# Copyright 2021 Google LLC
#
# 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 functools import partial
import operator as op
from typing import Callable, Optional, List, Tuple, Sequence, Set, Union, Any
import types

import jax
from jax import core
from jax import linear_util as lu
from jax.interpreters import ad
from jax.interpreters import batching
from jax.interpreters import partial_eval as pe
from jax.interpreters import mlir
from jax.tree_util import tree_flatten, tree_unflatten
from jax._src import ad_util
from jax._src import source_info_util
from jax._src import traceback_util
from jax._src.api_util import flatten_fun, shaped_abstractify
from jax._src.traceback_util import api_boundary
from jax._src.util import (unzip2, wraps, split_list, partition_list, safe_map,
                           safe_zip, merge_lists, weakref_lru_cache)

source_info_util.register_exclusion(__file__)
traceback_util.register_exclusion(__file__)

# TODO(mattjj): before this can be the standard remat implementation, we must:
#   [ ] fix up callers who use the 'concrete' option (now removed)

map = safe_map
zip = safe_zip


### Policies

def everything_saveable(*_, **__) -> bool:
  # This is the effective policy without any use of jax.remat.
  return True

def nothing_saveable(*_, **__) -> bool:
  # This is the effective policy when using jax.remat without explicit policy.
  return False

def checkpoint_dots(prim, *_, **__) -> bool:
  # Matrix multiplies are expensive, so let's save them (and nothing else).
  return prim in {jax._src.lax.lax.dot_general_p,
                  jax._src.lax.convolution.conv_general_dilated_p}

def dot_with_no_batch_dims(prim, *_, **params) -> bool:
  # This is a useful heuristic for transformers.
  if prim is jax._src.lax.lax.dot_general_p:
    (_, _), (lhs_b, rhs_b) = params['dimension_numbers']
    if not lhs_b and not rhs_b:
      return True
  return False

name_p = core.Primitive('name')

def save_any_names_but_these(*names_not_to_save):
  # Save named values, excluding the names given.
  names_not_to_save = frozenset(names_not_to_save)
  def policy(prim, *_, **params):
    if prim is name_p:
      return params['name'] not in names_not_to_save
    return False  # only allow saving named values
  return policy

def save_only_these_names(*names_which_can_be_saved):
  # Save named values, only among the names given.
  names_which_can_be_saved = set(names_which_can_be_saved)
  def policy(prim, *_, **params):
    if prim is name_p:
      return params['name'] in names_which_can_be_saved
    return False  # not saveable unless it's in the allow-list
  return policy

checkpoint_policies = types.SimpleNamespace(
    everything_saveable=everything_saveable,
    nothing_saveable=nothing_saveable,
    checkpoint_dots=checkpoint_dots,
    checkpoint_dots_with_no_batch_dims=dot_with_no_batch_dims,
    save_any_names_but_these=save_any_names_but_these,
    save_only_these_names=save_only_these_names,
)


### Main API

@api_boundary
def checkpoint(fun: Callable, *, prevent_cse: bool = True,
               policy: Optional[Callable[..., bool]] = None,
               static_argnums: Union[int, Tuple[int, ...]] = (),
               ) -> Callable:
  """Make ``fun`` recompute internal linearization points when differentiated.

  The :func:`jax.checkpoint` decorator, aliased to ``jax.remat``, provides a
  way to trade off computation time and memory cost in the context of automatic
  differentiation, especially with reverse-mode autodiff like :func:`jax.grad`
  and :func:`jax.vjp` but also with :func:`jax.linearize`.

  When differentiating a function in reverse-mode, by default all the
  linearization points (e.g. inputs to elementwise nonlinear primitive
  operations) are stored when evaluating the forward pass so that they can be
  reused on the backward pass. This evaluation strategy can lead to a high
  memory cost, or even to poor performance on hardware accelerators where memory
  access is much more expensive than FLOPs.

  An alternative evaluation strategy is for some of the linearization points to
  be recomputed (i.e. rematerialized) rather than stored. This approach can
  reduce memory usage at the cost of increased computation.

  This function decorator produces a new version of ``fun`` which follows
  the rematerialization strategy rather than the default store-everything
  strategy. That is, it returns a new version of ``fun`` which, when
  differentiated, doesn't store any of its intermediate linearization points.
  Instead, these linearization points are recomputed from the function's saved
  inputs.

  See the examples below.

  Args:
    fun: Function for which the autodiff evaluation strategy is to be changed
      from the default of storing all intermediate linearization points to
      recomputing them. Its arguments and return value should be arrays,
      scalars, or (nested) standard Python containers (tuple/list/dict) thereof.
    prevent_cse: Optional, boolean keyword-only argument indicating whether to
      prevent common subexpression elimination (CSE) optimizations in the HLO
      generated from differentiation. This CSE prevention has costs because it
      can foil other optimizations, and because it can incur high overheads on
      some backends, especially GPU. The default is True because otherwise,
      under a ``jit`` or ``pmap``, CSE can defeat the purpose of this decorator.
      But in some settings, like when used inside a ``scan``, this CSE
      prevention mechanism is unnecessary, in which case ``prevent_cse`` can be
      set to False.
    static_argnums: Optional, int or sequence of ints, a keyword-only argument
      indicating which argument values on which to specialize for tracing and
      caching purposes. Specifying arguments as static can avoid
      ConcretizationTypeErrors when tracing, but at the cost of more retracing
      overheads. See the example below.
    policy: Optional, callable keyword-only argument. It should be one of the
      attributes of ``jax.checkpoint_policies``. The callable takes as input a
      type-level specification of a first-order primitive application and
      returns a boolean indicating whether the corresponding output value(s) can
      be saved as residuals (or instead must be recomputed in the (co)tangent
      computation if needed).

  Returns:
    A function (callable) with the same input/output behavior as ``fun`` but
    which, when differentiated using e.g. :func:`jax.grad`, :func:`jax.vjp`, or
    :func:`jax.linearize`, recomputes rather than stores intermediate
    linearization points, thus potentially saving memory at the cost of extra
    computation.

  Here is a simple example:

  >>> import jax
  >>> import jax.numpy as jnp

  >>> @jax.checkpoint
  ... def g(x):
  ...   y = jnp.sin(x)
  ...   z = jnp.sin(y)
  ...   return z
  ...
  >>> jax.value_and_grad(g)(2.0)
  (DeviceArray(0.78907233, dtype=float32, weak_type=True), DeviceArray(-0.2556391, dtype=float32, weak_type=True))

  Here, the same value is produced whether or not the :func:`jax.checkpoint`
  decorator is present. When the decorator is not present, the values
  ``jnp.cos(2.0)`` and ``jnp.cos(jnp.sin(2.0))`` are computed on the forward
  pass and are stored for use in the backward pass, because they are needed
  on the backward pass and depend only on the primal inputs. When using
  :func:`jax.checkpoint`, the forward pass will compute only the primal outputs
  and only the primal inputs (``2.0``) will be stored for the backward pass.
  At that time, the value ``jnp.sin(2.0)`` is recomputed, along with the values
  ``jnp.cos(2.0)`` and ``jnp.cos(jnp.sin(2.0))``.

  While ``jax.checkpoint`` controls what values are stored from the forward-pass
  to be used on the backward pass, the total amount of memory required to
  evaluate a function or its VJP depends on many additional internal details of
  that function. Those details include which numerical primitives are used,
  how they're composed, where jit and control flow primitives like scan
  are used, and other factors.

  The :func:`jax.checkpoint` decorator can be applied recursively to express
  sophisticated autodiff rematerialization strategies. For example:

  >>> def recursive_checkpoint(funs):
  ...   if len(funs) == 1:
  ...     return funs[0]
  ...   elif len(funs) == 2:
  ...     f1, f2 = funs
  ...     return lambda x: f1(f2(x))
  ...   else:
  ...     f1 = recursive_checkpoint(funs[:len(funs)//2])
  ...     f2 = recursive_checkpoint(funs[len(funs)//2:])
  ...     return lambda x: f1(jax.checkpoint(f2)(x))
  ...

  If ``fun`` involves Python control flow that depends on argument values,
  it may be necessary to use the ``static_argnums`` parameter. For example,
  consider a boolean flag argument::

    from functools import partial

    @partial(jax.checkpoint, static_argnums=(1,))
    def foo(x, is_training):
      if is_training:
        ...
      else:
        ...

  Here, the use of ``static_argnums`` allows the ``if`` statement's condition
  to depends on the value of ``is_training``. The cost to using
  ``static_argnums`` is that it introduces re-tracing overheads across calls:
  in the example, ``foo`` is re-traced every time it is called with a new value
  of ``is_training``. In some situations, ``jax.ensure_compile_time_eval``
  is needed as well::

    @partial(jax.checkpoint, static_argnums=(1,))
    def foo(x, y):
      with jax.ensure_compile_time_eval():
        y_pos = y > 0
      if y_pos:
        ...
      else:
        ...

  As an alternative to using ``static_argnums`` (and
  ``jax.ensure_compile_time_eval``), it may be easier to compute some values
  outside the ``jax.checkpoint``-decorated function and then close over them.
  """
  @wraps(fun)
  @api_boundary
  def fun_remat(*args, **kwargs):
    fun_, args = _remat_static_argnums(fun, static_argnums, args)
    args_flat, in_tree = tree_flatten((args, kwargs))
    in_avals = [shaped_abstractify(x) for x in args_flat]
    jaxpr, consts, out_tree = _trace_to_jaxpr(fun_, in_tree, tuple(in_avals))
    out_flat = remat_p.bind(
        *consts, *args_flat, jaxpr=jaxpr, prevent_cse=prevent_cse,
        differentiated=False, policy=policy)
    return tree_unflatten(out_tree, out_flat)
  return fun_remat

remat = checkpoint  # alias

# This function is similar to api_util.argnums_partial, except the error
# messages are specific to jax.remat (and thus more actionable), the
# hashing/caching behavior is slightly different, and this function accepts a
# boolean for static_argnums. Perhaps the two could be de-duplicated.
def _remat_static_argnums(fun, static_argnums, args):
  if type(static_argnums) is int:
    static_argnums = (static_argnums,)
  elif not (type(static_argnums) is tuple and
            all(type(d) is int for d in static_argnums)):
    raise TypeError("the `static_argnums` argument to `jax.checkpoint` / "
                    "`jax.remat` must be an int, tuple of ints or, bool, but "
                    f"got value {static_argnums}")

  if not all(-len(args) <= d < len(args) for d in static_argnums):
    raise ValueError("the `static_argnums` argument to `jax.checkpoint` / "
                     "`jax.remat` can only take integer values greater than or "
                     "equal to `-len(args)` and less than `len(args)`, but got "
                     f"{static_argnums}")

  if not static_argnums:
    return fun, args
  nargs = len(args)
  static_argnums_ = frozenset(d % len(args) for d in static_argnums)
  dyn_args, static_args = [], []
  for i, x in enumerate(args):
    if i in static_argnums_: static_args.append(WrapHashably(x))
    else: dyn_args.append(x)
  new_fun = _dyn_args_fun(fun, static_argnums_, tuple(static_args), nargs)
  return new_fun, dyn_args

class WrapHashably:
  val: Any
  hash: Optional[int] = None
  hashable: bool

  def __init__(self, val):
    self.val = val
    try:
      self.hash = hash(val)
      self.hashable = True
    except:
      self.hash = id(val)
      self.hashable = False
  def __hash__(self):
    return self.hash
  def __eq__(self, other):
    if isinstance(other, WrapHashably):
      try: return self.val == other.val
      except: return self.val is other.val
    return False

# This caching is useful to avoid retracing even when static_argnums is used.
# See api_benchmark.py:bench_remat_eager_retracing_overheads_static_argnums.
# On that benchmark, including this caching makes a ~10x difference (which can
# be made arbitrary large by involving larger functions to be traced).
@weakref_lru_cache
def _dyn_args_fun(fun: Callable, static_argnums: Tuple[int, ...],
                  static_args: Tuple[WrapHashably, ...], nargs: int):
  def new_fun(*dyn_args, **kwargs):
    static_args_, dyn_args_ = iter(static_args), iter(dyn_args)
    full_args = [next(static_args_).val if i in static_argnums
                 else next(dyn_args_) for i in range(nargs)]
    return fun(*full_args, **kwargs)
  return new_fun

# This helper is similar to those in control_flow/common.py, but with
# remat-specific errors.
@weakref_lru_cache
def _trace_to_jaxpr(fun, in_tree, in_avals):
  debug = pe.debug_info(fun, in_tree, True, "checkpoint")
  flat_fun, out_tree = flatten_fun(lu.wrap_init(fun), in_tree)
  try:
    jaxpr, _, consts = pe.trace_to_jaxpr_dynamic(flat_fun, in_avals, debug)
  except core.ConcretizationTypeError as e:
    msg, = e.args
    if 'for checkpoint' not in msg:
      raise
    new_msg = msg + "\n\n" + (
        "Consider using the `static_argnums` parameter for `jax.remat` or "
        "`jax.checkpoint`. See the `jax.checkpoint` docstring and its example "
        "involving `static_argnums`:\n"
        "https://jax.readthedocs.io/en/latest/_autosummary/jax.checkpoint.html"
        "\n")
    new_e = core.ConcretizationTypeError.__new__(core.ConcretizationTypeError)
    new_e.args = (new_msg,)
    raise new_e from None
  return pe.convert_constvars_jaxpr(jaxpr), consts, out_tree()


### Utilities

def saved_residuals(f, *args, **kwargs) -> List[Tuple[core.AbstractValue, str]]:
  args, in_tree = tree_flatten((args, kwargs))

  def f_(*args):
    args, kwargs = tree_unflatten(in_tree, args)
    return f(*args, **kwargs)

  jaxpr = jax.make_jaxpr(lambda *args: jax.linearize(f_, *args)[1])(*args).jaxpr
  res_lits = [x for x in jaxpr.outvars if     isinstance(x, core.Literal)]
  res_vars = {x for x in jaxpr.outvars if not isinstance(x, core.Literal)}

  results = []

  for x in res_lits:
    results.append((x.aval, 'from a literal'))

  for v in jaxpr.constvars:
    if v in res_vars:
      results.append((v.aval, 'from a constant'))

  assert len(jaxpr.invars) == len(args)
  for i, v in enumerate(jaxpr.invars):
    if v in res_vars:
      src = f'from {pe.arg_info_pytree(f, in_tree, True, [i])}'
      results.append((v.aval, src))

  for eqn in jaxpr.eqns:
    src = source_info_util.summarize(eqn.source_info)
    for v in eqn.outvars:
      if v in res_vars:
        if eqn.primitive is name_p:
          results.append((v.aval, f"named '{eqn.params['name']}' from {src}"))
        else:
          results.append((v.aval, f'from {src}'))

  assert len(results) == len(jaxpr.outvars)
  return results

def print_saved_residuals(f, *args, **kwargs):
  for aval, src in saved_residuals(f, *args, **kwargs):
    print(f'{aval.str_short(short_dtypes=True)} {src}')


### Implementation

remat_p = core.Primitive('remat2')
remat_p.multiple_results = True

@remat_p.def_impl
def remat_impl(*args, jaxpr, prevent_cse, differentiated, policy):
  del prevent_cse, differentiated, policy  # Unused.
  return core.eval_jaxpr(jaxpr, (), *args)

@remat_p.def_effectful_abstract_eval
def remat_abstract_eval(*args, jaxpr, prevent_cse, differentiated, policy):
  del args, prevent_cse, differentiated, policy  # Unused.
  return [v.aval for v in jaxpr.outvars], jaxpr.effects

def remat_jvp(primals, tangents, jaxpr, prevent_cse, differentiated, policy):
  assert not jaxpr.constvars
  in_nonzeros = [type(t) is not ad_util.Zero for t in tangents]
  jaxpr_jvp_, out_nz = ad.jvp_jaxpr(pe.close_jaxpr(jaxpr), in_nonzeros, False)
  nonzero_tangents = [t for t in tangents if type(t) is not ad_util.Zero]
  jaxpr_jvp = pe.convert_constvars_jaxpr(jaxpr_jvp_.jaxpr)
  outs = remat_p.bind(
      *jaxpr_jvp_.consts, *primals, *nonzero_tangents, jaxpr=jaxpr_jvp,
      prevent_cse=prevent_cse, differentiated=differentiated, policy=policy)
  out_primals, out_tangents_ = split_list(outs, [len(jaxpr.outvars)])
  out_tangents_ = iter(out_tangents_)
  out_tangents = [next(out_tangents_) if nz else ad_util.Zero.from_value(p)
                  for p, nz in zip(out_primals, out_nz)]
  return out_primals, out_tangents
ad.primitive_jvps[remat_p] = remat_jvp

remat_allowed_effects: Set[core.Effect] = set()

def remat_partial_eval(trace, *tracers, jaxpr, **params):
  assert not jaxpr.constvars
  disallowed_effects = {eff for eff in jaxpr.effects
                        if eff not in remat_allowed_effects}
  if disallowed_effects:
    raise NotImplementedError(
        'Effects not supported in partial-eval of `checkpoint`/`remat`: '
        f'{disallowed_effects}')
  policy = params['policy'] or nothing_saveable
  in_unknowns = [not t.is_known() for t in tracers]
  jaxpr_known, jaxpr_staged, out_unknowns, out_inst, num_res = \
      pe.partial_eval_jaxpr_custom(
          jaxpr, in_unknowns, [True] * len(in_unknowns), False, False, policy)

  # DCE jaxpr_staged, keeping only instantiated outputs which are unknown
  _, out_inst_unknown = partition_list(out_inst, out_unknowns)
  jaxpr_unknown, in_used_staged = pe.dce_jaxpr(jaxpr_staged, out_inst_unknown)
  used_res, in_used_staged = split_list(in_used_staged, [num_res])

  # DCE jaxpr_known, keeping all known outputs but discarding dce'd res
  out_used_known = [True] * (len(out_unknowns) - sum(out_unknowns)) + used_res
  jaxpr_known, in_used_known = pe.dce_jaxpr(jaxpr_known, out_used_known)
  num_res = sum(used_res)

  # compute known outputs and residuals (hoisted out of remat primitive)
  _, in_consts_ = unzip2(t.pval for t in tracers if t.pval.is_known())
  _, in_consts = partition_list(in_used_known, in_consts_)
  out_consts = core.eval_jaxpr(jaxpr_known, (), *in_consts)
  out_knowns, residuals = split_list(out_consts, [len(out_consts)-num_res])

  # set up unknown outputs with a recipe to call remat
  res_tracers = map(trace.new_instantiated_const, residuals)
  _, tracers_staged = partition_list(in_used_staged, tracers)
  in_jaxpr_tracers = res_tracers + map(trace.instantiate_const, tracers_staged)
  out_jaxpr_tracers = [pe.JaxprTracer(trace, pe.PartialVal.unknown(x.aval), None)
                       for x in jaxpr_unknown.outvars]
  new_params = dict(params, jaxpr=jaxpr_unknown, differentiated=True)
  recipe = pe.new_eqn_recipe(in_jaxpr_tracers, out_jaxpr_tracers, remat_p,
                             new_params, jaxpr_unknown.effects,
                             source_info_util.current())
  for t in out_jaxpr_tracers: t.recipe = recipe

  # zip together known and unknown outputs
  return merge_lists(out_unknowns, out_knowns, out_jaxpr_tracers)
pe.custom_partial_eval_rules[remat_p] = remat_partial_eval

def remat_partial_eval_custom_params_updater(*args):
  *_, params_known, params_staged = args
  return params_known, dict(params_staged, differentiated=True)
pe.partial_eval_jaxpr_custom_rules[remat_p] = \
    partial(pe.call_partial_eval_custom_rule, 'jaxpr',
            remat_partial_eval_custom_params_updater)

def remat_transpose(reduce_axes, out_cts, *in_primals, jaxpr, **params):
  assert not jaxpr.constvars
  in_linear = [ad.is_undefined_primal(x) for x in in_primals]
  out_zeros = [type(ct) is ad_util.Zero for ct in out_cts]
  transposed_jaxpr_, in_zeros = transpose_jaxpr(
      pe.close_jaxpr(jaxpr), in_linear, out_zeros, reduce_axes)
  transposed_jaxpr, consts = transposed_jaxpr_.jaxpr, transposed_jaxpr_.consts
  transposed_jaxpr = pe.convert_constvars_jaxpr(transposed_jaxpr)
  args, _ = tree_flatten((in_primals, out_cts))
  in_cts_nz = remat_p.bind(*consts, *args, jaxpr=transposed_jaxpr, **params)
  in_cts_nz_, in_zeros_ = iter(in_cts_nz), iter(in_zeros)
  in_cts = [None if not ad.is_undefined_primal(x) else
            ad_util.Zero(x.aval) if next(in_zeros_) else next(in_cts_nz_)
            for x in in_primals]
  assert next(in_cts_nz_, None) is next(in_zeros_, None) is None
  return in_cts
ad.reducing_transposes[remat_p] = remat_transpose

# TODO(mattjj): move this to ad.py
def transpose_jaxpr(jaxpr: core.ClosedJaxpr, in_linear: Union[bool, Sequence[bool]],
                    out_zeros: Union[bool, Sequence[bool]],
                    reduce_axes: Sequence[core.AxisName],
                    ) -> Tuple[core.ClosedJaxpr, List[bool]]:
  if type(in_linear) is bool:
    in_linear = (in_linear,) * len(jaxpr.in_avals)
  if type(out_zeros) is bool:
    out_zeros = (out_zeros,) * len(jaxpr.out_avals)
  return _transpose_jaxpr(jaxpr, tuple(in_linear), tuple(out_zeros),
                          tuple(reduce_axes))

@weakref_lru_cache
def _transpose_jaxpr(jaxpr, in_lin, out_zeros, reduce_axes):
  in_avals = ([a for a,  lin in zip(jaxpr.in_avals,  in_lin   ) if not lin] +
              [a for a, zero in zip(jaxpr.out_avals, out_zeros) if not zero])
  cell = lambda: None

  @lu.wrap_init
  def transposed(*args_flat):
    ins_flat, out_cts_flat = split_list(args_flat, [len(in_lin) - sum(in_lin)])

    # Evaluate nonlinear parts using partial evaluation to get a linear jaxpr.
    ins_iter = iter(ins_flat)
    in_pvals = [pe.PartialVal.unknown(aval) if lin else
                pe.PartialVal.known(next(ins_iter))
                for aval, lin in zip(jaxpr.in_avals, in_lin)]
    assert next(ins_iter, None) is None
    lin_jaxpr, _, consts = pe.trace_to_jaxpr_nounits(
        lu.wrap_init(core.jaxpr_as_fun(jaxpr)), in_pvals, False)

    # Transpose the linear jaxpr (which only has linear inputs).
    out_cts_iter = iter(out_cts_flat)
    out_cts = [ad_util.Zero(aval) if zero else next(out_cts_iter)
               for aval, zero in zip(jaxpr.out_avals, out_zeros)]
    assert next(out_cts_iter, None) is None
    dummy_args = [ad.UndefinedPrimal(v.aval) for v in lin_jaxpr.invars]
    in_cts = ad.backward_pass(lin_jaxpr, reduce_axes, False, consts, dummy_args,
                              out_cts)

    # Identify symbolic zeros in the resulting cotangents, and return nonzeros.
    in_zeros = cell.in_cts_zero = [type(ct) is ad_util.Zero for ct in in_cts]
    in_cts_nz, _ = partition_list(in_zeros, in_cts)
    return in_cts_nz

  transposed_jaxpr_, _, consts = pe.trace_to_jaxpr_dynamic(transposed, in_avals)
  transposed_jaxpr = core.ClosedJaxpr(transposed_jaxpr_, consts)
  return transposed_jaxpr, cell.in_cts_zero  # type: ignore

def remat_vmap(axis_size, axis_name, main_type, args, dims, *, jaxpr, **params):
  assert not jaxpr.constvars
  jaxpr_batched_, out_batched = batching.batch_jaxpr_axes(
      pe.close_jaxpr(jaxpr), axis_size, dims,
      [batching.zero_if_mapped] * len(jaxpr.outvars),
      axis_name=axis_name, main_type=main_type)
  jaxpr_batched, consts = jaxpr_batched_.jaxpr, jaxpr_batched_.consts
  out_dims = [0 if b else None for b in out_batched]
  return remat_p.bind(*consts, *args, jaxpr=jaxpr_batched, **params), out_dims
batching.axis_primitive_batchers[remat_p] = remat_vmap

# TODO(mattjj,sharadmv): de-duplicate with pe.dce_jaxpr_call_rule
def remat_dce(used_outputs: List[bool], eqn: core.JaxprEqn
              ) -> Tuple[List[bool], Optional[core.JaxprEqn]]:
  new_jaxpr, used_inputs = pe.dce_jaxpr(eqn.params['jaxpr'], used_outputs)
  new_params = dict(eqn.params, jaxpr=new_jaxpr)
  if not any(used_inputs) and not any(used_outputs) and not new_jaxpr.effects:
    return used_inputs, None
  else:
    new_eqn = pe.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, new_jaxpr.effects, eqn.source_info)
    return used_inputs, new_eqn
pe.dce_rules[remat_p] = remat_dce


def checkpoint_name(x, name):
  return name_p.bind(x, name=name)

name_p.def_impl(lambda x, *, name: x)
name_p.def_abstract_eval(lambda x, *, name: x)

def name_jvp(primals, tangents, *, name):
  (x,), (xdot,) = primals, tangents
  return name_p.bind(x, name=name), xdot  # don't name the tangent value
ad.primitive_jvps[name_p] = name_jvp

mlir.register_lowering(name_p, lambda ctx, x, *, name: [x])

def name_batcher(args, dims, *, name):
  (x,), (d,) = args, dims
  return name_p.bind(x, name=name), d
batching.primitive_batchers[name_p] = name_batcher