rocm_jax/jax/_src/pjit.py

# 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.

import dataclasses
import inspect
import logging
import weakref
import numpy as np
from typing import (Callable, Sequence, Tuple, Union, cast, List, Optional,
                    Iterable, NamedTuple, Any)
import itertools as it
from functools import partial, lru_cache
import threading
import warnings

from jax._src import core
from jax._src import stages
from jax._src import dispatch
from jax._src import mesh as mesh_lib
from jax._src import linear_util as lu
from jax._src import op_shardings
from jax._src import sharding_impls
from jax._src import source_info_util
from jax._src import traceback_util
from jax._src import api
from jax._src import xla_bridge as xb
from jax._src.api_util import (
    argnums_partial_except, flatten_axes, flatten_fun, flatten_fun_nokwargs,
    donation_vector, shaped_abstractify, check_callable, resolve_argnums,
    argnames_partial_except, debug_info, result_paths, jaxpr_debug_info)
from jax._src.errors import JAXTypeError
from jax._src.interpreters import partial_eval as pe
from jax._src.partition_spec import PartitionSpec
from jax._src.interpreters import xla

from jax._src.config import config
from jax._src.interpreters import ad
from jax._src.interpreters import batching
from jax._src.interpreters import mlir
from jax._src.interpreters import pxla
from jax._src.lib.mlir import ir
from jax._src.lib.mlir.dialects import func as func_dialect
from jax._src.lib import xla_client as xc
from jax._src.sharding_impls import (
    NamedSharding, XLACompatibleSharding, GSPMDSharding,
    XLADeviceAssignment, SingleDeviceSharding, PmapSharding,
    AUTO, UNSPECIFIED, UnspecifiedValue,
    ParsedPartitionSpec, SpecSync, get_single_pspec, is_auto, is_unspecified,
    is_unspecified_or_auto, prepare_axis_resources, parse_flatten_op_sharding)
from jax._src.traceback_util import api_boundary
from jax._src.tree_util import (
    tree_map, tree_flatten, tree_unflatten, treedef_is_leaf, tree_structure,
    treedef_tuple, broadcast_prefix, all_leaves,
    prefix_errors, generate_key_paths)
from jax._src.util import (
    HashableFunction, safe_map, safe_zip, wraps,
    distributed_debug_log, split_list, weakref_lru_cache,
    merge_lists, flatten, unflatten)

map, unsafe_map = safe_map, map
zip, unsafe_zip = safe_zip, zip

traceback_util.register_exclusion(__file__)

PjitSharding = Union[GSPMDSharding, UnspecifiedValue, AUTO]
PjitShardingMinusUnspecified = Union[GSPMDSharding, AUTO]
MeshSharding = Union[NamedSharding, UnspecifiedValue, AUTO]
MeshShardingMinusUnspecified = Union[NamedSharding, AUTO]

logger = logging.getLogger(__name__)


def _try_infer_args(f, tree):
  dummy_args = tree_unflatten(tree, [False] * tree.num_leaves)
  try:
    return inspect.signature(f).bind(*dummy_args)
  except (TypeError, ValueError):
    return None


def _find_arg_mismatch(arg_list, fails, fun_name):
  first_err, second_err = fails
  mismatched_args_msg = []
  for name, inp_da, aval in arg_list:
    if first_err.m_type == pxla.MismatchType.ARG_SHARDING:
      if first_err.da == inp_da:
        mismatched_args_msg.append(
            (f"argument {name} of {fun_name} with shape {aval.str_short()} and "
             f"{first_err._dev_ids_plat_str}"))
        break

  for name, inp_da, aval in arg_list:
    if second_err.m_type == pxla.MismatchType.ARG_SHARDING:
      if second_err.da == inp_da:
        mismatched_args_msg.append(
            (f"argument {name} of {fun_name} with shape {aval.str_short()} and "
             f"{second_err._dev_ids_plat_str}"))
        break
  return mismatched_args_msg

# TODO(yashkatariya): Try to use debug_info that is populated in
# common_infer_params.
def _get_arg_names(fun, in_tree, args_flat):
  sig = _try_infer_args(fun, in_tree)
  args_aug = generate_key_paths(tree_unflatten(in_tree, args_flat))

  arg_names = []
  for arg_key, val in args_aug:
    ak, *rem_keys = arg_key
    if sig is not None:
      loc = ''.join(str(k) for k in rem_keys)
      arg_name = f'{list(sig.arguments.keys())[ak.idx]}{loc}'
    else:
      arg_name = ''
    arg_names.append(arg_name)
  return arg_names


def _device_assignment_mismatch_error(fun_name, fails, args_flat, api_name,
                                      arg_names):
  arg_list = []
  for a, n in zip(args_flat, arg_names):
    da = a.sharding._device_assignment if hasattr(a, 'sharding') else None
    arg_list.append((n, da, shaped_abstractify(a)))

  mismatched_args_msg = _find_arg_mismatch(arg_list, fails, fun_name)

  if len(mismatched_args_msg) == 2:
    first, second = mismatched_args_msg  # pylint: disable=unbalanced-tuple-unpacking
    extra_msg = f" Got {first} and {second}"
  elif len(mismatched_args_msg) == 1:
    first, second  = fails
    # Choose the failure left which is not already covered by ARG_SHARDING.
    left = second if first.m_type == pxla.MismatchType.ARG_SHARDING else first
    extra_msg = f" Got {mismatched_args_msg[0]} and{left._str(api_name)}"
  else:
    first, second = fails
    extra_msg = f" Got{first._str(api_name)} and{second._str(api_name)}"
  msg = (f"Received incompatible devices for {api_name}ted computation.{extra_msg}")
  return msg


def _python_pjit_helper(fun, infer_params_fn, *args, **kwargs):
  args_flat, _, params, in_tree, out_tree, _ = infer_params_fn(
      *args, **kwargs)
  for arg in args_flat:
    dispatch.check_arg(arg)
  try:
    out_flat = pjit_p.bind(*args_flat, **params)
  except pxla.DeviceAssignmentMismatchError as e:
    fails, = e.args
    api_name = 'jit' if params['resource_env'] is None else 'pjit'
    arg_names = _get_arg_names(fun, in_tree, args_flat)
    fun_name = getattr(fun, '__qualname__', getattr(fun, '__name__', str(fun)))
    msg = _device_assignment_mismatch_error(
        fun_name, fails, args_flat, api_name, arg_names)
    raise ValueError(msg) from None
  outs = tree_unflatten(out_tree, out_flat)
  return outs, out_flat, out_tree, args_flat


def _python_pjit(fun: Callable, infer_params_fn):

  @wraps(fun)
  @api_boundary
  def wrapped(*args, **kwargs):
    if config.jax_disable_jit:
      return fun(*args, **kwargs)
    return _python_pjit_helper(fun, infer_params_fn, *args, **kwargs)[0]

  def _python_pjit_evict_fn():
    _create_pjit_jaxpr.evict_function(fun)  # type: ignore
  wrapped.clear_cache = _python_pjit_evict_fn
  return wrapped


def _get_fastpath_data(executable, out_tree, args_flat, out_flat):
  use_fastpath = (
      executable is not None and
      isinstance(executable, pxla.MeshExecutable) and
      isinstance(executable.unsafe_call, pxla.ExecuteReplicated) and
      # No effects in computation
      not executable.unsafe_call.ordered_effects and
      not executable.unsafe_call.has_unordered_effects and
      not executable.unsafe_call.has_host_callbacks and
      all(isinstance(x, xc.ArrayImpl) for x in out_flat)
  )

  if use_fastpath:
    out_avals = [o.aval for o in out_flat]
    out_committed = [o._committed for o in out_flat]
    kept_var_bitvec = [i in executable._kept_var_idx
                       for i in range(len(args_flat))]
    fastpath_data = pxla.MeshExecutableFastpathData(
        executable.xla_executable, out_tree, executable._in_shardings,
        executable._out_shardings, out_avals, out_committed, kept_var_bitvec)
  else:
    fastpath_data = None
  return fastpath_data


class _MostRecentPjitCallExecutable(threading.local):
  def __init__(self):
    self.value = None

_most_recent_pjit_call_executable = _MostRecentPjitCallExecutable()


def _read_most_recent_pjit_call_executable():
  executable = _most_recent_pjit_call_executable.value
  _most_recent_pjit_call_executable.value = None
  return executable


def _cpp_pjit_evict_fn(self):
  self._clear_cache()
  _create_pjit_jaxpr.evict_function(self._fun)  # type: ignore


# The entries are doubled here from the default 4096 because _pjit_call_impl
# also has a cpp dispatch path and that would double the number of entries in
# the global shared cache.
_cpp_pjit_cache = xc._xla.PjitFunctionCache(capacity=8192)


def _cpp_pjit(fun: Callable, infer_params_fn, static_argnums, static_argnames,
              donate_argnums, pjit_has_explicit_sharding):

  @api_boundary
  def cache_miss(*args, **kwargs):
    outs, out_flat, out_tree, args_flat = _python_pjit_helper(
        fun, infer_params_fn, *args, **kwargs)
    executable = _read_most_recent_pjit_call_executable()
    fastpath_data = _get_fastpath_data(executable, out_tree, args_flat, out_flat)
    return outs, fastpath_data

  if pjit_has_explicit_sharding:
    global_cache = xc._xla.PjitFunctionCache()
  else:
    global_cache = _cpp_pjit_cache
  cpp_pjit_f = xc._xla.pjit(  # type: ignore
      getattr(fun, "__name__", "<unnamed function>"),  # type: ignore
      fun, cache_miss, static_argnums, static_argnames,  # type: ignore
      donate_argnums, global_cache)  # type: ignore

  cpp_pjitted_f = wraps(fun)(cpp_pjit_f)
  cpp_pjitted_f._fun = fun
  type(cpp_pjitted_f).clear_cache = _cpp_pjit_evict_fn
  return cpp_pjitted_f


def _resolve_axis_resources_and_shardings_arg(
    in_shardings, out_shardings, in_axis_resources, out_axis_resources):
  if not is_unspecified(in_shardings) and not is_unspecified(in_axis_resources):
    raise ValueError(
        'Setting both in_shardings and in_axis_resources is not '
        'allowed. in_axis_resources is deprecated. Please use in_shardings.')
  if not is_unspecified(out_shardings) and not is_unspecified(out_axis_resources):
    raise ValueError(
        'Setting both out_shardings and out_axis_resources is not '
        'allowed. out_axis_resources is deprecated. Please use out_shardings.')
  if (not is_unspecified(in_axis_resources) or
      not is_unspecified(out_axis_resources)):
    warnings.warn(
        'in_axis_resources and out_axis_resources are deprecated. Please use '
        'in_shardings and out_shardings as their replacement.',
        DeprecationWarning)

  if not is_unspecified(in_axis_resources):
    final_in_shardings = in_axis_resources
  else:
    final_in_shardings = in_shardings

  if not is_unspecified(out_axis_resources):
    final_out_shardings = out_axis_resources
  else:
    final_out_shardings = out_shardings
  return final_in_shardings, final_out_shardings


def pre_infer_params(fun, in_shardings, out_shardings,
                     donate_argnums, static_argnums, static_argnames, device,
                     backend, abstracted_axes):
  if abstracted_axes and not config.jax_dynamic_shapes:
    raise ValueError("abstracted_axes must be used with --jax_dynamic_shapes")

  check_callable(fun)

  if backend is not None or device is not None:
    warnings.warn(
        'backend and device argument on jit is deprecated. You can use a '
        '`jax.sharding.Mesh` context manager or device_put the arguments '
        'before passing them to `jit`. Please see '
        'https://jax.readthedocs.io/en/latest/notebooks/Distributed_arrays_and_automatic_parallelization.html '
        'for more information.', DeprecationWarning)
    if device is not None and backend is not None:
      raise ValueError("can't specify both a device and a backend for jit, "
                       f"got {device=} and {backend=}")
    if not is_unspecified(in_shardings):
      raise ValueError('If backend or device is specified on jit, then '
                       'in_shardings should not be specified.')
    if not is_unspecified(out_shardings):
      raise ValueError('If backend or device is specified on jit, then '
                       'out_shardings should not be specified.')

  if isinstance(in_shardings, list):
    # To be a tree prefix of the positional args tuple, in_axes can never be a
    # list: if in_axes is not a leaf, it must be a tuple of trees. However,
    # in cases like these users expect tuples and lists to be treated
    # essentially interchangeably, so we canonicalize lists to tuples here
    # rather than raising an error. https://github.com/google/jax/issues/2367
    in_shardings = tuple(in_shardings)

  in_shardings, _, _ = prepare_axis_resources(in_shardings, 'in_shardings')
  out_shardings, _, _ = prepare_axis_resources(out_shardings, 'out_shardings')

  donate_argnums, static_argnums, static_argnames = resolve_argnums(
      fun, donate_argnums, static_argnums, static_argnames)

  return (in_shardings, out_shardings, donate_argnums, static_argnums,
          static_argnames)


def post_infer_params(fun, infer_params_fn, static_argnums, static_argnames,
                      donate_argnums, abstracted_axes,
                      pjit_has_explicit_sharding):
  if abstracted_axes is None:
    wrapped = _cpp_pjit(fun, infer_params_fn, static_argnums, static_argnames,
                        donate_argnums, pjit_has_explicit_sharding)
  else:
    wrapped = _python_pjit(fun, infer_params_fn)

  @api_boundary
  def lower(*args, **kwargs):
    _experimental_lowering_platform = kwargs.pop(
        '_experimental_lowering_platform', None)
    (args_flat, flat_global_in_avals, params, in_tree, out_tree,
     donate_argnums) = infer_params_fn(*args, **kwargs)
    resource_env = params['resource_env']
    mesh = None if resource_env is None else resource_env.physical_mesh
    try:
      in_shardings = _resolve_in_shardings(
          args_flat, params['in_shardings'], params['out_shardings'], mesh)
      lowering = _pjit_lower(
          params['jaxpr'], in_shardings, params['out_shardings'],
          params['resource_env'], params['donated_invars'], params['name'],
          params['keep_unused'], params['inline'], always_lower=True,
          lowering_platform=_experimental_lowering_platform)
    except pxla.DeviceAssignmentMismatchError as e:
      fails, = e.args
      api_name = 'jit' if params['resource_env'] is None else 'pjit'
      arg_names = _get_arg_names(fun, in_tree, args_flat)
      fun_name = getattr(fun, '__qualname__', getattr(fun, '__name__', str(fun)))
      msg = _device_assignment_mismatch_error(
          fun_name, fails, args_flat, api_name, arg_names)
      raise ValueError(msg) from None

    if kwargs:
      args_kwargs_in_tree = in_tree
    else:
      args_kwargs_in_tree = treedef_tuple([in_tree, tree_flatten({})[1]])

    return stages.Lowered.from_flat_info(
        lowering, args_kwargs_in_tree, flat_global_in_avals, donate_argnums,
        out_tree)

  wrapped.lower = lower
  return wrapped


def _pjit_explicit_sharding(in_shardings, out_shardings, device,
                            backend) -> bool:
  in_shardings_flat, _ = tree_flatten(in_shardings)
  out_shardings_flat, _ = tree_flatten(out_shardings)
  return (device is not None or
          backend is not None or
          any(not is_unspecified(i) for i in in_shardings_flat) or
          any(not is_unspecified(i) for i in out_shardings_flat))


class PjitInfo(NamedTuple):
  fun: Callable
  in_shardings: Any
  out_shardings: Any
  static_argnums: Tuple[int, ...]
  static_argnames: Tuple[str, ...]
  donate_argnums: Tuple[int, ...]
  device: Optional[xc.Device]
  backend: Optional[str]
  keep_unused: bool
  inline: bool
  resource_env: Any
  abstracted_axes: Optional[Any]


def common_infer_params(pjit_info_args, *args, **kwargs):
  (fun, user_in_shardings, user_out_shardings, static_argnums, static_argnames,
   donate_argnums, device, backend, keep_unused, inline,
   resource_env, abstracted_axes) = pjit_info_args

  if kwargs and not is_unspecified(user_in_shardings):
    raise ValueError(
        "pjit does not support kwargs when in_shardings is specified.")

  if resource_env is not None:
    pjit_mesh = resource_env.physical_mesh
  else:
    pjit_mesh = None

  if (backend or device) and pjit_mesh is not None and not pjit_mesh.empty:
    raise ValueError(
        "Mesh context manager should not be used with jit when backend or "
        "device is also specified as an argument to jit.")

  axes_specs = _flat_axes_specs(abstracted_axes, *args, **kwargs)

  jit_name = 'jit' if resource_env is None else 'pjit'
  dbg = debug_info(jit_name, fun, args, kwargs, static_argnums, static_argnames)
  f = lu.wrap_init(fun)
  f, res_paths = result_paths(f)
  f, dyn_args = argnums_partial_except(f, static_argnums, args,
                                       allow_invalid=True)
  del args

  # TODO(yashkatariya): Merge the nokwargs and kwargs path. One blocker is
  # flatten_axes which if kwargs are present in the treedef (even empty {}),
  # leads to wrong expansion.
  if kwargs:
    f, dyn_kwargs = argnames_partial_except(f, static_argnames, kwargs)
    explicit_args, in_tree = tree_flatten((dyn_args, dyn_kwargs))
    flat_fun, out_tree = flatten_fun(f, in_tree)
  else:
    explicit_args, in_tree = tree_flatten(dyn_args)
    flat_fun, out_tree = flatten_fun_nokwargs(f, in_tree)
    dyn_kwargs = ()
  del kwargs

  if donate_argnums and not config.jax_debug_nans:
    donated_invars = donation_vector(donate_argnums, dyn_args, dyn_kwargs)
  else:
    donated_invars = (False,) * len(explicit_args)

  # If backend or device is set as an arg on jit, then resolve them to
  # in_shardings and out_shardings as if user passed in in_shardings
  # and out_shardings.
  device_or_backend_set = False
  if backend or device:
    in_shardings = out_shardings = _create_sharding_with_device_backend(
        device, backend)
    device_or_backend_set = True
  else:
    in_shardings = tree_map(
        lambda x: _create_sharding_for_array(pjit_mesh, x, 'in_shardings',
                                             jit_name),
        user_in_shardings)
    out_shardings = tree_map(
        lambda x: _create_sharding_for_array(pjit_mesh, x, 'out_shardings',
                                             jit_name),
        user_out_shardings)

  del user_in_shardings, user_out_shardings

  if config.jax_dynamic_shapes:
    in_type = pe.infer_lambda_input_type(axes_specs, explicit_args)
    in_avals = tuple(a for a, e in in_type if e)
  else:
    avals = []
    for i, a in enumerate(explicit_args):
      try:
        avals.append(shaped_abstractify(a))
      except OverflowError as e:
        arg_path = (f"argument path is {dbg.arg_names[i]}" if dbg
                    else f"flattened argument number is {i}")
        raise OverflowError(
          "An overflow was encountered while parsing an argument to a jitted "
          f"computation, whose {arg_path}."
        ) from e
    in_type = in_avals = tuple(avals)

  canonicalized_in_shardings_flat = _process_in_axis_resources(
      hashable_pytree(in_shardings), in_avals, in_tree, resource_env, dbg,
      device_or_backend_set)

  jaxpr, consts, canonicalized_out_shardings_flat = _pjit_jaxpr(
      flat_fun, hashable_pytree(out_shardings), in_type, dbg,
      device_or_backend_set, HashableFunction(out_tree, closure=()),
      HashableFunction(res_paths, closure=()))

  assert len(explicit_args) == len(canonicalized_in_shardings_flat)

  if config.jax_dynamic_shapes:
    implicit_args = _extract_implicit_args(in_type, explicit_args)
  else:
    implicit_args = []
  args_flat = [*implicit_args, *explicit_args]

  num_extra_args = len(implicit_args) + len(consts)
  canonicalized_in_shardings_flat = \
      (UNSPECIFIED,) * num_extra_args + canonicalized_in_shardings_flat
  donated_invars = (False,) * num_extra_args + donated_invars
  assert (len(canonicalized_in_shardings_flat) == len(donated_invars) ==
          len(consts) + len(args_flat))

  # in_shardings and out_shardings here are all GSPMDSharding.
  params = dict(
      jaxpr=jaxpr,
      in_shardings=canonicalized_in_shardings_flat,
      out_shardings=canonicalized_out_shardings_flat,
      resource_env=resource_env,
      donated_invars=donated_invars,
      name=getattr(flat_fun, '__name__', '<unnamed function>'),
      keep_unused=keep_unused,
      inline=inline,
  )
  return (consts + args_flat, in_type, params, in_tree, out_tree(),
          donate_argnums)

def _extract_implicit_args(
  in_type: Sequence[Tuple[core.AbstractValue, bool]],
  explicit_args: Sequence[Any]
) -> Sequence[core.Tracer]:
  """
  Given an input type and explicitly-passed arguments (per the user-facing API
  calling convention), extract implicit axis size arguments from shapes of
  explicit arguments (for the trace-time / jaxpr-level calling convention).
  """
  # First, using `in_type` construct a list to represent the full argument list,
  # leaving the implicit arguments as None placeholders for now.
  explicit_args_ = iter(explicit_args)
  args = [next(explicit_args_) if expl else None for _, expl in in_type]
  assert next(explicit_args_, None) is None
  del explicit_args, explicit_args_

  # Next, populate the implicit arguments using the DBIdxs in `in_type`.
  for i, (aval, explicit) in enumerate(in_type):
    if not explicit or not isinstance(aval, core.DShapedArray):
      continue  # can't populate an implicit argument
    arg = args[i]
    assert arg is not None
    for d1, d2 in zip(aval.shape, arg.aval.shape):
      if isinstance(d1, core.DBIdx):
        if args[d1.val] is None:
          args[d1.val] = d2
        assert core.same_referent(args[d1.val], d2)
  assert all(x is not None for x in args)
  return [x for x, (_, e) in zip(args, in_type) if not e]  # type: ignore

def _flat_axes_specs(abstracted_axes, *args, **kwargs
                     ) -> Optional[List[pe.AbstractedAxesSpec]]:
  if abstracted_axes is None: return None
  if kwargs: raise NotImplementedError
  def ax_leaf(l):
    return (isinstance(l, dict) and all_leaves(l.values()) or
            isinstance(l, tuple) and all_leaves(l, lambda x: x is None))
  return broadcast_prefix(abstracted_axes, args, ax_leaf)


# in_shardings and out_shardings can't be None as the default value
# because `None` means that the input is fully replicated.
def pjit(
    fun: Callable,
    in_shardings=UNSPECIFIED,
    out_shardings=UNSPECIFIED,
    in_axis_resources=UNSPECIFIED,
    out_axis_resources=UNSPECIFIED,
    static_argnums: Union[int, Sequence[int], None] = None,
    static_argnames: Union[str, Iterable[str], None] = None,
    donate_argnums: Union[int, Sequence[int]] = (),
    keep_unused: bool = False,
    device: Optional[xc.Device] = None,
    backend: Optional[str] = None,
    inline: bool = False,
    abstracted_axes: Optional[Any] = None,
) -> stages.Wrapped:
  """Makes ``fun`` compiled and automatically partitioned across multiple devices.

  NOTE: This function is now equivalent to jax.jit please use that instead.
  The returned function has semantics equivalent to those of ``fun``, but is
  compiled to an XLA computation that runs across multiple devices
  (e.g. multiple GPUs or multiple TPU cores). This can be useful if the jitted
  version of ``fun`` would not fit in a single device's memory, or to speed up
  ``fun`` by running each operation in parallel across multiple devices.

  The partitioning over devices happens automatically based on the
  propagation of the input partitioning specified in ``in_shardings`` and
  the output partitioning specified in ``out_shardings``. The resources
  specified in those two arguments must refer to mesh axes, as defined by
  the :py:func:`jax.sharding.Mesh` context manager. Note that the mesh
  definition at :func:`~pjit` application time is ignored, and the returned function
  will use the mesh definition available at each call site.

  Inputs to a :func:`~pjit`'d function will be automatically partitioned across devices
  if they're not already correctly partitioned based on ``in_shardings``.
  In some scenarios, ensuring that the inputs are already correctly pre-partitioned
  can increase performance. For example, if passing the output of one
  :func:`~pjit`'d function to another :func:`~pjit`’d function (or the same
  :func:`~pjit`’d function in a loop), make sure the relevant
  ``out_shardings`` match the corresponding ``in_shardings``.

  .. note::
    **Multi-process platforms:** On multi-process platforms such as TPU pods,
    :func:`~pjit` can be used to run computations across all available devices across
    processes. To achieve this, :func:`~pjit` is designed to be used in SPMD Python
    programs, where every process is running the same Python code such that all
    processes run the same :func:`~pjit`'d function in the same order.

    When running in this configuration, the mesh should contain devices across
    all processes. However, any input argument dimensions partitioned over
    multi-process mesh axes should be of size equal to the corresponding *local*
    mesh axis size, and outputs will be similarly sized according to the local
    mesh. ``fun`` will still be executed across *all* devices in the mesh,
    including those from other processes, and will be given a global view of the
    data spread across multiple processes as a single array. However, outside
    of :func:`~pjit` every process only "sees" its local piece of the input and output,
    corresponding to its local sub-mesh.

    This means that each process's participating local devices must form a
    _contiguous_ local sub-mesh within the full global mesh. A contiguous
    sub-mesh is one where all of its devices are adjacent within the global
    mesh, and form a rectangular prism.

    The SPMD model also requires that the same multi-process :func:`~pjit`'d
    functions must be run in the same order on all processes, but they can be
    interspersed with arbitrary operations running in a single process.

  Args:
    fun: Function to be compiled. Should be a pure function, as side-effects may
      only be executed once. Its arguments and return value should be arrays,
      scalars, or (nested) standard Python containers (tuple/list/dict) thereof.
      Positional arguments indicated by ``static_argnums`` can be anything at
      all, provided they are hashable and have an equality operation defined.
      Static arguments are included as part of a compilation cache key, which is
      why hash and equality operators must be defined.
    in_shardings: Pytree of structure matching that of arguments to ``fun``,
      with all actual arguments replaced by resource assignment specifications.
      It is also valid to specify a pytree prefix (e.g. one value in place of a
      whole subtree), in which case the leaves get broadcast to all values in
      that subtree.

      The ``in_shardings`` argument is optional. JAX will infer the shardings
      from the input :py:class:`jax.Array`'s, and defaults to replicating the input
      if the sharding cannot be inferred.

      The valid resource assignment specifications are:

      - :py:class:`XLACompatibleSharding`, which will decide how the value
        will be partitioned. With this, using a mesh context manager is not
        required.
      - For backwards compatibility, in_shardings still supports ingesting
        :py:class:`PartitionSpec` and :py:obj:`None`. These 2 options can
        *only* be used with the mesh context manager.

        - :py:obj:`None`, in which case the value will be replicated on all devices
        - :py:class:`PartitionSpec`, a tuple of length at most equal to the rank
          of the partitioned value. Each element can be a :py:obj:`None`, a mesh
          axis or a tuple of mesh axes, and specifies the set of resources assigned
          to partition the value's dimension matching its position in the spec.

      The size of every dimension has to be a multiple of the total number of
      resources assigned to it.
    out_shardings: Like ``in_shardings``, but specifies resource
      assignment for function outputs.
      The ``out_shardings`` argument is optional. If not specified, :py:func:`jax.jit`
      will use GSPMD's sharding propagation to determine how to shard the outputs.
    in_axis_resources: (Deprecated) Please use in_shardings.
    out_axis_resources: (Deprecated) Please use out_shardings.
    static_argnums: An optional int or collection of ints that specify which
      positional arguments to treat as static (compile-time constant).
      Operations that only depend on static arguments will be constant-folded in
      Python (during tracing), and so the corresponding argument values can be
      any Python object.

      Static arguments should be hashable, meaning both ``__hash__`` and
      ``__eq__`` are implemented, and immutable. Calling the jitted function
      with different values for these constants will trigger recompilation.
      Arguments that are not arrays or containers thereof must be marked as
      static.

      If ``static_argnums`` is not provided, no arguments are treated as static.
    static_argnames: An optional string or collection of strings specifying
      which named arguments to treat as static (compile-time constant). See the
      comment on ``static_argnums`` for details. If not
      provided but ``static_argnums`` is set, the default is based on calling
      ``inspect.signature(fun)`` to find corresponding named arguments.
    donate_argnums: Specify which argument buffers are "donated" to the computation.
      It is safe to donate argument buffers if you no longer need them once the
      computation has finished. In some cases XLA can make use of donated
      buffers to reduce the amount of memory needed to perform a computation,
      for example recycling one of your input buffers to store a result. You
      should not reuse buffers that you donate to a computation, JAX will raise
      an error if you try to.
      For more details on buffer donation see the `FAQ <https://jax.readthedocs.io/en/latest/faq.html#buffer-donation>`_.
    keep_unused: If `False` (the default), arguments that JAX determines to be
      unused by `fun` *may* be dropped from resulting compiled XLA executables.
      Such arguments will not be transferred to the device nor provided to the
      underlying executable. If `True`, unused arguments will not be pruned.
    device: This argument is deprecated. Please put your arguments on the
      device you want before passing them to jit.
      Optional, the Device the jitted function will run on. (Available devices
      can be retrieved via :py:func:`jax.devices`.) The default is inherited
      from XLA's DeviceAssignment logic and is usually to use
      ``jax.devices()[0]``.
    backend: This argument is deprecated. Please put your arguments on the
      backend you want before passing them to jit.
      Optional, a string representing the XLA backend: ``'cpu'``, ``'gpu'``, or
      ``'tpu'``.

  Returns:
    A wrapped version of ``fun``, set up for just-in-time compilation and
    automatically partitioned by the mesh available at each call site.

  For example, a convolution operator can be automatically partitioned over
  an arbitrary set of devices by a single :func:`~pjit` application:

  >>> import jax
  >>> import jax.numpy as jnp
  >>> import numpy as np
  >>> from jax.sharding import Mesh, PartitionSpec
  >>> from jax.experimental.pjit import pjit
  >>>
  >>> x = jnp.arange(8, dtype=jnp.float32)
  >>> f = pjit(lambda x: jax.numpy.convolve(x, jnp.asarray([0.5, 1.0, 0.5]), 'same'),
  ...         in_shardings=None, out_shardings=PartitionSpec('devices'))
  >>> with Mesh(np.array(jax.devices()), ('devices',)):
  ...   print(f(x))  # doctest: +SKIP
  [ 0.5  2.   4.   6.   8.  10.  12.  10. ]
  """
  in_shardings, out_shardings = _resolve_axis_resources_and_shardings_arg(
      in_shardings, out_shardings, in_axis_resources, out_axis_resources)

  (in_shardings, out_shardings, donate_argnums, static_argnums,
   static_argnames) = pre_infer_params(
       fun, in_shardings, out_shardings, donate_argnums,
       static_argnums, static_argnames, device, backend, abstracted_axes)

  def infer_params(*args, **kwargs):
    # Putting this outside of wrapped would make resources lexically scoped
    resource_env = mesh_lib.thread_resources.env
    pjit_info_args = PjitInfo(
          fun=fun, in_shardings=in_shardings,
          out_shardings=out_shardings, static_argnums=static_argnums,
          static_argnames=static_argnames, donate_argnums=donate_argnums,
          device=device, backend=backend, keep_unused=keep_unused,
          inline=inline, resource_env=resource_env,
          abstracted_axes=abstracted_axes)
    return common_infer_params(pjit_info_args, *args, **kwargs)

  has_explicit_sharding = _pjit_explicit_sharding(
      in_shardings, out_shardings, device, backend)
  return post_infer_params(fun, infer_params, static_argnums, static_argnames,
                           donate_argnums, abstracted_axes,
                           has_explicit_sharding)


def hashable_pytree(pytree):
  vals, treedef = tree_flatten(pytree)
  vals = tuple(vals)
  return HashableFunction(lambda: tree_unflatten(treedef, vals),
                          closure=(treedef, vals))


@lru_cache(maxsize=4096)
def _create_mesh_pspec_sharding_from_parsed_pspec(mesh, x):
  if is_unspecified_or_auto(x):
    return x
  return pxla.create_mesh_pspec_sharding(mesh, x.user_spec, x)


def _create_sharding_for_array(mesh, x, name, api_name):
  if isinstance(x, XLACompatibleSharding) or is_unspecified_or_auto(x):
    return x
  if mesh is None:
    msg = ('jax.jit only supports `XLACompatibleSharding`s being passed to'
           f' {name}. Looks like you are passing either `PartitionSpec` or `None`'
           f' which is not allowed in jax.jit.\n')
    if name == 'in_shardings':
      msg += (f'Note that {name} argument is optional. JAX will infer the shardings'
              " from the input jax.Array's and will default to replicating the"
              ' input if the sharding cannot be inferred.')
    elif name == 'out_shardings':
      msg += (f'Note that {name} is optional. If not specified, jax.jit will'
              " use GSPMD's sharding propagation to figure out what the sharding"
              ' of the output(s) should be.')
    raise RuntimeError(msg)
  if mesh.empty:
    raise RuntimeError(
        f'{api_name} requires a non-empty mesh if you are passing'
        f' `PartitionSpec`s or `None` to {name}! Is a mesh defined at the call'
        f' site? Alternatively, provide `XLACompatibleSharding`s to {name} and'
        ' then the mesh context manager is not required.')
  # A nice user error is raised in prepare_axis_resources.
  assert isinstance(x, ParsedPartitionSpec), x
  return _create_mesh_pspec_sharding_from_parsed_pspec(mesh, x)


def _create_sharding_with_device_backend(device, backend):
  if device is not None:
    assert backend is None
    out = SingleDeviceSharding(device)
  elif backend is not None:
    assert device is None
    out = SingleDeviceSharding(
        xb.get_backend(backend).get_default_device_assignment(1)[0])
  return out


def flatten_axis_resources(what, tree, shardings, tupled_args):
  try:
    return tuple(flatten_axes(what, tree, shardings, tupled_args=tupled_args))
  except ValueError:
    pass  # Raise a tree prefix error below

  # Tree leaves are always valid prefixes, so if there was a prefix error as
  # assumed here, axis_resources must not be a leaf.
  assert not treedef_is_leaf(tree_structure(shardings))

  # Check the type directly rather than using isinstance because of namedtuples.
  if tupled_args and (type(shardings) is not tuple or
                      len(shardings) != len(tree.children())):
    # We know axis_resources is meant to be a tuple corresponding to the args
    # tuple, but while it is a non-leaf pytree, either it wasn't a tuple or it
    # wasn't the right length.
    msg = (f"{what} specification must be a tree prefix of the positional "
           f"arguments tuple passed to the `pjit`-decorated function. In "
           f"particular, {what} must either be a None, a PartitionSpec, or "
           f"a tuple of length equal to the number of positional arguments.")
    # If `tree` represents an args tuple, then `axis_resources` must be a tuple.
    # TODO(mattjj,apaszke): disable implicit list casts, remove 'or list' below
    if type(shardings) is not tuple:
      msg += f" But {what} is not a tuple: got {type(shardings)} instead."
    elif len(shardings) != len(tree.children()):
      msg += (f" But {what} is the wrong length: got a tuple or list of length "
              f"{len(shardings)} for an args tuple of length "
              f"{len(tree.children())}.")

    # As an extra hint, let's check if the user just forgot to wrap
    # shardings in a singleton tuple.
    if len(tree.children()) == 1:
      try: flatten_axes(what, tree, (shardings,))
      except ValueError: pass  # That's not the issue.
      else:
        msg += (f" Given the corresponding argument being "
                f"passed, it looks like {what} might need to be wrapped in "
                f"a singleton tuple.")

    raise ValueError(msg)

  axis_tree = shardings

  # Because we only have the `tree` treedef and not the full pytree here,
  # we construct a dummy tree to compare against. Revise this in callers?
  dummy_tree = tree_unflatten(tree, [PytreeLeaf()] * tree.num_leaves)
  errors = prefix_errors(axis_tree, dummy_tree)
  if errors:
    e = errors[0]  # Only show information about the first disagreement found.
    raise e(what)

  # At this point we've failed to find a tree prefix error.
  assert False, "Please open a bug report!"  # This should be unreachable.

class PytreeLeaf:
  def __repr__(self): return "pytree leaf"


@lru_cache(maxsize=4096)
def _process_in_axis_resources(in_shardings_thunk, in_avals, in_tree,
                               resource_env, debug_info, device_or_backend_set):
  orig_in_shardings = in_shardings_thunk()
  # Only do this if original in_shardings are unspecified. If it is AUTO, go
  # via flatten_axis_resources.
  if is_unspecified(orig_in_shardings):
    in_shardings_flat = (orig_in_shardings,) * len(in_avals)
  else:
    in_shardings_flat = flatten_axis_resources(
          "pjit in_shardings", in_tree, orig_in_shardings,
          tupled_args=True)

  if not config.jax_dynamic_shapes:
    pjit_check_aval_sharding(in_shardings_flat, in_avals,
                             None if debug_info is None else debug_info.arg_names,
                             "pjit arguments", allow_uneven_sharding=False)
  canonicalized_shardings = tuple(
      i if is_unspecified_or_auto(i) else
      to_gspmd_sharding(i, aval.ndim, device_or_backend_set)
      for i, aval in zip(in_shardings_flat, in_avals))
  return canonicalized_shardings


@lu.cache
def _create_pjit_jaxpr(fun, in_type, debug_info, out_paths):
  with dispatch.log_elapsed_time(
      "Finished tracing + transforming {fun_name} for pjit in {elapsed_time} sec",
      fun_name=fun.__name__, event=dispatch.JAXPR_TRACE_EVENT):
    pe_debug = debug_info and pe.debug_info_final(fun, debug_info.traced_for)
    if config.jax_dynamic_shapes:
      jaxpr, global_out_avals, consts = pe.trace_to_jaxpr_dynamic2(
          lu.annotate(fun, in_type), debug_info=pe_debug)
    else:
      jaxpr, global_out_avals, consts = pe.trace_to_jaxpr_dynamic(
          fun, in_type, debug_info=pe_debug)

  if not config.jax_dynamic_shapes:
    jaxpr = jaxpr_debug_info(jaxpr, debug_info, out_paths())

  if any(isinstance(c, core.Tracer) for c in consts):
    closed_jaxpr = pe.close_jaxpr(pe.convert_constvars_jaxpr(jaxpr))
    final_consts = consts
  else:
    closed_jaxpr = core.ClosedJaxpr(jaxpr, consts)
    final_consts = []
  return closed_jaxpr, final_consts, global_out_avals


@lru_cache(maxsize=4096)
def _check_and_canonicalize_out_shardings(
    out_shardings_thunk, out_tree, out_type, debug_info, device_or_backend_set):
  orig_out_shardings = out_shardings_thunk()
  # TODO(yashkatariya): Remove the if branch and fix flatten_axis_resources
  # instead. This condition exists because flatten_axis_resources passes in an
  # `object()` while unflattening which breaks assertion is user defined
  # pytrees (which shouldn't exist but they do).
  if (is_unspecified(orig_out_shardings) or
      isinstance(orig_out_shardings, XLACompatibleSharding)):
    out_shardings_flat = (orig_out_shardings,) * len(out_type)
  else:
    out_shardings_flat = flatten_axis_resources(
        "pjit out_shardings", out_tree(), orig_out_shardings,
        tupled_args=False)

  if not config.jax_dynamic_shapes:
    pjit_check_aval_sharding(
        out_shardings_flat, out_type,
        None if debug_info is None else debug_info.result_paths,
        "pjit outputs", allow_uneven_sharding=False)

  canonicalized_out_shardings_flat = tuple(
      o if is_unspecified(o) or is_auto(o) else
      to_gspmd_sharding(o, aval.ndim, device_or_backend_set)
      for o, aval in zip(out_shardings_flat, out_type)
  )
  return canonicalized_out_shardings_flat


def _pjit_jaxpr(fun, out_shardings_thunk, in_type, debug_info,
                device_or_backend_set, out_tree, result_paths):
  jaxpr, final_consts, out_type = _create_pjit_jaxpr(
      fun, in_type, debug_info, result_paths)
  canonicalized_out_shardings_flat = _check_and_canonicalize_out_shardings(
      out_shardings_thunk, out_tree, tuple(out_type), jaxpr.jaxpr.debug_info,
      device_or_backend_set)
  # lu.cache needs to be able to create weakrefs to outputs, so we can't return a plain tuple
  return jaxpr, final_consts, canonicalized_out_shardings_flat


def pjit_check_aval_sharding(
    shardings, flat_avals, names: Optional[Tuple[str, ...]],
    what_aval: str, allow_uneven_sharding: bool):
  new_names = [''] * len(shardings) if names is None else names
  for aval, s, name in zip(flat_avals, shardings, new_names):
    if is_unspecified_or_auto(s):
      continue
    name_str = f' with pytree key path {name}' if name else ''
    shape = aval.shape
    try:
      # Sharding interfaces can implement `is_compatible_aval` as an optional
      # method to raise a more meaningful error.
      if hasattr(s, 'is_compatible_aval'):
        s.is_compatible_aval(shape)
      else:
        s._to_xla_op_sharding(len(shape))
    except ValueError as e:
      raise ValueError(
          f'One of {what_aval}{name_str} is incompatible with its sharding '
          f'annotation {s}: {str(e)}')
    # Use the `OpSharding` proto to find out how many ways each dimension of
    # the aval is sharded. This approach will work across all
    # XLACompatibleSharding.
    op_sharding = s._to_xla_op_sharding(len(shape))
    assert op_sharding is not None
    num_ways_dim_sharded, _ = op_shardings.get_num_ways_dim_sharded(
        cast(xc.OpSharding, op_sharding))
    for i, size in enumerate(num_ways_dim_sharded):
      if not allow_uneven_sharding and shape[i] % size != 0:
        raise ValueError(f"One of {what_aval}{name_str} was given the sharding "
                         f"of {s}, which implies that "
                         f"the global size of its dimension {i} should be "
                         f"divisible by {size}, but it is equal to {shape[i]} "
                         f"(full shape: {shape})")


# -------------------- pjit rules --------------------

pjit_p = core.AxisPrimitive("pjit")
pjit_p.multiple_results = True


def _resolve_in_shardings(
    args, pjit_in_shardings: Sequence[PjitSharding],
    out_shardings: Sequence[PjitSharding],
    pjit_mesh: Optional[pxla.Mesh]) -> Sequence[PjitSharding]:
  # If True, means that device or backend is set by the user on pjit and it
  # has the same semantics as device_put i.e. doesn't matter which device the
  # arg is on, reshard it to the device mentioned. So don't do any of the
  # checks and just return the pjit_in_shardings directly. `shard_args` will
  # handle the resharding.
  if pxla.check_device_backend_on_shardings(pjit_in_shardings):
    return pjit_in_shardings

  committed_arg_shardings = []
  for a in args:
    if hasattr(a, 'sharding'):
      arg_s = a.sharding
      if not isinstance(arg_s, XLACompatibleSharding):
        raise ValueError(f'One of the argument to pjit got sharding {arg_s} '
                         'which is not a subclass of XLACompatibleSharding.')
      # Don't consider PmapSharding inputs as committed. They will get resharded
      # unconditionally.
      if isinstance(arg_s, PmapSharding):
        continue
      if getattr(a, '_committed', True):
        committed_arg_shardings.append((arg_s, pxla.MismatchType.ARG_SHARDING, None))

  # Check if the device_assignment across inputs, outputs and arguments is the
  # same.
  pxla._get_and_check_device_assignment(
      it.chain(
          committed_arg_shardings,
          [(i, pxla.MismatchType.IN_SHARDING, None) for i in pjit_in_shardings],
          [(o, pxla.MismatchType.OUT_SHARDING, None) for o in out_shardings]),
      (None if pjit_mesh is None or pjit_mesh.empty else list(pjit_mesh.devices.flat)))

  resolved_in_shardings = []
  for arg, pjit_in_s in zip(args, pjit_in_shardings):
    arg_s, committed = ((arg.sharding, getattr(arg, '_committed', True))
                        if hasattr(arg, 'sharding') else (UNSPECIFIED, False))
    if is_unspecified(pjit_in_s):
      if is_unspecified(arg_s):
        resolved_in_shardings.append(arg_s)
      else:
        if committed:
          # If the arg has a PmapSharding, then reshard it unconditionally.
          if isinstance(arg_s, PmapSharding):
            resolved_in_shardings.append(UNSPECIFIED)
          else:
            resolved_in_shardings.append(to_gspmd_sharding(
                cast(XLACompatibleSharding, arg_s), arg.ndim))
        else:
          if dispatch.is_single_device_sharding(arg_s):
            resolved_in_shardings.append(UNSPECIFIED)
          else:
            raise NotImplementedError('Having uncommitted Array sharded on '
                                      'multiple devices is not supported.')
    else:
      if (isinstance(arg, np.ndarray) and
          not pjit_in_s.is_fully_replicated and  # type: ignore
          xb.process_count() > 1):
        raise ValueError(
            'Passing non-trivial shardings for numpy '
            'inputs is not allowed. To fix this error, either specify a '
            'replicated sharding explicitly or use '
            '`jax.experimental.multihost_utils.host_local_array_to_global_array(...)` '
            'to convert your host local numpy inputs to a jax.Array which you '
            'can pass to pjit. '
            'If the numpy input is the same on each process, then you can use '
            '`jax.make_array_from_callback(...) to create a `jax.Array` which '
            'you can pass to pjit. '
            'Please see the jax.Array migration guide for more information '
            'https://jax.readthedocs.io/en/latest/jax_array_migration.html#handling-of-host-local-inputs-to-pjit-like-batch-etc. '
            f'Got arg shape: {arg.shape}, arg value: {arg}')
      if not is_unspecified(arg_s):
        if (committed and
            not isinstance(arg_s, PmapSharding) and
            not op_shardings.are_op_shardings_equal(
                pjit_in_s._to_xla_op_sharding(arg.ndim),  # type: ignore
                arg_s._to_xla_op_sharding(arg.ndim))):
          op =  getattr(pjit_in_s, '_original_sharding', pjit_in_s)
          raise ValueError('Sharding passed to pjit does not match the sharding '
                           'on the respective arg. '
                           f'Got pjit sharding: {op},\n'
                           f'arg sharding: {arg_s} for arg shape: {arg.shape}, '
                           f'arg value: {arg}')
      resolved_in_shardings.append(pjit_in_s)

  return tuple(resolved_in_shardings)


def _pjit_call_impl_python(
    *args, jaxpr, in_shardings, out_shardings, resource_env, donated_invars,
    name, keep_unused, inline):
  global _most_recent_pjit_call_executable

  in_shardings = _resolve_in_shardings(
      args, in_shardings, out_shardings,
      resource_env.physical_mesh if resource_env is not None else None)

  compiled = _pjit_lower(
      jaxpr, in_shardings, out_shardings, resource_env,
      donated_invars, name, keep_unused, inline,
      always_lower=False, lowering_platform=None).compile()
  _most_recent_pjit_call_executable.value = compiled
  # This check is expensive so only do it if enable_checks is on.
  if compiled._auto_spmd_lowering and config.jax_enable_checks:
    pxla.check_gda_or_array_xla_sharding_match(args, compiled._in_shardings,
                                               jaxpr.jaxpr.debug_info)
  if config.jax_distributed_debug:
    # Defensively only perform fingerprint logic if debug logging is enabled
    # NOTE(skyewm): I didn't benchmark this
    fingerprint = None
    if hasattr(compiled.runtime_executable(), "fingerprint"):
      fingerprint = compiled.runtime_executable().fingerprint
    if fingerprint is not None:
      fingerprint = fingerprint.hex()
    distributed_debug_log(("Running pjit'd function", name),
                          ("in_shardings", in_shardings),
                          ("out_shardings", out_shardings),
                          ("abstract args", map(xla.abstractify, args)),
                          ("fingerprint", fingerprint))
  try:
    return compiled.unsafe_call(*args), compiled
  except FloatingPointError:
    assert config.jax_debug_nans or config.jax_debug_infs  # compiled_fun can only raise in this case

    _ = core.jaxpr_as_fun(jaxpr)(*args)  # may raise, not return

    # If control reaches this line, we got a NaN on the output of `compiled`
    # but not `fun.call_wrapped` on the same arguments. Let's tell the user.
    msg = ("An invalid value was encountered in the output of the "
           f"`jit`-decorated function {name}. Because "
           "config.jax_debug_nans and/or config.jax_debug_infs is set, the "
           "de-optimized function (i.e., the function as if the `jit` "
           "decorator were removed) was called in an attempt to get a more "
           "precise error message. However, the de-optimized function did not "
           "produce invalid values during its execution. This behavior can "
           "result from `jit` optimizations causing the invalid value to be "
           "produced. It may also arise from having nan/inf constants as "
           "outputs, like `jax.jit(lambda ...: jax.numpy.nan)(...)`. "
           "\n\n"
           "It may be possible to avoid the invalid value by removing the "
           "`jit` decorator, at the cost of losing optimizations. "
           "\n\n"
           "If you see this error, consider opening a bug report at "
           "https://github.com/google/jax.")
    raise FloatingPointError(msg)


@weakref_lru_cache
def _get_jaxpr_as_fun(jaxpr, in_shardings, out_shardings, resource_env,
                      donated_invars, name, keep_unused, inline):
  # The input jaxpr to `_get_jaxpr_as_fun` is under a weakref_lru_cache so
  # returning `core.jaxpr_as_fun(jaxpr)` directly creates a strong reference to
  # the jaxpr defeating the purpose of weakref_lru_cache. So return a function
  # that closes over a weakrefed jaxpr and gets called inside that function.
  # This way there won't be a strong reference to the jaxpr from the output
  # function.
  jaxpr = weakref.ref(jaxpr)
  return lambda *args: core.jaxpr_as_fun(jaxpr())(*args)  # pylint: disable=unnecessary-lambda


def _pjit_call_impl(*args, jaxpr,
                    in_shardings, out_shardings, resource_env,
                    donated_invars, name, keep_unused, inline):
  def call_impl_cache_miss(*args_, **kwargs_):
    out_flat, compiled = _pjit_call_impl_python(
        *args, jaxpr=jaxpr, in_shardings=in_shardings,
        out_shardings=out_shardings, resource_env=resource_env,
        donated_invars=donated_invars, name=name, keep_unused=keep_unused,
        inline=inline)
    fastpath_data = _get_fastpath_data(
        compiled, tree_structure(out_flat), args, out_flat)
    return out_flat, fastpath_data

  f = _get_jaxpr_as_fun(
      jaxpr, tuple(getattr(i, '_original_sharding', i) for i in in_shardings),
      tuple(getattr(o, '_original_sharding', o) for o in out_shardings),
      resource_env, donated_invars, name, keep_unused, inline)
  donated_argnums = [i for i, d in enumerate(donated_invars) if d]
  return xc._xla.pjit(name, f, call_impl_cache_miss, [], [], donated_argnums,
                      _cpp_pjit_cache)(*args)

pjit_p.def_impl(_pjit_call_impl)


@dataclasses.dataclass(frozen=True)
class SameDeviceAssignmentTuple:
  shardings: Tuple[PjitSharding, ...]
  # device_assignment is Optional because shardings can contain `AUTO` and in
  # that case `mesh` is compulsory to be used. So in that case
  # `_pjit_lower_cached` cache, resource_env will check against the devices.
  device_assignment: Optional[XLADeviceAssignment]

  def __hash__(self):
    shardings_hash = tuple(
        s._op_sharding_hash if isinstance(s, GSPMDSharding) else s  # type: ignore
        for s in self.shardings)
    if self.device_assignment is None:
      return hash(shardings_hash)
    else:
      return hash((shardings_hash, *self.device_assignment))

  def __eq__(self, other):
    if not isinstance(other, SameDeviceAssignmentTuple):
      return False
    eq = []
    for s, o in zip(self.shardings, other.shardings):
      s = getattr(s, "_original_sharding", s)
      o = getattr(o, "_original_sharding", o)
      if isinstance(s, GSPMDSharding) and isinstance(o, GSPMDSharding):
        eq.append(op_shardings.are_op_shardings_equal(
            s._op_sharding, o._op_sharding))
      else:
        eq.append(s == o)
    return all(eq) and self.device_assignment == other.device_assignment


def _pjit_lower(
    jaxpr: core.ClosedJaxpr,
    in_shardings,
    out_shardings,
    *args, **kwargs):
  da = _fast_path_get_device_assignment(it.chain(in_shardings, out_shardings))
  in_shardings = SameDeviceAssignmentTuple(tuple(in_shardings), da)
  out_shardings = SameDeviceAssignmentTuple(tuple(out_shardings), da)
  return _pjit_lower_cached(jaxpr, in_shardings, out_shardings, *args, **kwargs)


@weakref_lru_cache
def _pjit_lower_cached(
    jaxpr: core.ClosedJaxpr,
    sdat_in_shardings: SameDeviceAssignmentTuple,
    sdat_out_shardings: SameDeviceAssignmentTuple,
    resource_env,
    donated_invars,
    name: str,
    keep_unused: bool,
    inline: bool,
    always_lower: bool,
    *,
    lowering_platform: Optional[str]):
  in_shardings: Tuple[PjitShardingMinusUnspecified, ...] = cast(
      Tuple[PjitShardingMinusUnspecified, ...], sdat_in_shardings.shardings)
  out_shardings: Tuple[PjitSharding, ...] = sdat_out_shardings.shardings

  if resource_env is not None:
    pxla.resource_typecheck(jaxpr, resource_env, {}, lambda: "pjit")

  if resource_env is not None:
    mesh = resource_env.physical_mesh
    api_name = 'pjit'
  else:
    # resource_env is `None` in the jit wrapper around pjit.
    mesh = None
    api_name = 'jit'

  # For `pjit(xmap)` cases, it needs to take the `lower_mesh_computation` path
  # because `xmap` only supports SPMDAxisContext right now.
  if dispatch.jaxpr_has_primitive(jaxpr.jaxpr, 'xmap'):
    return pxla.lower_mesh_computation(
      jaxpr, api_name, name, mesh,
      in_shardings, out_shardings, donated_invars,
      True, jaxpr.in_avals, tiling_method=None,
      lowering_platform=lowering_platform)
  else:
    return pxla.lower_sharding_computation(
        jaxpr, api_name, name, in_shardings, out_shardings,
        tuple(donated_invars), tuple(jaxpr.in_avals),
        keep_unused=keep_unused, inline=inline, always_lower=always_lower,
        devices_from_context=(
            None if mesh is None or mesh.empty else list(mesh.devices.flat)),
        lowering_platform=lowering_platform)


def pjit_staging_rule(trace, *args, **params):
  if (params["inline"] and
      all(is_unspecified(i) for i in params["in_shardings"]) and
      all(is_unspecified(o) for o in params["out_shardings"])):
    jaxpr = params['jaxpr']
    return core.eval_jaxpr(jaxpr.jaxpr, jaxpr.consts, *args,
                           propagate_source_info=False)
  elif config.jax_dynamic_shapes:
    source_info = source_info_util.current()
    out_tracers = []
    for aval in _out_type(params['jaxpr']):
      if type(aval) is core.DShapedArray:
        shape = [args[d.val] if type(d) is core.InDBIdx else
                 out_tracers[d.val] if type(d) is core.OutDBIdx else
                 d for d in aval.shape]
        aval = aval.update(shape=tuple(core.get_referent(d) for d in shape))
      out_tracers.append(pe.DynamicJaxprTracer(trace, aval, source_info))
    eqn = core.new_jaxpr_eqn(
      map(trace.getvar, args), map(trace.makevar, out_tracers), pjit_p, params,
      params['jaxpr'].effects, source_info)
    trace.frame.add_eqn(eqn)
    return out_tracers
  else:
    return trace.default_process_primitive(pjit_p, args, params)
pe.custom_staging_rules[pjit_p] = pjit_staging_rule

# TODO(mattjj): remove/trivialize this when jaxprs have type annotation on them,
# since it's actually not possible in general to infer the type from the term
def _out_type(jaxpr: core.ClosedJaxpr) -> List[core.AbstractValue]:
  out = []
  in_idx = {v: i for i, v in enumerate(jaxpr.jaxpr.invars)}
  out_idx = {x: i for i, x in enumerate(jaxpr.jaxpr.invars)
             if type(x) is core.Var}
  for x in jaxpr.jaxpr.outvars:
    aval = x.aval
    if type(aval) is core.DShapedArray:
      shape = [core.InDBIdx(in_idx[d]) if d in in_idx else
               core.OutDBIdx(out_idx[d]) if d in out_idx else
               d for d in x.aval.shape]
      aval = aval.update(shape=tuple(shape))
    out.append(aval)
  return out


def _pjit_typecheck(ctx_factory, *in_atoms, jaxpr, **params):
  return core._check_call(ctx_factory, pjit_p, in_atoms,
                          dict(params, call_jaxpr=jaxpr.jaxpr))
core.custom_typechecks[pjit_p] = _pjit_typecheck


def _pjit_abstract_eval(*args, jaxpr, out_shardings, resource_env, **_):
  return jaxpr.out_avals, jaxpr.effects
pjit_p.def_effectful_abstract_eval(_pjit_abstract_eval)


def _pjit_lowering(ctx, *args, name, jaxpr, in_shardings,
                   out_shardings, resource_env, donated_invars,
                   keep_unused, inline):
  effects = list(ctx.tokens_in.effects())
  output_types = map(mlir.aval_to_ir_types, ctx.avals_out)
  output_types = [mlir.token_type()] * len(effects) + output_types
  flat_output_types = flatten(output_types)

  arg_shardings = [None if is_unspecified(i) else i._to_xla_op_sharding(aval.ndim)
                   for aval, i in zip(ctx.avals_in, in_shardings)]
  result_shardings = [None if is_unspecified(o) else o._to_xla_op_sharding(aval.ndim)
                      for aval, o in zip(ctx.avals_out, out_shardings)]

  # TODO(b/228598865): inlined calls cannot have shardings set directly on the
  # inputs or outputs because they are lost during MLIR->HLO conversion.
  # using_sharding_annotation=False means we add an identity operation instead.
  func = mlir.lower_jaxpr_to_fun(
      ctx.module_context, name, jaxpr, effects, arg_shardings=arg_shardings,
      result_shardings=result_shardings, use_sharding_annotations=False,
      api_name=('jit' if resource_env is None else 'pjit'))
  tokens_in = [ctx.tokens_in.get(eff) for eff in effects]
  args = (*ctx.dim_var_values, *tokens_in, *args)
  call = func_dialect.CallOp(flat_output_types,
                             ir.FlatSymbolRefAttr.get(func.name.value),
                             mlir.flatten_lowering_ir_args(args))
  out_nodes = unflatten(call.results, map(len, output_types))
  tokens, out_nodes = split_list(out_nodes, [len(effects)])
  tokens_out = ctx.tokens_in.update_tokens(mlir.TokenSet(zip(effects, tokens)))
  ctx.set_tokens_out(tokens_out)
  return out_nodes

mlir.register_lowering(pjit_p, _pjit_lowering)


def _pjit_batcher(insert_axis, spmd_axis_name,
                  axis_size, axis_name, main_type,
                  vals_in, dims_in,
                  jaxpr, in_shardings, out_shardings,
                  resource_env, donated_invars, name, keep_unused, inline):
  new_jaxpr, axes_out = batching.batch_jaxpr2(
      jaxpr, axis_size, dims_in, axis_name=axis_name,
      spmd_axis_name=spmd_axis_name, main_type=main_type)

  # `insert_axis` is set to True only for some `xmap` uses.
  new_parts = (axis_name,) if insert_axis else (
      () if spmd_axis_name is None else spmd_axis_name)

  if resource_env is not None:
    mesh = resource_env.physical_mesh
  else:
    mesh = None

  in_shardings = tuple(
      _pjit_batcher_for_sharding(i, axis_in, new_parts, mesh, aval.ndim)
      if axis_in is not None else i
      for axis_in, i, aval in zip(dims_in, in_shardings, new_jaxpr.in_avals))
  out_shardings = tuple(
      _pjit_batcher_for_sharding(o, axis_out, new_parts, mesh, aval.ndim)
      if axis_out is not None else o
      for axis_out, o, aval in zip(axes_out, out_shardings, new_jaxpr.out_avals))
  vals_out = pjit_p.bind(
    *vals_in,
    jaxpr=new_jaxpr,
    in_shardings=in_shardings,
    out_shardings=out_shardings,
    resource_env=resource_env,
    donated_invars=donated_invars,
    name=name,
    keep_unused=keep_unused,
    inline=inline)
  return vals_out, axes_out

batching.spmd_axis_primitive_batchers[pjit_p] = partial(_pjit_batcher, False)
batching.axis_primitive_batchers[pjit_p] = partial(_pjit_batcher, False, None)
pxla.spmd_primitive_batchers[pjit_p] = partial(_pjit_batcher, True, None)

def _pjit_batcher_for_sharding(
    s: Union[GSPMDSharding, UnspecifiedValue],
    dim: int, val: Tuple[str, ...], mesh, ndim: int):
  if is_unspecified(s):
    return s
  if not val:
    if sharding_impls.is_op_sharding_replicated(s._op_sharding):  # type: ignore
      return s
    new_op = s._op_sharding.clone()  # type: ignore
    tad = list(new_op.tile_assignment_dimensions)
    tad.insert(dim, 1)
    new_op.tile_assignment_dimensions = tad
    new_gs = GSPMDSharding(s._device_assignment, new_op)  # type: ignore
    if hasattr(s, '_original_sharding'):
      vmapped_s, _ = pxla._get_out_sharding_from_orig_sharding(
          [new_gs], [None], s._original_sharding, None, [False])[0]  # type: ignore
      new_gs = to_gspmd_sharding(vmapped_s, ndim)
    return new_gs
  else:
    assert isinstance(s, GSPMDSharding)
    if isinstance(getattr(s, '_original_sharding', None), NamedSharding):
      mesh = s._original_sharding.mesh  # type: ignore
    assert mesh is not None and not mesh.empty
    parsed_pspec = parse_flatten_op_sharding(s._op_sharding, mesh)[0]  # type: ignore
    parsed_pspec = parsed_pspec.insert_axis_partitions(dim, val)
    mps = NamedSharding._from_parsed_pspec(mesh, parsed_pspec)
    return GSPMDSharding(mps._device_assignment, mps._to_xla_op_sharding(ndim))


def _pjit_jvp(primals_in, tangents_in,
              jaxpr, in_shardings, out_shardings,
              resource_env, donated_invars, name, keep_unused, inline):
  is_nz_tangents_in = [type(t) is not ad.Zero for t in tangents_in]
  jaxpr_jvp, is_nz_tangents_out = ad.jvp_jaxpr(
      jaxpr, is_nz_tangents_in, instantiate=False)

  def _filter_zeros(is_nz_l, l):
    return (x for nz, x in zip(is_nz_l, l) if nz)
  _filter_zeros_in = partial(_filter_zeros, is_nz_tangents_in)
  _filter_zeros_out = partial(_filter_zeros, is_nz_tangents_out)
  outputs = pjit_p.bind(
      *primals_in, *_filter_zeros_in(tangents_in),
      jaxpr=jaxpr_jvp,
      in_shardings=(*in_shardings, *_filter_zeros_in(in_shardings)),
      out_shardings=(*out_shardings, *_filter_zeros_out(out_shardings)),
      resource_env=resource_env,
      donated_invars=(*donated_invars, *_filter_zeros_in(donated_invars)),
      name=name,
      keep_unused=keep_unused,
      inline=inline)

  primals_out, tangents_out = split_list(outputs, [len(jaxpr.jaxpr.outvars)])
  assert len(primals_out) == len(jaxpr.jaxpr.outvars)
  tangents_out_it = iter(tangents_out)
  return primals_out, [next(tangents_out_it) if nz else ad.Zero(aval)
                       for nz, aval in zip(is_nz_tangents_out, jaxpr.out_avals)]
ad.primitive_jvps[pjit_p] = _pjit_jvp


@weakref_lru_cache
def _known_jaxpr_fwd(known_jaxpr: core.ClosedJaxpr,
                     fwds_known: Tuple[Optional[int]]) -> core.ClosedJaxpr:
  updated_jaxpr = known_jaxpr.jaxpr.replace(
      outvars=[x for x, i in zip(known_jaxpr.jaxpr.outvars, fwds_known)
               if i is None])
  return known_jaxpr.replace(jaxpr=updated_jaxpr)


def _pjit_partial_eval(trace, *in_tracers,
                       jaxpr, in_shardings, out_shardings,
                       resource_env, donated_invars, name, keep_unused, inline):
  in_pvals = [t.pval for t in in_tracers]

  known_ins = tuple(pv.is_known() for pv in in_pvals)
  unknown_ins = tuple(not k for k in known_ins)
  known_jaxpr, unknown_jaxpr, unknown_outs, res_avals = pe.partial_eval_jaxpr_nounits(
      jaxpr, unknown_ins, instantiate=False)
  unknown_outs = tuple(unknown_outs)
  known_outs = tuple(not uk for uk in unknown_outs)
  num_residuals = len(res_avals)

  def keep_where(l, should_keep):
    return tuple(x for x, keep in unsafe_zip(l, should_keep) if keep)

  residual_shardings = (UNSPECIFIED,) * num_residuals
  # Compute the known outputs
  known_params = dict(
      jaxpr=known_jaxpr,
      in_shardings=keep_where(in_shardings, known_ins),
      out_shardings=(
          keep_where(out_shardings, known_outs) + residual_shardings),
      resource_env=resource_env,
      donated_invars=keep_where(donated_invars, known_ins),
      name=name,
      keep_unused=keep_unused,
      inline=inline)

  fwds_known = pe._jaxpr_forwarding(known_params['jaxpr'].jaxpr)

  # Only forward the outvars where the out_sharding is UNSPECIFIED.
  known_user_out_shardings = keep_where(known_params['out_shardings'], known_outs)
  fwds_known_user = [
      fwd if is_unspecified(os) else None
      for os, fwd in zip(known_user_out_shardings,
                              fwds_known[:len(known_user_out_shardings)])]
  fwds_known = fwds_known_user + fwds_known[len(known_user_out_shardings):]
  del fwds_known_user

  # Remove forwarded outvars and out_shardings
  known_params['jaxpr'] = _known_jaxpr_fwd(known_params['jaxpr'], tuple(fwds_known))
  known_out_shardings = tuple(
      s for s, i in zip(known_params['out_shardings'], fwds_known) if i is None)
  known_params['out_shardings'] = known_out_shardings
  del known_out_shardings

  assert len(known_params['out_shardings']) == len(known_params['jaxpr'].out_avals)

  # Bind known things to pjit_p.
  known_inputs = [pv.get_known() for pv in in_pvals if pv.is_known()]
  all_known_outs = pjit_p.bind(*known_inputs, **known_params)

  known_outs_iter = iter(all_known_outs)
  all_known_outs = [next(known_outs_iter)
                    if fwd_idx is None else known_inputs[fwd_idx]
                    for fwd_idx in fwds_known]
  assert next(known_outs_iter, None) is None
  del known_outs_iter, known_inputs

  if num_residuals:
    known_out_vals, residual_vals = \
        split_list(all_known_outs, [len(all_known_outs) - num_residuals])
  else:
    known_out_vals, residual_vals = all_known_outs, ()
  residual_tracers = [trace.new_instantiated_const(residual) for residual in residual_vals]

  # The convention of partial_eval_jaxpr_nounits is to place residual binders
  # at the front of the jaxpr produced, so we move them to the back since both
  # the jaxpr equation built below and the pjit transpose rule assume a
  # residual-inputs-last convention.
  unknown_jaxpr = pe.move_binders_to_back(
      unknown_jaxpr, [True] * num_residuals + [False] * sum(unknown_ins))
  # Prepare unknown tracers
  unknown_params = dict(
      jaxpr=unknown_jaxpr,
      in_shardings=(keep_where(in_shardings, unknown_ins) + residual_shardings),
      out_shardings=keep_where(out_shardings, unknown_outs),
      resource_env=resource_env,
      donated_invars=(keep_where(donated_invars, unknown_ins) +
                      (False,) * num_residuals),
      name=name,
      keep_unused=keep_unused,
      inline=inline)
  unknown_tracers_in = [t for t in in_tracers if not t.pval.is_known()]
  unknown_out_avals = unknown_jaxpr.out_avals
  unknown_tracers_out = [
      pe.JaxprTracer(trace, pe.PartialVal.unknown(aval), None)
      for aval in unknown_out_avals
  ]
  eqn = pe.new_eqn_recipe((*unknown_tracers_in, *residual_tracers),
                          unknown_tracers_out,
                          pjit_p,
                          unknown_params,
                          unknown_jaxpr.effects,
                          source_info_util.current())
  for t in unknown_tracers_out: t.recipe = eqn
  return merge_lists(unknown_outs, known_out_vals, unknown_tracers_out)

pe.custom_partial_eval_rules[pjit_p] = _pjit_partial_eval


def _pjit_partial_eval_custom_params_updater(
    unks_in: Sequence[bool], inst_in: Sequence[bool],
    kept_outs_known: Sequence[bool], kept_outs_staged: Sequence[bool],
    num_res: int, params_known: dict, params_staged: dict
  ) -> Tuple[dict, dict]:
  # prune inputs to jaxpr_known according to unks_in
  donated_invars_known, _ = pe.partition_list(unks_in, params_known['donated_invars'])
  in_shardings_known, _ = pe.partition_list(unks_in, params_known['in_shardings'])
  if num_res == 0:
    residual_shardings = []
  else:
    residual_shardings = [UNSPECIFIED] * num_res
  _, out_shardings_known = pe.partition_list(kept_outs_known, params_known['out_shardings'])
  new_params_known = dict(params_known,
                          in_shardings=tuple(in_shardings_known),
                          out_shardings=(*out_shardings_known, *residual_shardings),
                          donated_invars=tuple(donated_invars_known))
  assert len(new_params_known['in_shardings']) == len(params_known['jaxpr'].in_avals)
  assert len(new_params_known['out_shardings']) == len(params_known['jaxpr'].out_avals)

  # added num_res new inputs to jaxpr_staged, and pruning according to inst_in
  _, donated_invars_staged = pe.partition_list(inst_in, params_staged['donated_invars'])
  donated_invars_staged = [False] * num_res + donated_invars_staged
  _, in_shardings_staged = pe.partition_list(inst_in, params_staged['in_shardings'])
  in_shardings_staged = [*residual_shardings, *in_shardings_staged]

  _, out_shardings_staged = pe.partition_list(kept_outs_staged, params_staged['out_shardings'])

  new_params_staged = dict(params_staged,
                           in_shardings=tuple(in_shardings_staged),
                           out_shardings=tuple(out_shardings_staged),
                           donated_invars=tuple(donated_invars_staged))
  assert len(new_params_staged['in_shardings']) == len(params_staged['jaxpr'].in_avals)
  assert len(new_params_staged['out_shardings']) == len(params_staged['jaxpr'].out_avals)
  return new_params_known, new_params_staged

pe.partial_eval_jaxpr_custom_rules[pjit_p] = \
    partial(pe.closed_call_partial_eval_custom_rule, 'jaxpr',
            _pjit_partial_eval_custom_params_updater)


@lu.cache
def _pjit_transpose_trace(fun, in_avals):
  transpose_jaxpr, _, consts = pe.trace_to_jaxpr_dynamic(fun, in_avals)
  transpose_jaxpr = core.ClosedJaxpr(transpose_jaxpr, consts)
  return transpose_jaxpr


def _pjit_transpose(reduce_axes, cts_in, *primals_in,
                    jaxpr, in_shardings, out_shardings,
                    resource_env, donated_invars, name, keep_unused, inline):
  def prune_type(ty, xs, maybe_zeros):
    return tuple(x for x, mz in zip(xs, maybe_zeros) if type(mz) is not ty)

  body = lu.wrap_init(ad.closed_backward_pass)
  body = lu.hashable_partial(body, jaxpr, reduce_axes, False)
  primals_and_nz_cts_in, in_treedef = tree_flatten((primals_in, cts_in))
  body, cts_out_treedef_thunk = flatten_fun_nokwargs(body, in_treedef)

  transpose_in_shardings = (
    *prune_type(ad.UndefinedPrimal, in_shardings, primals_in),
    *prune_type(ad.Zero, out_shardings, cts_in)
  )
  global_cts_in_avals = tuple(core.raise_to_shaped(core.get_aval(ct))
                              for ct in primals_and_nz_cts_in)

  transpose_jaxpr = _pjit_transpose_trace(body, global_cts_in_avals)
  cts_out_treedef = cts_out_treedef_thunk()
  transpose_out_shardings = prune_type(
      ad.Zero,
      in_shardings,
      tree_unflatten(cts_out_treedef, [object()] * cts_out_treedef.num_leaves))

  nz_cts_out = pjit_p.bind(
      *primals_and_nz_cts_in,
      jaxpr=transpose_jaxpr,
      in_shardings=transpose_in_shardings,
      out_shardings=transpose_out_shardings,
      resource_env=resource_env,
      donated_invars=(False,) * len(primals_and_nz_cts_in),
      name=name,
      keep_unused=keep_unused,
      inline=inline)
  return tree_unflatten(cts_out_treedef, nz_cts_out)
ad.reducing_transposes[pjit_p] = _pjit_transpose


@weakref_lru_cache
def _dce_jaxpr_pjit(
    jaxpr: core.ClosedJaxpr, used_outputs: Tuple[bool]
) -> Tuple[core.ClosedJaxpr, List[bool]]:
  new_jaxpr, used_inputs = pe.dce_jaxpr(jaxpr.jaxpr, used_outputs)
  return core.ClosedJaxpr(new_jaxpr, jaxpr.consts), used_inputs


def dce_jaxpr_pjit_rule(used_outputs: List[bool], eqn: core.JaxprEqn
                        ) -> Tuple[List[bool], Optional[core.JaxprEqn]]:
  dced_jaxpr, used_inputs = _dce_jaxpr_pjit(
      eqn.params['jaxpr'], tuple(used_outputs))

  def keep_where(xs, keeps):
    return tuple(x for x, keep in zip(xs, keeps) if keep)

  eqn_params = eqn.params
  new_params = dict(
      eqn_params,
      jaxpr=dced_jaxpr,
      in_shardings=keep_where(eqn_params["in_shardings"], used_inputs),
      out_shardings=keep_where(eqn_params["out_shardings"], used_outputs),
      donated_invars=keep_where(eqn_params["donated_invars"], used_inputs),
  )
  if not any(used_inputs) and not any(used_outputs) and not dced_jaxpr.effects:
    return used_inputs, None
  else:
    new_eqn = core.new_jaxpr_eqn(
        [v for v, used in zip(eqn.invars, used_inputs) if used],
        [v for v, used in zip(eqn.outvars, used_outputs) if used],
        eqn.primitive, new_params, dced_jaxpr.effects, eqn.source_info)
    return used_inputs, new_eqn

pe.dce_rules[pjit_p] = dce_jaxpr_pjit_rule


def _check_resources_against_named_axes(what, aval, pos_axis_resources, named_axis_resources):
  pjit_resources = set(
      it.chain.from_iterable([d for d in pos_axis_resources if d is not None]))
  aval_resources = set(it.chain.from_iterable(
    named_axis_resources[a] for a in aval.named_shape))
  overlap = pjit_resources & aval_resources
  if overlap:
    raise JAXTypeError(
        f"{what} has an axis resources specification of "
        f"{pos_axis_resources.unsynced_user_spec(SpecSync.DIM_PERMUTE)} "
        f"that uses one or more mesh axes already used by xmap to partition "
        f"a named axis appearing in its named_shape (both use mesh axes "
        f"{mesh_lib.show_axes(overlap)})")

def _resource_typing_pjit(avals, params, source_info, resource_env, named_axis_resources):
  jaxpr = params["jaxpr"]
  what = "pjit input"
  if (resource_env is not None and params['resource_env'] is not None and
      resource_env.physical_mesh != params['resource_env'].physical_mesh):
      raise RuntimeError("Changing the physical mesh is not allowed inside pjit.")

  for aval, s in zip(jaxpr.in_avals, params['in_shardings']):
    if is_unspecified(s) or is_auto(s):
      continue
    elif hasattr(s, '_original_sharding') and hasattr(
        s._original_sharding, '_parsed_pspec'):
      parsed_pspec = s._original_sharding._parsed_pspec
    else:
      if resource_env is not None:
        parsed_pspec = parse_flatten_op_sharding(
            s._op_sharding, resource_env.physical_mesh)[0]
      else:
        parsed_pspec = None
    if parsed_pspec is not None:
      _check_resources_against_named_axes(what, aval, parsed_pspec,
                                          named_axis_resources)

  pxla.resource_typecheck(
      jaxpr.jaxpr, resource_env, named_axis_resources,
      lambda: (f"a pjit'ed function {params['name']} "
               f"(pjit called at {source_info_util.summarize(source_info)})"))

  what = "pjit output"
  for aval, s in zip(jaxpr.out_avals, params['out_shardings']):
    if is_unspecified(s) or is_auto(s):
      continue
    elif hasattr(s, '_original_sharding') and hasattr(
        s._original_sharding, '_parsed_pspec'):
      parsed_pspec = s._original_sharding._parsed_pspec
    else:
      if resource_env is not None:
        parsed_pspec = parse_flatten_op_sharding(
            s._op_sharding, resource_env.physical_mesh)[0]
      else:
        parsed_pspec = None
    if parsed_pspec is not None:
      _check_resources_against_named_axes(what, aval, parsed_pspec,
                                          named_axis_resources)

pxla.custom_resource_typing_rules[pjit_p] = _resource_typing_pjit


def _pjit_pp_rule(eqn, context, settings):
  params = dict(eqn.params)
  del params['inline']
  if not any(params['donated_invars']):
    del params['donated_invars']
  if all(is_unspecified(s) for s in params['in_shardings']):
    del params['in_shardings']
  if all(is_unspecified(s) for s in params['out_shardings']):
    del params['out_shardings']
  if not params['keep_unused']:
    del params['keep_unused']
  if (params['resource_env'] is None or
      params['resource_env'].physical_mesh.empty):
    del params['resource_env']
  return core._pp_eqn(eqn.replace(params=params), context, settings)
core.pp_eqn_rules[pjit_p] = _pjit_pp_rule


# -------------------- with_sharding_constraint --------------------

def with_sharding_constraint(x, shardings):
  """Mechanism to constrain the sharding of an Array inside a jitted computation

  This is a strict constraint for the GSPMD partitioner and not a hint. For examples
  of how to use this function, see `Distributed arrays and automatic parallelization`_.

  Args:
    x: PyTree of jax.Arrays which will have their shardings constrainted
    shardings: PyTree of sharding specifications. Valid values are the same as for
      the ``in_shardings`` argument of :func:`jax.experimental.pjit`.
  Returns:
    x_with_shardings: PyTree of jax.Arrays with specified sharding constraints.

  .. _Distributed arrays and automatic parallelization: https://jax.readthedocs.io/en/latest/notebooks/Distributed_arrays_and_automatic_parallelization.html
  """
  x_flat, tree = tree_flatten(x)
  user_shardings, _, _ = prepare_axis_resources(
      shardings, "shardings", allow_unconstrained_dims=True)
  del shardings

  user_shardings_flat = tuple(
      flatten_axes("with_sharding_constraint shardings", tree, user_shardings))
  del user_shardings

  resource_env = mesh_lib.thread_resources.env
  mesh = resource_env.physical_mesh

  shardings_flat = [_create_sharding_for_array(mesh, a, 'shardings',
                                               'with_sharding_constraint')
                    for a in user_shardings_flat]
  unconstrained_dims = [get_unconstrained_dims(s)
                        if isinstance(s, NamedSharding) else {}
                        for s in shardings_flat]
  del user_shardings_flat

  pjit_check_aval_sharding(
      shardings_flat, x_flat, None, "with_sharding_constraint arguments",
      allow_uneven_sharding=True)

  outs = [sharding_constraint_p.bind(xf, sharding=to_gspmd_sharding(i, xf.ndim),
                                     resource_env=resource_env,
                                     unconstrained_dims=ud)
          for xf, i, ud in zip(x_flat, shardings_flat, unconstrained_dims)]
  return tree_unflatten(tree, outs)

def _identity_fn(x): return x

def _sharding_constraint_impl(x, sharding, resource_env, unconstrained_dims):
  if hasattr(x, 'sharding') and x.sharding.is_equivalent_to(sharding, x.ndim):
    return x
  # Run a jit here to raise good errors when device assignment don't match.
  return api.jit(_identity_fn, out_shardings=sharding)(x)


sharding_constraint_p = core.Primitive("sharding_constraint")
sharding_constraint_p.def_impl(_sharding_constraint_impl)
sharding_constraint_p.def_abstract_eval(lambda x, **_: x)
ad.deflinear2(sharding_constraint_p,
              lambda ct, _, **params: (sharding_constraint_p.bind(ct, **params),))

def _sharding_constraint_hlo_lowering(ctx, x_node, *, sharding,
                                      resource_env, unconstrained_dims):
  aval, = ctx.avals_in
  out_aval, = ctx.avals_out
  axis_ctx = ctx.module_context.axis_context
  # axis_ctx and manual_axes is *only used with xmap* and xmap only works with
  # NamedSharding. So convert the GSPMDSharding to NamedSharding
  # and then convert it back with the added special axes.
  if isinstance(axis_ctx, sharding_impls.SPMDAxisContext):
    mesh = resource_env.physical_mesh
    parsed_pspec = parse_flatten_op_sharding(sharding._op_sharding, mesh)[0]
    mps = NamedSharding._from_parsed_pspec(mesh, parsed_pspec)
    sharding = GSPMDSharding(
        mps._device_assignment, mps._to_xla_op_sharding(aval.ndim, axis_ctx=axis_ctx))
  return [
      mlir.wrap_with_sharding_op(ctx,
          x_node, out_aval,
          sharding._to_xla_op_sharding(aval.ndim),
          unspecified_dims=unconstrained_dims)
  ]
mlir.register_lowering(sharding_constraint_p,
                       _sharding_constraint_hlo_lowering)


def _sharding_constraint_batcher(insert_axis, spmd_axis_name, axis_size,
                                 axis_name, main_type, vals_in, dims_in,
                                 sharding, resource_env, unconstrained_dims):
  x, = vals_in
  d, = dims_in
  # None means unconstrained in ParsedPartitionSpec
  new_parts = (axis_name,) if insert_axis else (
      None if spmd_axis_name is None else spmd_axis_name)
  unconstrained_dims = {ud + (d <= ud) for ud in unconstrained_dims}
  if new_parts is None:
    unconstrained_dims.add(d)
  y = sharding_constraint_p.bind(
      x,
      sharding=_pjit_batcher_for_sharding(
          sharding, d, new_parts, resource_env.physical_mesh, x.ndim),
      resource_env=resource_env,
      unconstrained_dims=unconstrained_dims)
  return y, d
batching.spmd_axis_primitive_batchers[sharding_constraint_p] = partial(
    _sharding_constraint_batcher, False)
batching.axis_primitive_batchers[sharding_constraint_p] = partial(
    _sharding_constraint_batcher, False, None)
pxla.spmd_primitive_batchers[sharding_constraint_p] = partial(
    _sharding_constraint_batcher, True, None)


def _resource_typing_sharding_constraint(avals, params, source_info,
                                         resource_env, named_axis_resources):
  aval, = avals
  if hasattr(params['sharding'], '_original_sharding'):
    parsed_pspec = params['sharding']._original_sharding._parsed_pspec
  else:
    parsed_pspec = parse_flatten_op_sharding(
        params['sharding']._op_sharding, resource_env.physical_mesh)[0]
  _check_resources_against_named_axes(
    "with_sharding_constraint input", aval, parsed_pspec, named_axis_resources)

pxla.custom_resource_typing_rules[sharding_constraint_p] = \
    _resource_typing_sharding_constraint

# -------------------- helpers --------------------

@lru_cache(maxsize=2048)
def to_gspmd_sharding(s: XLACompatibleSharding, ndim: int,
                      device_or_backend_set: bool = False) -> GSPMDSharding:
  if isinstance(s, GSPMDSharding):
    return s
  gs = GSPMDSharding(s._device_assignment, s._to_xla_op_sharding(ndim))
  gs._original_sharding = s
  if device_or_backend_set:
    gs._original_sharding._device_backend = device_or_backend_set
  return gs


def get_unconstrained_dims(sharding: NamedSharding):
  assert sharding._parsed_pspec is not None
  return {i for i, axes in enumerate(sharding._parsed_pspec)
          if axes is None}


def _fast_path_get_device_assignment(
    shardings: Iterable[PjitSharding]) -> Optional[XLADeviceAssignment]:
  da = None
  for i in shardings:
    if is_unspecified(i):
      continue
    if is_auto(i):
      return i.mesh._flat_devices_tuple  # type: ignore
    return i._device_assignment  # type: ignore
  return da


def _get_partition_spec(ppspec: Sequence[ParsedPartitionSpec]) -> Sequence[PartitionSpec]:
  return [get_single_pspec(p) for p in ppspec]


def _get_op_sharding_from_executable(
    executable) -> Tuple[Sequence[xc.OpSharding], Sequence[xc.OpSharding]]:
  in_op_shardings: List[xc.OpSharding] = []
  parameter_shardings_from_xla = executable.get_parameter_shardings()
  if parameter_shardings_from_xla is not None:
    in_op_shardings = parameter_shardings_from_xla

  out_op_shardings: List[xc.OpSharding] = []
  output_shardings_from_xla = executable.get_output_shardings()
  if output_shardings_from_xla is not None:
    out_op_shardings = output_shardings_from_xla

  return in_op_shardings, out_op_shardings


def _get_ppspec_from_executable(executable, mesh) -> Tuple[Sequence[ParsedPartitionSpec], Sequence[ParsedPartitionSpec]]:
  input_op_shardings: Sequence[xc.OpSharding] = executable.hlo_modules()[0].spmd_parameters_shardings
  output_op_sharding: xc.OpSharding = executable.hlo_modules()[0].spmd_output_sharding
  in_ppspec: List[ParsedPartitionSpec] = []
  for s in input_op_shardings:
    in_ppspec.extend(parse_flatten_op_sharding(s, mesh))
  out_ppspec = parse_flatten_op_sharding(output_op_sharding, mesh)
  return in_ppspec, out_ppspec


def _get_pspec_from_executable(
    executable, mesh: pxla.Mesh
) -> Tuple[Tuple[PartitionSpec, ...], Tuple[PartitionSpec, ...]]:
  in_ppspec, out_ppspec = _get_ppspec_from_executable(executable, mesh)
  out_partition_spec = _get_partition_spec(out_ppspec)
  in_partition_spec = _get_partition_spec(in_ppspec)
  return tuple(in_partition_spec), tuple(out_partition_spec)