# Copyright 2021 The JAX Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from __future__ import annotations

import collections
from collections import OrderedDict
from collections.abc import Mapping, Sequence
import dataclasses
import enum
import functools
import itertools
import math
from typing import Any, NamedTuple, Union, cast

from jax._src import mesh as mesh_lib
from jax._src import sharding
from jax._src import sharding_specs
from jax._src import tree_util
from jax._src import util
from jax._src import xla_bridge
from jax._src import core
from jax._src.lib import xla_client as xc
from jax._src.lib import xla_extension_version
from jax._src.op_shardings import (
    are_op_shardings_equal, get_num_ways_dim_sharded, is_op_sharding_replicated)
from jax._src.partition_spec import PartitionSpec
from jax._src.util import safe_map, safe_zip, use_cpp_class, use_cpp_method
import numpy as np


Shape = tuple[int, ...]
Device = xc.Device
Index = tuple[slice, ...]
XLADeviceAssignment = tuple[Device, ...]
# TODO(yashkatariya): Remove this after 3 months of deprecation.
XLACompatibleSharding = sharding.Sharding

@dataclasses.dataclass(frozen=True)
class TransferToMemoryKind:
  memory_kind: str


@util.cache(max_size=128, trace_context_in_key=False)
def _check_mesh_resource_axis(mesh, parsed_pspec, _manual_axes):
  try:
    for p in parsed_pspec:
      if p is not None:
        for r in p:
          mesh.shape[r]
          if r in _manual_axes:
            raise ValueError(
                f"Axis: {r} of {parsed_pspec.get_partition_spec()} "
                f"is also found in manual_axes: {_manual_axes}.") from None
  except KeyError as e:
    raise ValueError(f"Resource axis: {e.args[0]} of {parsed_pspec.user_spec} is "
                     "undefined.") from None


def hashed_index(x) -> int:
  # This works for both `pjit`/`xmap` indices and `pmap` indices (which might
  # have an integer instead of a slice).
  assert all(v.step is None for v in x if isinstance(v, slice))
  return hash(tuple((v.start, v.stop) if isinstance(v, slice) else v for v in x))


@util.cache(max_size=4096, trace_context_in_key=False)
def device_replica_id_map(sharding, global_shape: Shape) -> Mapping[Device, int]:
  try:
    device_indices_map_fn = sharding.devices_indices_map
  except AttributeError:
    raise ValueError(
        f'Cannot calculate replica ids from sharding: {sharding}. Please '
        'create a device to index mapping for your sharding from which replica '
        'ids will be calculated.') from None

  index_to_replica: dict[int, int] = collections.Counter()
  out = {}
  for device, index in device_indices_map_fn(global_shape).items():
    h_index = hashed_index(index)
    replica_id = index_to_replica[h_index]
    index_to_replica[h_index] += 1
    out[device] = replica_id
  return out


@util.cache(max_size=4096, trace_context_in_key=False)
def named_sharding_to_xla_hlo_sharding(
    self, num_dimensions: int) -> xc.HloSharding:
  mesh_shape = self.mesh.shape
  array_mapping = get_array_mapping(self._parsed_pspec)
  mesh_axis_pos = {name: i for i, name in enumerate(self.mesh.axis_names)}

  special_axes = {}
  if self._manual_axes:
    axis_names = self.mesh.axis_names
    for manual_axis in self._manual_axes:
      special_axes[axis_names.index(manual_axis)] = xc.OpSharding.Type.MANUAL

  replicated_mesh_axes = []
  for i, (axis_name, axis_val) in enumerate(mesh_shape.items()):
    if axis_name not in array_mapping:  # type: ignore
      replicated_mesh_axes.append((i, axis_val))

  if len(replicated_mesh_axes) == len(mesh_shape) and not special_axes:
    return xc.HloSharding.replicate()

  mesh_permutation = []
  new_mesh_shape = [1] * num_dimensions
  for name, pos in sorted(array_mapping.items(), key=lambda x: x[1]):  # type: ignore
    new_mesh_shape[pos] *= mesh_shape[name]
    mesh_permutation.append(mesh_axis_pos[name])

  last_tile_dims = []
  if replicated_mesh_axes:
    axes_by_type = collections.defaultdict(list)
    size_by_type = collections.defaultdict(lambda: 1)  # type: ignore
    assert {x[0] for x in replicated_mesh_axes}.issuperset(set(special_axes.keys()))
    for i, size in replicated_mesh_axes:
      ty = special_axes.get(i, xc.OpSharding.Type.REPLICATED)
      axes_by_type[ty].append(i)
      size_by_type[ty] *= size
    for ty, axes in sorted(axes_by_type.items(), key=lambda x: x[0].value):
      last_tile_dims.append(ty)
      new_mesh_shape.append(size_by_type[ty])
      mesh_permutation.extend(axes)

  # Explanation of the parameters of `HloSharding.iota_tile`.
  # This is the HloShardingV2 format:
  #   * dims: How many ways each dimension is sharded.
  #       Replicated/Manual dims are added added at the end
  #   * reshape_dims: This is the just the shape of the mesh.
  #   * transpose_perm: This is the order in which mesh axes in PartitionSpec
  #       appear relative to mesh.axis_names order.
  #   * subgroup_types: List of type of OpSharding. Type can be REPLICATED and MANUAL.
  # Let's see an example:
  #   Consider input_shape=(8, 4, 2, 2), mesh={'a': 2, 'b': 2, 'c': 2, 'd': 2}
  #   and partition_spec=P(None, ('d', 'b'), 'c').
  #   Arguments to iota_tile will be:
  #     dims = [1, 4, 2, 1, 2]  # 'a' is replicated hence `2` is at the end.
  #     reshape_dims = [2, 2, 2, 2]
  #     transpose_perm = [3, 1, 2, 0]  # 'a' is replicated hence 0 is at the end
  #     subgroup_types = [xc.OpSharding.Type.REPLICATED]
  return xc.HloSharding.iota_tile(
      dims=new_mesh_shape, reshape_dims=tuple(self.mesh.shape.values()),
      transpose_perm=mesh_permutation, subgroup_types=last_tile_dims)


@use_cpp_class(xc.NamedSharding)
class NamedSharding(sharding.Sharding):
  r"""A :class:`NamedSharding` expresses sharding using named axes.

  A :class:`NamedSharding` is a pair of a :class:`Mesh` of devices and
  :class:`PartitionSpec` which describes how to shard an array across that
  mesh.

  A :class:`Mesh` is a multidimensional NumPy array of JAX devices,
  where each axis of the mesh has a name, e.g. ``'x'`` or ``'y'``.

  A :class:`PartitionSpec` is a tuple, whose elements can be a ``None``,
  a mesh axis, or a tuple of mesh axes. Each element describes how an input
  dimension is partitioned across zero or more mesh dimensions. For example,
  ``PartitionSpec('x', 'y')`` says that the first dimension of data
  is sharded across ``x`` axis of the mesh, and the second dimension is sharded
  across ``y`` axis of the mesh.

  The Distributed arrays and automatic parallelization
  (https://jax.readthedocs.io/en/latest/notebooks/Distributed_arrays_and_automatic_parallelization.html#namedsharding-gives-a-way-to-express-shardings-with-names)
  tutorial has more details and diagrams that explain how
  :class:`Mesh` and :class:`PartitionSpec` are used.

  Args:
    mesh: A :class:`jax.sharding.Mesh` object.
    spec: A :class:`jax.sharding.PartitionSpec` object.

  Example:

    >>> from jax.sharding import Mesh
    >>> from jax.sharding import PartitionSpec as P
    >>> mesh = Mesh(np.array(jax.devices()).reshape(2, 4), ('x', 'y'))
    >>> spec = P('x', 'y')
    >>> named_sharding = jax.sharding.NamedSharding(mesh, spec)
  """

  mesh: mesh_lib.Mesh
  spec: PartitionSpec
  _memory_kind: str | None
  _parsed_pspec: ParsedPartitionSpec
  _manual_axes: frozenset[MeshAxisName]

  @use_cpp_method()
  def __init__(
      self, mesh: mesh_lib.Mesh, spec: PartitionSpec, *,
      memory_kind: str | None = None, _parsed_pspec=None,
      _manual_axes=frozenset()):
    self.mesh = mesh
    self.spec = spec
    self._memory_kind = memory_kind
    self._manual_axes = _manual_axes
    self._parsed_pspec = preprocess(self.mesh, self.spec, _parsed_pspec)

  def __repr__(self):
    mesh_repr = ", ".join(f"'{k}': {v}" for k, v in self.mesh.shape.items())
    mem = '' if self.memory_kind is None else f', memory_kind={self.memory_kind}'
    return f'NamedSharding(mesh=Mesh({mesh_repr}), spec={self.spec}{mem})'

  def __reduce__(self):
    return (type(self), (self.mesh, self.spec),
            {'memory_kind': self.memory_kind,
             '_manual_axes': self._manual_axes})

  @property
  def memory_kind(self) -> str | None:
    return self._memory_kind

  def __hash__(self):
    if not hasattr(self, '_hash'):
      self._hash = hash(
          (self.mesh, self.memory_kind, self._parsed_pspec, self._manual_axes))
    return self._hash

  def __eq__(self, other):
    if not isinstance(other, NamedSharding):
      return False
    if self is other:
      return True
    if (self._parsed_pspec != other._parsed_pspec
        or self.memory_kind != other.memory_kind
        or self._manual_axes != other._manual_axes):
      return False
    return self.mesh is other.mesh or self.mesh == other.mesh

  def check_compatible_aval(self, aval_shape: Shape) -> None:
    assert self._parsed_pspec is not None
    if len(aval_shape) < len(self._parsed_pspec):
      extra_msg = (' For scalars the PartitionSpec should be P()'
                   if len(aval_shape) == 0 else '')
      raise ValueError(
          f"Sharding {self} is only valid for values of rank at least "
          f"{len(self._parsed_pspec)}, but was applied to a value of rank "
          f"{len(aval_shape)}.{extra_msg}")

  @classmethod
  def _from_parsed_pspec(
      cls, mesh, parsed_pspec, *, memory_kind=None, _manual_axes=frozenset()
  ):
    return cls(mesh, parsed_pspec.get_partition_spec(),
                memory_kind=memory_kind, _parsed_pspec=parsed_pspec,
                _manual_axes=_manual_axes)

  @property
  def device_set(self) -> set[Device]:
    return self.mesh._flat_devices_set

  @property
  def _device_assignment(self) -> XLADeviceAssignment:
    return self.mesh._flat_devices_tuple

  @property
  def is_fully_addressable(self) -> bool:
    # Speed up `is_fully_addressable` since there is a high chance that the
    # mesh across multiple NamedSharding objects will be the same.
    return not self.mesh.is_multi_process

  @property
  def addressable_devices(self) -> set[Device]:
    # Override addressable devices because there is a high chance that the mesh
    # across multiple NamedSharding objects will be the same.
    return self.mesh._local_devices_set

  @functools.cached_property
  def is_fully_replicated(self) -> bool:
    if self.mesh.size == 1:
      return True
    array_mapping = cast(ParsedPartitionSpec, get_array_mapping(self._parsed_pspec))
    mesh_shape = self.mesh.shape
    num_partitions = 1
    for name in array_mapping:
      num_partitions *= mesh_shape[name]
    return num_partitions == 1

  def with_memory_kind(self, kind: str) -> NamedSharding:
    return NamedSharding(self.mesh, self.spec, memory_kind=kind)

  def _to_xla_hlo_sharding(self, num_dimensions: int) -> xc.HloSharding:
    return named_sharding_to_xla_hlo_sharding(self, num_dimensions)


@util.cache(max_size=128, trace_context_in_key=False)
def get_replicated_hlo_sharding():
  return xc.HloSharding.replicate()


@use_cpp_class(xc.SingleDeviceSharding)
class SingleDeviceSharding(sharding.Sharding):
  """A :class:`Sharding` that places its data on a single device.

  Args:
    device: A single :py:class:`Device`.

  Example:

    >>> single_device_sharding = jax.sharding.SingleDeviceSharding(
    ...     jax.devices()[0])
  """

  _device: Device
  _memory_kind: str | None

  @use_cpp_method()
  def __init__(self, device: Device, *, memory_kind: str | None = None):
    self._device = device
    self._memory_kind = memory_kind

  def __reduce__(self):
    return type(self), (self._device,), {'memory_kind': self._memory_kind}

  def __repr__(self):
    mem = '' if self._memory_kind is None else f', memory_kind={self._memory_kind}'
    return f"SingleDeviceSharding(device={self._device!r}{mem})"

  def __hash__(self):
    if not hasattr(self, '_hash'):
      self._hash = hash((self._device, self.memory_kind))
    return self._hash

  def __eq__(self, other):
    if not isinstance(other, SingleDeviceSharding):
      return False
    if self is other:
      return True
    return (self._device == other._device and
            self.memory_kind == other.memory_kind)

  @property
  def device_set(self) -> set[Device]:
    return {self._device}

  @property
  def memory_kind(self) -> str | None:
    return self._memory_kind

  def with_memory_kind(self, kind: str) -> SingleDeviceSharding:
    return SingleDeviceSharding(self._device, memory_kind=kind)

  def devices_indices_map(self, global_shape: Shape) -> Mapping[Device, Index]:  # type: ignore
    return {self._device: (slice(None),) * len(global_shape)}

  @property
  def _device_assignment(self) -> XLADeviceAssignment:
    return (self._device,)

  def _to_xla_hlo_sharding(self, num_dimensions: int) -> xc.HloSharding:
    return get_replicated_hlo_sharding()

  @property
  def is_fully_replicated(self) -> bool:
    return True

  @property
  def is_fully_addressable(self) -> bool:
    return True


@util.cache(max_size=4096, trace_context_in_key=False)
def pmap_sharding_devices_indices_map(
    self, global_shape: Shape) -> Mapping[Device, Index]:
  self.shard_shape(global_shape)  # raises a good error message
  indices = sharding_specs.spec_to_indices(global_shape, self.sharding_spec)
  return dict(safe_zip(self.devices.flat, indices))  # type: ignore[arg-type]


@use_cpp_class(xc.PmapSharding)
class PmapSharding(sharding.Sharding):
  """Describes a sharding used by :func:`jax.pmap`."""
  devices: np.ndarray
  sharding_spec: sharding_specs.ShardingSpec
  _internal_device_list: xc.DeviceList

  @use_cpp_method()
  def __init__(self, devices: Sequence[Device] | np.ndarray,
               sharding_spec: sharding_specs.ShardingSpec):
    self.devices = np.asarray(devices)
    # The sharding spec should be pmap's sharding spec.
    self.sharding_spec = sharding_spec

  def __reduce__(self):
    return (type(self), (self.devices, self.sharding_spec),
            {'memory_kind': self.memory_kind})

  def __eq__(self, other):
    if not isinstance(other, PmapSharding):
      return False
    if self is other:
      return True
    return (self.sharding_spec == other.sharding_spec and
            self.devices.shape == other.devices.shape and
            self._internal_device_list == other._internal_device_list)

  def __hash__(self):
    if not hasattr(self, '_hash'):
      self._hash = hash((self._internal_device_list, self.sharding_spec))
    return self._hash

  def __str__(self):
    device_ids = [d.id for d in self.devices.flat]
    return (f'PmapSharding(sharding_spec={self.sharding_spec}, '
            f'{device_ids=}, '
            f'device_platform={self.devices.flat[0].platform.upper()}, '
            f'device_shape={self.devices.shape})')

  def __repr__(self):
    return (f'PmapSharding(sharding_spec={self.sharding_spec}, '
            f'devices={self.devices})')

  def is_equivalent_to(self: PmapSharding, other: PmapSharding,  # type: ignore
                       ndim: int) -> bool:
    return self == other

  # TODO(yashkatariya): Expose `sharded_dim_size` in the API if required.
  @classmethod
  def default(cls, shape: Shape, sharded_dim: int = 0,
              devices: Sequence[xc.Device] | None = None) -> PmapSharding:
    """Creates a :class:`PmapSharding` which matches the default placement
    used by :func:`jax.pmap`.

    Args:
      shape: The shape of the input array.
      sharded_dim: Dimension the input array is sharded on. Defaults to 0.
      devices: Optional sequence of devices to use. If omitted, the implicit
      device order used by pmap is used, which is the order of
        :func:`jax.local_devices`.
    """
    # The dtype doesn't matter here. Its only used for creating the
    # sharding_spec.
    sharding_spec = sharding_specs.create_pmap_sharding_spec(
        tuple(shape), sharded_dim)

    num_ways_sharded = None
    for s in sharding_spec.sharding:
      if isinstance(s, sharding_specs.Unstacked):
        assert num_ways_sharded is None
        num_ways_sharded = s.size
      elif isinstance(s, sharding_specs.Chunked):
        assert num_ways_sharded is None
        if len(s.chunks) == 1:
          num_ways_sharded = s.chunks[0]
        else:
          raise NotImplementedError(
              'Multiple chunks in Chunked dimension not supported.')

    if num_ways_sharded is None:
      raise NotImplementedError(
          '`None` to sharded_dim is not supported. Please file a jax '
          'issue if you need this feature.')

    if devices is None:
      pmap_devices: np.ndarray = np.array(
          xla_bridge.local_devices()[:num_ways_sharded])
    else:
      pmap_devices = np.array(devices)
    return cls(pmap_devices, sharding_spec)

  @functools.cached_property
  def device_set(self) -> set[Device]:
    return set(self.devices.flat)

  def devices_indices_map(self, global_shape: Shape) -> Mapping[Device, Index]:
    return pmap_sharding_devices_indices_map(self, global_shape)

  @functools.cached_property
  def _device_assignment(self) -> XLADeviceAssignment:
    return tuple(self.devices.flat)

  @property
  def memory_kind(self) -> str | None:
    try:
      return self._internal_device_list.default_memory_kind
    except:
      return None

  def with_memory_kind(self, kind: str):
    raise NotImplementedError("pmap does not support memories.")

  def _to_xla_hlo_sharding(self, num_dimensions: int) -> xc.HloSharding:
    raise NotImplementedError("pmap doesn't use OpSharding.")

  @functools.cached_property
  def is_fully_replicated(self) -> bool:
    for s in self.sharding_spec.sharding:
      if isinstance(s, (sharding_specs.Unstacked, sharding_specs.Chunked)):
        return False
    return True

  @functools.cached_property
  def is_fully_addressable(self) -> bool:
    return self._internal_device_list.is_fully_addressable

  def shard_shape(self, global_shape: Shape) -> Shape:
    sharded_dim = None
    sharded_dim_size = None
    for i, s in enumerate(self.sharding_spec.sharding):
      if isinstance(s, sharding_specs.Unstacked):
        sharded_dim = i
        sharded_dim_size = s.size
        sharded_shape = util.tuple_delete(global_shape, sharded_dim)
        break
      elif isinstance(s, sharding_specs.Chunked):
        sharded_dim = i
        assert len(s.chunks) == 1, s.chunks
        sharded_dim_size = s.chunks[0]
        sharded_shape = util.tuple_update(global_shape, sharded_dim, 1)
        break
    if sharded_dim is None:
      return global_shape
    if global_shape[sharded_dim] != sharded_dim_size:
      raise ValueError(
          f'The sharded dimension must be equal to the number of '
          f'devices passed to PmapSharding. Got sharded dimension {sharded_dim} '
          f'with value {global_shape[sharded_dim]} in shape {global_shape} and '
          f'the number of devices={len(self._device_assignment)}')
    return sharded_shape


def _op_sharding_to_pos_sharding(
    op_sharding: xc.OpSharding | xc.HloSharding,
    device_assignment: Sequence[xc.Device],
    memory_kind: str | None = None) -> PositionalSharding:
  if isinstance(op_sharding, xc.OpSharding):
    op_sharding = xc.HloSharding.from_proto(op_sharding)

  if op_sharding.is_replicated():
    return PositionalSharding(
        device_assignment, memory_kind=memory_kind).replicate()

  if len(op_sharding.subgroup_types()) > 1:
    raise NotImplementedError(
        'Unhandled HloSharding type. Please open a bug report!'
    )

  name = device_assignment[0].platform.upper()
  ids = np.array(
      [DeviceIdSet(name, i) for i in op_sharding.tile_assignment_devices()]
  )
  p = PositionalSharding._remake(tuple(device_assignment), ids,
                                 memory_kind=memory_kind)
  p = p.reshape(op_sharding.tile_assignment_dimensions())
  if op_sharding.replicate_on_last_tile_dim():
    p = p.replicate(-1, keepdims=False)
  return p


@util.cache(max_size=4096, trace_context_in_key=False)
def _positional_sharding_to_xla_hlo_sharding(
    self, num_dimensions: int) -> xc.HloSharding:
  if self.shape == (1,) * self.ndim:
    return get_replicated_hlo_sharding()

  pbuf = xc.OpSharding()
  shape = self.shape[self.ndim - num_dimensions:]  # 'rank promotion' of val
  set_size, = {len(device_set) for device_set in self._ids.flat}
  pbuf.type = xc.OpSharding.Type.OTHER
  if set_size > 1:
    pbuf.last_tile_dims = [xc.OpSharding.Type.REPLICATED]
    pbuf.tile_assignment_dimensions = (*shape, set_size)
  else:
    pbuf.tile_assignment_dimensions = shape
  pbuf.tile_assignment_devices = [i for ids in self._ids.flat for i in ids]
  product_of_dims = math.prod(pbuf.tile_assignment_dimensions)
  num_devices = len(pbuf.tile_assignment_devices)
  assert product_of_dims == num_devices, (product_of_dims, num_devices)
  return xc.HloSharding.from_proto(pbuf)


class PositionalSharding(sharding.Sharding):
  _devices: tuple[xc.Device, ...]
  _memory_kind: str | None
  _ids: np.ndarray  # dtype DeviceIdSet

  def __init__(self, devices: Sequence[xc.Device] | np.ndarray,
               *, memory_kind: str | None = None):
    super().__init__()
    if not isinstance(devices, np.ndarray):
      devices = np.array(devices, dtype='object')
    if not devices.size:
      raise ValueError(f"{self.__class__.__name__}.__init__ requires at least "
                       f"one device, got {devices}")
    self._devices = tuple(devices.flat)
    self._memory_kind = memory_kind
    name = self._devices[0].platform.upper()
    self._ids = np.array([DeviceIdSet(name, i) for i in range(devices.size)],
                         dtype='object').reshape(devices.shape)
    self._internal_device_list = xc.DeviceList(self._devices)
    self._memory_kind = xc.check_and_canonicalize_memory_kind(
        self._memory_kind, self._internal_device_list)

  @property
  def shape(self):
    return self._ids.shape

  @property
  def ndim(self):
    return self._ids.ndim

  def __repr__(self) -> str:
    cls_name = self.__class__.__name__
    ids = self._ids.copy()
    platform_name = self._devices[0].platform.upper()
    for idx, x in np.ndenumerate(ids):
      ids[idx] = DeviceIdSet(platform_name, *(self._devices[i].id for i in x))
    body = np.array2string(ids, prefix=cls_name + '(', suffix=')',
                           max_line_width=100)
    mem = '' if self._memory_kind is None else f', memory_kind={self._memory_kind}'
    return f'{cls_name}({body}{mem}, shape={self.shape})'

  def reshape(self, *shape) -> PositionalSharding:
    return self._remake(self._devices, self._ids.reshape(*shape))

  def transpose(self, *axes) -> PositionalSharding:
    return self._remake(self._devices, self._ids.transpose(*axes))
  T = property(transpose)

  def replicate(self, axis=None, keepdims=True) -> PositionalSharding:
    new_ids = self._ids.sum(axis=axis, keepdims=keepdims)  # union
    return self._remake(self._devices, new_ids)

  def check_compatible_aval(self, aval_shape: Shape) -> None:
    if len(aval_shape) != len(self.shape):
      raise ValueError(
          f"Sharding {self} is only valid for values of rank "
          f"{len(self.shape)}, but was applied to a value of rank "
          f"{len(aval_shape)}")

  @classmethod
  def _remake(
      cls, devices: tuple[xc.Device, ...], ids: np.ndarray,
      *, memory_kind: str | None = None) -> PositionalSharding:
    self = cls.__new__(cls)
    self._devices = devices
    self._ids = ids
    self._internal_device_list = xc.DeviceList(self._devices)
    self._memory_kind = xc.check_and_canonicalize_memory_kind(
        memory_kind, self._internal_device_list)
    return self

  # Hashable

  def __hash__(self) -> int:
    if not hasattr(self, '_hash'):
      self._hash = hash((self._internal_device_list, self.memory_kind))
    return self._hash

  def __eq__(self, other) -> bool:
    if not isinstance(other, PositionalSharding):
      return False
    if self is other:
      return True
    all_ids_equal = np.array_equal(self._ids,other._ids)
    mem_kind_equal = self.memory_kind == other.memory_kind
    if self._devices is other._devices and mem_kind_equal and all_ids_equal:
      return True
    return (mem_kind_equal and all_ids_equal and
            self._internal_device_list == other._internal_device_list)

  # Sharding interface

  @functools.cached_property
  def device_set(self) -> set[xc.Device]:
    return set(self._devices)

  @property
  def memory_kind(self) -> str | None:
    return self._memory_kind

  def with_memory_kind(self, kind: str) -> PositionalSharding:
    return PositionalSharding(self._devices, memory_kind=kind)

  @functools.cached_property
  def is_fully_replicated(self) -> bool:
    return self.shape == (1,) * self.ndim

  # sharding.Sharding interface

  @property
  def _device_assignment(self) -> XLADeviceAssignment:
    return self._devices

  def _to_xla_hlo_sharding(self, num_dimensions: int) -> xc.HloSharding:
    return _positional_sharding_to_xla_hlo_sharding(self, num_dimensions)

  @functools.cached_property
  def is_fully_addressable(self) -> bool:
    return self._internal_device_list.is_fully_addressable


class DeviceIdSet:
  _name: str
  _ids: frozenset[int]
  def __init__(self, name, *ids):
    self._name = name
    self._ids = frozenset(ids)

  def __iter__(self):
    return iter(sorted(self._ids))

  def __add__(self, other) -> DeviceIdSet:
    assert isinstance(other, DeviceIdSet)
    return DeviceIdSet(self._name, *(self._ids | other._ids))

  def __len__(self) -> int:
    return len(self._ids)

  def __repr__(self) -> str:
    ids = ', '.join(safe_map(str, sorted(self._ids)))
    return f'{{{self._name} {ids}}}'

  def __hash__(self) -> int:
    return hash((self._name, self._ids))

  def __eq__(self, other) -> bool:
    return (isinstance(other, DeviceIdSet) and self._name == other._name and
            self._ids == other._ids)


@use_cpp_class(xc.GSPMDSharding)
class GSPMDSharding(sharding.Sharding):
  _devices: tuple[Device, ...]
  _hlo_sharding: xc.HloSharding
  _memory_kind: str | None
  _device_list: xc.DeviceList | None
  _internal_device_list: xc.DeviceList

  @use_cpp_method()
  def __init__(self, devices: Sequence[Device],
               op_sharding: xc.OpSharding | xc.HloSharding,
               *, memory_kind: str | None = None,
               _device_list: xc.DeviceList | None = None):
    self._devices = tuple(devices)
    if isinstance(op_sharding, xc.OpSharding):
      self._hlo_sharding = xc.HloSharding.from_proto(op_sharding)
    else:
      self._hlo_sharding = op_sharding
    self._memory_kind = memory_kind

  def __reduce__(self):
    return (type(self), (self._devices, self._hlo_sharding.to_proto()),
            {'memory_kind': self._memory_kind})

  @functools.cached_property
  def _hlo_sharding_hash(self):
    if self.is_fully_replicated:
      return hash(get_replicated_hlo_sharding())
    return hash(self._hlo_sharding)

  def __eq__(self, other):
    if not isinstance(other, GSPMDSharding):
      return False
    if self is other:
      return True
    return (are_op_shardings_equal(self._hlo_sharding, other._hlo_sharding)
            and self.memory_kind == other.memory_kind
            and self._internal_device_list == other._internal_device_list)

  def __hash__(self):
    if not hasattr(self, '_hash'):
      self._hash = hash((self._internal_device_list, self._hlo_sharding_hash,
                        self.memory_kind))
    return self._hash

  def __repr__(self):
    mem = '' if self._memory_kind is None else f', memory_kind={self._memory_kind}'
    return f'GSPMDSharding({self._hlo_sharding!r}{mem})'

  def check_compatible_aval(self, aval_shape: Shape) -> None:
    num_ways_dim_sharded, _ = get_num_ways_dim_sharded(self._hlo_sharding)
    if len(aval_shape) < len(num_ways_dim_sharded):
      raise ValueError(
          f"Sharding {self} is only valid for values of rank at least "
          f"{len(num_ways_dim_sharded)}, but was applied to a value of rank "
          f"{len(aval_shape)}")

  @functools.cached_property
  def device_set(self) -> set[Device]:
    return set(self._devices)

  @property
  def memory_kind(self) -> str | None:
    return self._memory_kind

  def with_memory_kind(self, kind: str) -> GSPMDSharding:
    return GSPMDSharding(self._devices, self._hlo_sharding, memory_kind=kind)

  @property
  def _device_assignment(self) -> XLADeviceAssignment:
    return self._devices

  def _to_xla_hlo_sharding(self, num_dimensions: int) -> xc.HloSharding:
    return self._hlo_sharding

  @functools.cached_property
  def is_fully_replicated(self) -> bool:
    return is_op_sharding_replicated(self._hlo_sharding)

  @functools.cached_property
  def is_fully_addressable(self) -> bool:
    return self._internal_device_list.is_fully_addressable

  @classmethod
  def get_replicated(cls, device_assignment, *, memory_kind: str | None = None):
    return cls(tuple(device_assignment), get_replicated_hlo_sharding(),
               memory_kind=memory_kind)


class AUTO:

  def __init__(self, mesh: mesh_lib.Mesh):
    self.mesh = mesh


def is_auto(x):
  return isinstance(x, AUTO)


class UnspecifiedValue:
  def __repr__(self):
    return "UnspecifiedValue"
UNSPECIFIED = UnspecifiedValue()

def is_unspecified(x):
  return isinstance(x, UnspecifiedValue)

def is_unspecified_or_auto(x):
  return is_auto(x) or is_unspecified(x)


MeshAxisName = Any

"""
ArrayMapping specifies how an ndarray should map to mesh axes.

Note that the ordering is crucial for the cases when this mapping is non-injective
(i.e. when multiple mesh axes map to the same positional axis). Then, the
order of entries of the mapping determines a major-to-minor order on mesh axes,
according to which chunks of the value along the repeated dimension will be assigned.

For example, consider a mapping {'x': 1, 'y': 1} and a mesh with shape {'x': 2, 'y': 3}.
The second dimension of the value would get chunked into 6 pieces, and assigned to the
mesh in a way that treats 'y' as the fastest changing (minor) dimension. In this case,
that would mean that a flat list of chunks would get assigned to a flattened list of
mesh devices without any modifications. If the mapping was {'y': 1, 'x': 1}, then the
mesh devices ndarray would have to be transposed before flattening and assignment.
"""
ArrayMapping = OrderedDict[MeshAxisName, int]
ArrayMappingOrAutoOrUnspecified = Union[ArrayMapping, AUTO, UnspecifiedValue]

def array_mapping_to_axis_resources(array_mapping: ArrayMapping):
  if not array_mapping:
    return PartitionSpec()
  max_index = -1
  reverse_map = collections.defaultdict(list)
  for axis, index in array_mapping.items():
    reverse_map[index].append(axis)
    if index > max_index:
      max_index = index
  partitions = []
  for i in range(max_index + 1):
    axis = reverse_map[i]
    if axis:
      partitions.append(axis[0] if len(axis) == 1 else tuple(axis))
    else:
      partitions.append(None)
  return PartitionSpec(*partitions)

def get_array_mapping(
    axis_resources: ParsedPartitionSpec | AUTO | UnspecifiedValue
) -> ArrayMappingOrAutoOrUnspecified:
  # TODO(yashkatariya): Use `TypeGuard` on `is_auto` when it is supported.
  # Don't use `is_auto` here to satisfy pytype and mypy.
  if isinstance(axis_resources, (AUTO, UnspecifiedValue)):
    return axis_resources
  return OrderedDict((axis, i)
                     for i, axes in enumerate(axis_resources)
                     if axes is not None for axis in axes)


get_single_pspec = lambda p: array_mapping_to_axis_resources(
    cast(ArrayMapping, get_array_mapping(p)))


class SpecSync(enum.IntEnum):
  """Encodes how much out of sync the real value of partitions is compared to the user specified one.

  We use this to make sure we don't show garbage modified values while claiming
  that the users have specified them like that.
  """
  OUT_OF_SYNC = 0  # Arbitrary changes, including new axes inserted
  DIM_PERMUTE = 1  # Dimensions permuted, but no new sharding axes
  IN_SYNC = 2  # Entirely in sync

class ParsedPartitionSpec:
  __slots__ = ('unsafe_user_spec', 'partitions', 'sync')

  def __init__(self, user_spec, partitions, sync=SpecSync.IN_SYNC):
    self.unsafe_user_spec = user_spec
    # None in partitions represents unconstrained dim.
    # TODO(yashkatariya): May use a sentinel value.
    self.partitions = tuple(partitions)
    self.sync = sync

  @property
  def user_spec(self):
    return self.unsynced_user_spec(SpecSync.IN_SYNC)

  def get_partition_spec(self) -> PartitionSpec:
    if self.sync < SpecSync.IN_SYNC:
      return get_single_pspec(self)
    else:
      if isinstance(self.unsafe_user_spec, PartitionSpec):
        return self.unsafe_user_spec
      else:
        return get_single_pspec(self)

  def unsynced_user_spec(self, min_sync):
    if self.sync < min_sync:
      raise AssertionError(f"Please open a bug report! ({self.sync} >= {min_sync})")
    return self.unsafe_user_spec

  def insert_axis_partitions(self, dim, val):
    parts = self.partitions
    too_short = dim - len(parts)
    if too_short > 0:
      parts += ((),) * too_short
    new_partitions = util.tuple_insert(parts, dim, val)
    new_sync = SpecSync.DIM_PERMUTE if (val == () or val is None) else SpecSync.OUT_OF_SYNC
    return ParsedPartitionSpec(self.unsafe_user_spec, new_partitions, sync=new_sync)

  @classmethod
  def from_user_input(cls, entry, arg_name, allow_unconstrained_dims=False):
    if entry is None:
      return cls(entry, ())
    if not isinstance(entry, PartitionSpec):
      raise TypeError(f"{arg_name} are expected to be "
                      f"PartitionSpec instances or None, but got {entry}")
    axis_specs = []
    for axis_spec in entry:
      if axis_spec is None:
        axis_spec = ()
      elif isinstance(axis_spec, (list, tuple)):
        axis_spec = tuple(axis_spec)
      elif axis_spec == PartitionSpec.UNCONSTRAINED:
        if not allow_unconstrained_dims:
          raise ValueError(f"Unconstrained dims are not allowed: {entry}")
        axis_spec = None
      else:
        axis_spec = (axis_spec,)
      axis_specs.append(axis_spec)
    new_entry = PartitionSpec(
        *[tuple(e) if isinstance(e, (list, tuple)) else e for e in entry])
    return cls(new_entry, axis_specs)

  def __hash__(self):
    return hash((self.partitions, self.sync))

  def __eq__(self, other):
    return (self.partitions == other.partitions and
            self.sync == other.sync)

  def __len__(self):
    return len(self.partitions)

  def __getitem__(self, i):
    return self.partitions[i]

  def __iter__(self):
    return iter(self.partitions)

  def __repr__(self):
    return (f"ParsedPartitionSpec(partitions={self.partitions}, "
            f"unsafe_user_spec={self.unsafe_user_spec}, "
            f"sync={self.sync})")

class CanonicalizedParsedPartitionSpec(ParsedPartitionSpec):
  """ParsedPartitionSpecs that are canonicalized.

  ParsedPartitionSpecs may contain trailing empty tuples, that make them
  semantically different in general, and yet in some situations we prefer
  to regard them as equivalent. For example, partitions of () and ((),)
  cannot be always considered equivalent, since the first one is a valid
  spec for a scalar value, while the second is not! However, when either of
  those are applied to a 2D array, they both mean that the array is fully
  replicated.

  So CanonicalizedParsedPartitionSpecs removes the trailing empty tuples from
  partitions.
  """

  def __init__(self, parsed_pspec: ParsedPartitionSpec):
    partitions = list(parsed_pspec.partitions)
    while partitions and partitions[-1] == ():
      partitions.pop()

    super().__init__(parsed_pspec.unsafe_user_spec, partitions,
                     parsed_pspec.sync)

  def __repr__(self):
    return (f"CanonicalizedParsedPartitionSpec(partitions={self.partitions}, "
            f"unsafe_user_spec={self.unsafe_user_spec}, "
            f"sync={self.sync})")


def preprocess(mesh, spec, parsed_pspec, _manual_axes=frozenset()):
  # This split exists because you can pass `_parsed_pspec` that has been
  # modified from the original. For example: Adding extra dimension to
  # axis_resources for vmap handlers. In such cases you need to preserve the
  # `sync` attribute of parsed pspecs.
  # PartitionSpec is inferred from the parsed pspec in this case.
  # TODO(yaskatariya): Remove this and replace this with a normalized
  # representation of Parsed Pspec
  if parsed_pspec is None:
    parsed_pspec = prepare_axis_resources(
        PartitionSpec() if spec is None else spec,
        "NamedSharding spec", allow_unconstrained_dims=True)

  _check_mesh_resource_axis(mesh, parsed_pspec, _manual_axes)
  return parsed_pspec

# fallback for c++ .
preprocess_with_manual = preprocess

def prepare_axis_resources(axis_resources,
                           arg_name,
                           allow_unconstrained_dims=False):
  # PyTrees don't treat None values as leaves, so we use an is_leaf function.
  entries, treedef = tree_util.tree_flatten(
      axis_resources, is_leaf=lambda x: x is None)
  what = f"{arg_name} leaf specifications"

  new_entries = []
  for entry in entries:
    if is_unspecified_or_auto(entry) or entry is None:
      new_entries.append(entry)
    elif isinstance(entry, sharding.Sharding):
      if isinstance(entry, PmapSharding):
        raise ValueError(f'One of {what} got sharding {entry} which is not '
                         'allowed.')
      if xla_extension_version < 270:
        if not isinstance(entry, XLACompatibleSharding):
          raise ValueError(f'One of {what} got sharding {entry} which is not a '
                           'subclass of XLACompatibleSharding.')
      new_entries.append(entry)
    else:
      new_entries.append(ParsedPartitionSpec.from_user_input(
          entry, what, allow_unconstrained_dims=allow_unconstrained_dims))

  _check_unique_resources(new_entries, arg_name)
  return tree_util.tree_unflatten(treedef, new_entries)


def _check_unique_resources(axis_resources, arg_name):
  for arg_axis_resources in axis_resources:
    if not arg_axis_resources: continue
    if (is_unspecified_or_auto(arg_axis_resources) or
        isinstance(arg_axis_resources, sharding.Sharding)):
      continue
    constrained_dims = [d for d in arg_axis_resources if d is not None]
    resource_counts = collections.Counter(
        itertools.chain.from_iterable(constrained_dims))
    if not resource_counts: continue
    if resource_counts.most_common(1)[0][1] > 1:
      multiple_uses = [r for r, c in resource_counts.items() if c > 1]
      if multiple_uses:
        raise ValueError(f"A single {arg_name} specification can map every mesh axis "
                         f"to at most one positional dimension, but {arg_axis_resources.user_spec} "
                         f"has duplicate entries for {mesh_lib.show_axes(multiple_uses)}")

# Axis environments

class AxisEnv(NamedTuple):
  """Represents a pmap mesh (only along the replica axes)."""
  nreps: int
  names: tuple[Any, ...]
  sizes: tuple[int, ...]


@dataclasses.dataclass(frozen=True)
class SPMDAxisContext:
  """A hardware axis context for parallel computations that use the GSPMD partitioner.

  This includes the mesh that will later by used to execute this computation,
  as well as a set of mesh axes that are currently (e.g. because the current lowering
  is invoked inside an xmap) lowered in the MANUAL sharding mode.
  """
  mesh: mesh_lib.Mesh
  manual_axes: frozenset[MeshAxisName] = frozenset()

  @property
  def axis_env(self):
    # All collectives that touch axis_env should remember to set use_global_device_ids
    # when this context is enabled!
    return self.unsafe_axis_env

  @property
  def unsafe_axis_env(self):
    return AxisEnv(
        nreps=self.mesh.size,
        names=self.mesh.axis_names,
        sizes=tuple(self.mesh.shape.values()))

  def extend_manual(self, axes: frozenset[MeshAxisName]) -> SPMDAxisContext:
    return SPMDAxisContext(self.mesh, self.manual_axes | axes)


@dataclasses.dataclass(frozen=True)
class ReplicaAxisContext:
  """A hardware axis context for parallel computations that are partitioned by JAX.

  Unlike in the SPMDAxisContext, this means that JAX might need to emit calls to
  explicit collectives.
  """
  axis_env: AxisEnv


@dataclasses.dataclass(frozen=True)
class ShardingContext:
  """A hardware axis context for parallel computations that use the sharding
  interface.

  This context also uses the GSPMD partitioner.
  """
  num_devices: int
  device_assignment: tuple[xc.Device, ...] | None = None

  def __post_init__(self):
    if self.device_assignment is not None:
      assert isinstance(self.device_assignment, tuple)
      assert self.num_devices == len(self.device_assignment)

  # Similar to SPMDContext as ShardingContext also uses the GSPMD partitioner.
  @property
  def axis_env(self):
    return AxisEnv(nreps=1, names=(), sizes=())


# -------------------- XLA OpSharding to PartitionSpec --------------------
# Note that OpSharding is more expressive than PartitionSpecs, so it's not
# always possible to convert them, but the code below should at least
# support handle all cases when this is possible.

def strides_for_sizes(sizes):
  """Returns an array of strides for major-to-minor sizes."""
  return np.cumprod(sizes[::-1])[::-1] // np.asarray(sizes)

def unflatten_array(named_sizes, assignment):
  """Recovers the ordering of axis names based on a device assignment.

  The device assignments that this function can convert into axis orders
  are of the form::

    np.arange(np.prod(named_sizes.values())).transpose(...).flatten()

  for some transposition ``...``. This is satisfied by all OpSharding assignments
  generated from partition specs.

  Arguments:
    named_sizes: A dictionary mapping axis names to their sizes.
    assignment: A permutation of integers between 0 and the product of all
      named sizes.

  Returns:
    A major-to-minor list of axis names that corresponds to the given assignment.
  """
  named_sizes = {name: size for name, size in named_sizes.items() if size != 1}
  sizes = np.fromiter(named_sizes.values(), dtype=np.int64)
  strides = strides_for_sizes(sizes)
  dims = explode_superdims(sizes, unflatten_superdims(assignment))
  dim_to_name = {(size, stride): name for size, stride, name in zip(sizes, strides, named_sizes)}
  return [dim_to_name[d] for d in dims]

def unflatten_superdims(assignment):
  """Unflatten a list of dimension sizes and their strides that generates assignment.

  If this function succeeds for a given ``assignment``, then the following property
  should be satisfied::

    dims_with_strides = unflatten_superdims(assignment)
    base_array = np.arange(map(fst, sorted(dims_with_strides, key=snd, reverse=True)))
    assignment == base_array.transpose(argsort(dims_with_strides, key=snd, reverse=True)).flatten()

  That is, the returned dimensions list all sizes of the base array (with strides
  indicating their initial order). The order of dimensions in the list corresponds
  to the permutation that applied to the base array generates the assignment.
  """
  def check(cond):
    if cond: return
    raise NotImplementedError("Failed to convert OpSharding into a ShardingSpec. "
                              "Please open a bug report!")
  flat_assignment = np.asarray(assignment, dtype=np.int64)
  check(flat_assignment[0] == 0)
  dims = []
  while flat_assignment.size > 1:
    stride = flat_assignment[1]
    for i in range(len(flat_assignment)):
      if flat_assignment[i] != i * stride: break
    else:
      # After this loop i should point to an "element after the sequence", so
      # we have to increment it if the whole array is a strided sequence.
      i += 1
    size = i
    dims.append((size, stride))
    assert size > 1  # Ensure progress
    flat_assignment = flat_assignment[::size]
  return dims

def explode_superdims(sizes, dims):
  """Explode superdims to fit a known shape.

  The unflattening process might mistakenly generate too few too large dimensions.
  For example, ``unflatten_superdims(np.arange(n))`` always returns ``[(n, 1)]``.
  This function takes a list of such contiguous super-dimensions and splits them
  into smaller dimensions such that::

    set(map(fst, explode_superdims(sizes, dims))) == set(sizes)
  """
  strides_to_sizes = {stride: size for size, stride in zip(sizes, strides_for_sizes(sizes))}
  dims = list(reversed(dims))
  final_dims = []
  for size, stride in dims:
    target_size = strides_to_sizes[stride]
    new_dims = []
    while size > target_size:
      assert target_size > 1  # Ensure progress
      assert size % target_size == 0
      new_dims.append((target_size, stride))
      size //= target_size
      stride *= target_size
      target_size = strides_to_sizes[stride]
    assert size == target_size
    new_dims.append((size, stride))
    final_dims += reversed(new_dims)
  return final_dims

def parse_flatten_op_sharding(hlo_sharding: xc.OpSharding | xc.HloSharding,
                              mesh: mesh_lib.Mesh) -> Sequence[ParsedPartitionSpec]:
  if isinstance(hlo_sharding, xc.OpSharding):
    hlo_sharding = xc.HloSharding.from_proto(hlo_sharding)
  if hlo_sharding.tuple_elements():
    out: list[ParsedPartitionSpec] = []
    for s in hlo_sharding.tuple_elements():
      out.extend(parse_flatten_op_sharding(s, mesh))
    return out
  elif hlo_sharding.is_replicated():
    return [CanonicalizedParsedPartitionSpec(
        ParsedPartitionSpec(PartitionSpec(), ()))]
  elif hlo_sharding.is_tiled():
    mesh_shape = mesh.shape
    mesh_axis_order = unflatten_array(
        mesh.shape, hlo_sharding.tile_assignment_devices()
    )
    mesh_axis = iter(mesh_axis_order)
    shape = hlo_sharding.tile_assignment_dimensions()
    partitions = []
    for dim_size in shape:
      dim_partitions = []
      while dim_size > 1:
        axis = next(mesh_axis)
        axis_size = mesh_shape[axis]
        assert dim_size % axis_size == 0
        dim_size //= axis_size
        dim_partitions.append(axis)
      partitions.append(tuple(dim_partitions))
    if len(hlo_sharding.subgroup_types()) > 1:
      raise NotImplementedError(
          'Unhandled HloSharding type. Please open a bug report!'
      )
    if hlo_sharding.replicate_on_last_tile_dim():
      partitions = partitions[:-1]
    return [CanonicalizedParsedPartitionSpec(
        ParsedPartitionSpec('<internally generated spec>', partitions))]
  else:
    raise AssertionError("Unhandled OpSharding type. Please open a bug report!")


def _slice_as_tuple(s: slice):
  assert s.step is None
  return (s.start, s.stop)


class NonUniformShardingError(ValueError):
  """Raised when sharding is not uniform across processes."""


def get_process_index_and_count(
    tensor_sharding: sharding.Sharding,
    dim: int,
    ndims: int,
) -> tuple[int, int]:
  """Get current process index and number of unique processes for given dimension.

  This function facilitates mapping of process-level data to individual
  devices. Each process can use its index to obtain the data corresponding
  to that index. If process level data is sharded on multiple dimensions
  this function can be used to build the cross product of indices in
  each sharded axis. Processes that need to load the same data will have
  the same index. For shardings whose per-process data is not distributed
  on a grid, the number of distinct shards will be such that it is possible to
  build the target shape while maintaining a "cube" shape of local-process data.

  For example, in case of 4 hosts with sharding distributed like so:

  1234
  2143

  For dim 0 (rows): all processes need to access all rows, so we return (0, 1)
  For dim 1 (cols):
     process 1 and 2 returns index 0 out of 2 (need cols 0 and 1),
     process 3 and 4 returns index 1 out of 2 (need cols 2 and 3).

  On the other hand, for a sharding like:

  1212
  3434

  Dim 0 (rows): process 1 and 2 returns (0, 2), process 3 and 4 returns (1, 2)
  Dim 1 (cols): process 1 and 3 returns (0, 2), process 2 and 4 returns (1, 2)

  Note: This function requires sharding to be process uniform in dimension
  `dim`:
   each process has the same number of addressable indices in that
  dimension and all index sets across processes are either disjoint or the same.

  For sharding to be process uniform the addressable shards doesn't need to
  form contiguous subtensor, or even a sparse grid  and  in case of
  interleaved high-dimensional tensor it is possible for sharding to be
  process uniform only in some dimensions but not others.

  For example:
    1111 and 12 and 1212 and 1212
    2222     21     2121     1212

  are all sharding uniform, in both dimensions. However

    1122
    2121
    1121
    1222

  is uniform in dimension 0 (both hosts access all rows), but
  is not uniform in dimension 1 (host 1 accesses columns: 0, 1, and 3),
  while host 2 accesses (0, 1, 2, 3).

  Returns:
    A tuple of (index, num_distinct_shards) for the given dimension.
    It is guaranteed that `index` will cover 0 to `num_distinct_shards - 1`,
    across all processes.

  Raises:
    NonUniformShardingError: if the sharding is not process uniform in dimension
    `dim`.
  """
  # TODO(sandler, yashkatariya): Consider making this function public.

  if (
      tensor_sharding.is_fully_addressable
      or tensor_sharding.is_fully_replicated
  ):
    return (0, 1)
  num_devices = len(tensor_sharding.device_set)
  # Get device to indices map, we don't care about the concrete
  # global shape here, only to get the distribution of shards across the tensor
  # using (num_devices, num_devices, ...)  This is a universal shape that is
  # compatible with any mesh with num_devices.
  device_map = tensor_sharding.devices_indices_map((num_devices,) * ndims)

  # Get the slices for 'dim' for all devices.
  global_slice = {k: v[dim] for k, v in device_map.items()}

  # Contains mapping from process_index to a set of slices for that process.
  process_to_slice = collections.defaultdict(set)
  # Contains global set of slices across all processes.
  all_slices = set()

  # Compute the set of slices for each process and the global set of slices.
  for d, v in global_slice.items():
    key = (v.start, v.stop)
    process_to_slice[d.process_index].add(key)
    all_slices.add(key)

  # Get the set of slices for the current process which we will use to compute
  # the index of the current process.
  current_pid = next(iter(tensor_sharding.addressable_devices)).process_index
  addressable_slices = frozenset(process_to_slice[current_pid])

  # Verify that all processes have the same number of slices.
  slices_per_process = len(addressable_slices)
  if any(len(x) != slices_per_process for x in process_to_slice.values()):
    raise NonUniformShardingError(
        f'{tensor_sharding=} is non-uniform on {dim=} as some processes have '
        'different number of slices.'
    )
  unique_processes = list({frozenset(x) for x in process_to_slice.values()})

  # After removing duplicate processes all unique slices should
  # cover the dimension exactly once. If they don' it means that
  # the sharding is not uniform.
  if sum(len(h) for h in unique_processes) != len(all_slices):
    raise NonUniformShardingError(
        f'{tensor_sharding=} is non-uniform on {dim=}'
    )
  return (unique_processes.index(addressable_slices), len(unique_processes))


def local_to_global_shape(
    sharding: sharding.Sharding,
    local_shape: Shape,
) -> tuple[int | None, ...]:
  """Computes the global shape given the per process if possible.

  The returned shape will have the size of the global tensor in that dimension
  or None, if it is not computable. The latter can happen when sharding
  is not uniform along that dimension, e.g. different hosts require
  different shapes, or if different processes have partial data overlap.

  If at most one dimension is sharded the shape is always computable.
  Generally, global shape is computable for most practical meshes (including
  topology aware such as meshes returned by mesh_utils.create_device_mesh)

  Some examples: Suppose mesh is {'a': 2, 'b': 2, 'c': 2} with 2 devices
  per host, 4 hosts total. For different specs we get:
  - P():
      global_shape = local_shape

  - P(('a', 'b', 'c'), None):
      global_shape =  (4 * local_shape[0], local_shape[1])
      Note: per device shape is (local_shape[0] / 2, local_shape[1])

  - P(('a', 'b'), None)
      global_shape =  (4 * local_shape[0], local_shape[1])
      # NB: the same global shape as above, since sharding along 'c' dimension
      # happens to be within process, and thus doesn't affect the global shape.
      # The underlying difference will be in the per *device* shape, which
      # would be  (local_shape[0], local_shape[1]) in this case.

  - P(None, ('a', 'c'))
      global_shape = (local_shape[0], 2 * local_shape[1])
      # Per device shape is (local_shape[0], local_shape[1] / 2)
  - P(('a', 'c'), 'b'):
      global_shape = (2 * local_shape[0], 2 * local_shape[1])
      # Per device shape is (local_shape[0] / 2, local_shape[1])
  - If devices in the Mesh are randomly permuted: For any partition spec
  which shards more than 1 axis:  e.g. P('a', ('b', 'c')):
      global_shape = (None, None)

  Args:
    local_shape: global shape of the tensor.

  Returns:
    global_shape with Nones in non-uniform dimensions.
  """

  global_shape : list[int | None] = [None] * len(local_shape)
  for i, local_dim in enumerate(local_shape):
    try:
      _, shard_count = get_process_index_and_count(
          sharding, i, ndims=len(local_shape)
      )
      global_shape[i] = local_dim * shard_count
    except NonUniformShardingError:
      global_shape[i] = None
      continue

  return tuple(global_shape)


def num_addressable_indices(
    tensor_sharding: sharding.Sharding,
    dim: int,
    global_shape: Shape,
) -> int:
  """Returns the number of indices for given dimension this host has access to.

  Each host can have multiple number of devices that are spanning
  possibly discontiguous slices of data. This function computes the
  total number of unique indices for dimension `dim` that any of its
  addressable devices hold.

  In most cases the addressable indices form a sparse grid (and in some
  cases a subcube), and thus each host will hold the same of number of
  indices for each dimension.  However, it is possible to design a mesh that
  addressable shards form a complicated pattern. In that case, the returned
  value is the number of indices that are addressable by at least one device.

  For example, suppose the sharding looks like this: (number indicates
  the host index)

    1221
    1221
    0000

  Then on host 1 and 2, both dim 0 (rows), and  dim=1 (cols) will have size 2,
  while on host 0, dim 0  will have size 1, and dim 1 will have size 4.

  Args:
    tensor_sharding: Sharding of the tensor.
    dim: dimension along which to compute the number of addressable indices.
    global_shape: global shape of the tensor.

  Returns:
    The number of indices for dimension  `dim` that this host holds.
  """
  # TODO(sandler, yashkatariya): Consider making this function public.
  addressables = tensor_sharding.addressable_devices_indices_map(global_shape)
  addressables = cast(Mapping[sharding.Device, Index], addressables)
  num_unique_slices = len({
      _slice_as_tuple(addressable[dim]) for addressable in addressables.values()
  })
  shard_size = tensor_sharding.shard_shape(global_shape)[dim]
  return shard_size * num_unique_slices


def physical_hlo_sharding(aval, hlo_sharding: xc.HloSharding) -> xc.HloSharding:
  elt_aval = aval.dtype._rules.physical_element_aval(aval.dtype)
  new_op_sharding = hlo_sharding.to_proto().clone()
  partitions, num_replicas = get_num_ways_dim_sharded(hlo_sharding)
  suffix = [] if num_replicas == 1 else [num_replicas]
  tad = partitions + [1] * elt_aval.ndim + suffix
  new_op_sharding.tile_assignment_dimensions = tad
  return xc.HloSharding.from_proto(new_op_sharding)

def is_single_device_sharding(sharding: sharding.Sharding) -> bool:
  # Special case PmapSharding here because PmapSharding maps away an axis
  # and needs to be handled separately.test_pjit_single_device_sharding_add
  return len(sharding.device_set) == 1 and not isinstance(sharding, PmapSharding)

def make_key_array_phys_sharding(aval, sharding):
  if is_single_device_sharding(sharding):
    return sharding
  elif isinstance(sharding, PmapSharding):
    elt_aval = aval.dtype._rules.physical_element_aval(aval.dtype)
    trailing_sharding = [sharding_specs.NoSharding()] * elt_aval.ndim
    phys_sharding_spec = sharding_specs.ShardingSpec(
        sharding=(*sharding.sharding_spec.sharding, *trailing_sharding),
        mesh_mapping=sharding.sharding_spec.mesh_mapping)
    return PmapSharding(devices=sharding.devices,
                        sharding_spec=phys_sharding_spec)
  elif isinstance(sharding, NamedSharding):
    elt_aval = aval.dtype._rules.physical_element_aval(aval.dtype)
    trailing_spec = [None] * elt_aval.ndim
    return NamedSharding(
        sharding.mesh,
        PartitionSpec(*sharding.spec, *trailing_spec))
  else:
    hlos = sharding._to_xla_hlo_sharding(aval.ndim)
    return GSPMDSharding(
        sharding._device_assignment, physical_hlo_sharding(aval, hlos))


def physical_sharding(
    aval, sharding: sharding.Sharding) -> sharding.Sharding:
  return make_key_array_phys_sharding(aval, sharding)


def get_logical_gspmd_sharding(aval, phys_sharding):
  elt_aval = aval.dtype._rules.physical_element_aval(aval.dtype)
  phys_hlo_sharding = phys_sharding._to_xla_hlo_sharding(
      aval.ndim + elt_aval.ndim)
  partitions, num_replicas = get_num_ways_dim_sharded(phys_hlo_sharding)
  suffix = [] if num_replicas == 1 else [num_replicas]
  # Create logical sharding by cutting off the replicated trailing dims.
  logical_op_sharding = phys_hlo_sharding.to_proto().clone()
  tad = partitions[:-elt_aval.ndim] + suffix
  logical_op_sharding.tile_assignment_dimensions = tad
  return GSPMDSharding(phys_sharding._device_assignment,
                       xc.HloSharding.from_proto(logical_op_sharding))

def check_replicated_trailing_dims(sharding: sharding.Sharding, aval):
  if isinstance(sharding, PmapSharding):
    return
  phys_aval = core.physical_aval(aval)
  hlo_s = sharding._to_xla_hlo_sharding(phys_aval.ndim)
  partitions, _ = get_num_ways_dim_sharded(hlo_s)
  num_trailing_dims = phys_aval.ndim - aval.ndim
  if not all(i == 1 for i in partitions[-num_trailing_dims:]):
    raise AssertionError(
        "The trailing dims of extended dtypes should be replicated. Got"
        f" sharding: {sharding}, partitions: {partitions}, "
        f"num_trailing_dims: {num_trailing_dims}")

def logical_sharding(aval, phys_sharding) -> sharding.Sharding:
  # The trailing dims should always be replicated.
  check_replicated_trailing_dims(phys_sharding, aval)

  if is_single_device_sharding(phys_sharding):
    return phys_sharding
  elif isinstance(phys_sharding, PmapSharding):
    elt_aval = aval.dtype._rules.physical_element_aval(aval.dtype)
    logical_sharding_spec = sharding_specs.ShardingSpec(
        sharding=phys_sharding.sharding_spec.sharding[:-elt_aval.ndim],
        mesh_mapping=phys_sharding.sharding_spec.mesh_mapping)
    return PmapSharding(devices=phys_sharding.devices,
                        sharding_spec=logical_sharding_spec)
  elif isinstance(phys_sharding, NamedSharding):
    logical_gs = get_logical_gspmd_sharding(aval, phys_sharding)
    return _gspmd_to_named_sharding_via_mesh(
        logical_gs, phys_sharding.mesh)
  else:
    return get_logical_gspmd_sharding(aval, phys_sharding)


@util.cache()
def create_mesh_pspec_sharding(
    mesh: mesh_lib.Mesh, pspec: PartitionSpec | None, parsed_pspec=None,
    memory_kind: str | None = None) -> NamedSharding:
  if pspec is None:
    pspec, parsed_pspec = PartitionSpec(), None
  return NamedSharding(mesh, pspec, _parsed_pspec=parsed_pspec,
                       memory_kind=memory_kind)


def _gspmd_to_named_sharding_via_mesh(
    out_s: GSPMDSharding, mesh: mesh_lib.Mesh) -> NamedSharding:
  parsed_pspec = parse_flatten_op_sharding(
      out_s._hlo_sharding, mesh)[0]
  return create_mesh_pspec_sharding(
      mesh, parsed_pspec.get_partition_spec(), parsed_pspec,
      out_s.memory_kind)