorted(enumerate(args), key=lambda v: (v[1].ndim, -v[0]))[-1][0]
          # Trim using depth/boundary setting for array of highest rank
          return trim_internal(x, depth[i], boundary[i])
      else:
          return x
  
  
  def coerce_depth(ndim, depth):
      default = 0
      if depth is None:
          depth = default
      if isinstance(depth, Integral):
          depth = (depth,) * ndim
      if isinstance(depth, tuple):
          depth = dict(zip(range(ndim), depth))
      if isinstance(depth, dict):
          depth = {ax: depth.get(ax, default) for ax in range(ndim)}
      return coerce_depth_type(ndim, depth)
  
  
  def coerce_depth_type(ndim, depth):
      for i in range(ndim):
          if isinstance(depth[i], tuple):
              depth[i] = tuple(int(d) for d in depth[i])
          else:
              depth[i] = int(depth[i])
      return depth
  
  
  def coerce_boundary(ndim, boundary):
      default = "reflect"
      if boundary is None:
          boundary = default
      if not isinstance(boundary, (tuple, dict)):
          boundary = (boundary,) * ndim
      if isinstance(boundary, tuple):
          boundary = dict(zip(range(ndim), boundary))
      if isinstance(boundary, dict):
          boundary = {ax: boundary.get(ax, default) for ax in range(ndim)}
      return boundary
  