code: # Copyright 2020 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.
  """Experimental module transforms JAX functions to be executed by TensorFlow."""
  from functools import partial
  import contextlib
  import os
  import re
  import threading
  from typing import Any, Callable, Dict, Iterable, List, Optional, Sequence, Tuple, Union
  
  import jax
  from jax import lax
  from jax import config
  from jax import core, custom_derivatives
  from jax import linear_util as lu
  from jax import random, tree_util
  from jax import numpy as jnp
  from jax.experimental import maps
  from jax.experimental import pjit
  from jax.interpreters import ad
  from jax.interpreters import partial_eval
  from jax.interpreters import pxla
  from jax.interpreters import xla
  
  import jax._src.prng
  import jax._src.random
  from jax._src import ad_checkpoint
  from jax._src import ad_util
  from jax._src import api
  from jax._src import api_util
  from jax._src import dispatch
  from jax._src import dtypes
  from jax._src import source_info_util
  from jax._src import util
  from jax._src.lax import control_flow as lax_control_flow
  from jax._src.lax import lax as lax_internal
  from jax._src.lax import linalg as lax_linalg
  from jax._src.lax import slicing as lax_slicing
  from jax._src.lax import windowed_reductions as lax_windowed_reductions
  from jax._src.lib import xla_client
  
  from jax.experimental.jax2tf import shape_poly
  from jax.experimental.jax2tf import impl_no_xla
  
  import numpy as np
  import tensorflow as tf  # type: ignore[import]
  
  # These don't have public equivalents.
  # pylint: disable=g-direct-tensorflow-import
  from tensorflow.compiler.tf2xla.python import xla as tfxla  # type: ignore[import]
  from tensorflow.compiler.xla import xla_data_pb2  # type: ignore[import]
  from tensorflow.core.framework import attr_value_pb2  # type: ignore[import]
  from tensorflow.compiler.xla.experimental.xla_sharding import xla_sharding  # type: ignore[import]
  from tensorflow.python.framework import ops as tf_ops  # type: ignore[import]
  # pylint: enable=g-direct-tensorflow-import
  
  PolyShape = shape_poly.PolyShape
  
  # A temporary internal flag, to enable the wrapping of jax.jit functions
  # with tf.function(jit_compile=True). See #7389. This change has triggered a
  # number of failures in TF. We keep this until we are confident that it does
  # not create problems.
  # TODO(b/207464757): figure out why this change breaks test
  _WRAP_JAX_JIT_WITH_TF_FUNCTION = False
  
  # The scope name need to be a valid TensorFlow name. See
  # https://github.com/tensorflow/tensorflow/blob/r2.3/tensorflow/core/framework/node_def_util.cc#L731
  _VALID_SCOPE_REGEX = re.compile("^[A-Za-z0-9.][A-Za-z0-9_.\\/>-]*$")
  _INVALID_SCOPE_CHAR = re.compile("[^A-Za-z0-9_.\\/>-]")
  
  map = util.safe_map
  zip = util.safe_zip
  
  
  def _sanitize_scope_name(name):
    scope_name = _INVALID_SCOPE_CHAR.sub("_", name)
    if not _VALID_SCOPE_REGEX.match(scope_name):
      scope_name = ".{}".format(scope_name)
    return scope_name
  
  
  # A value suitable in a TF tracing context: tf.Tensor, tf.Variable,
  # or Python scalar or numpy.ndarray. (A tf.EagerTensor is a tf.Tensor.)
  TfVal = Any
  DType = Any
  PrecisionType = int  # Enum xla_data.PrecisionConfig.Precision
  
  def _is_tfval(v: TfVal) -> bool:
    if isinstance(v, (tf.Tensor, tf.Variable)):
      return True
    try:
      # Include all convertible types, even if not supported on accelerators.
      with tf.device("CPU"):
        tf.constant(v)
      return True
    except:
      return False
  
  
  # The implementation rules for primitives. The rule will be called with the
  # arguments (TfVal) and must return TfVal (or a sequence thereof,
  # if primitive.multiple_results). The vast majority of primitives do not need
  # to worry about core.unit inputs or results. The exception are primarily the
  # control-flow primitives.
  tf_impl: Dict[core.Primitive, Callable[..., Any]] = {}
  
  # Some primitive implementation rules need the abstract values of arguments
  # and the results. This is the case for the primitives implemented using
  # _convert_jax_impl and those that need to adjust the shape of the outputs
  # due to missing TF shape inference rules for TFXLA ops. The rules for these
  # primitives should be added to `tf_impl_with_avals`.
  # The abstract value are passed to the implementation as two special kwargs
  # `_in_avals` (a tuple of core.ShapedArray) and `_out_aval` (a
  # core.ShapedArray, or a tuple thereof when primitive.multiple_results).
  tf_impl_with_avals: Dict[core.Primitive, Callable[..., Any]] = {}
  
  # XLA is not linked in all environments when converting a primitive. If this is
  # the case, we first search for implementation rules for primitives in the
  # following map. These implementations are workarounds, making use of TF ops
  # that do work when XLA is not linked in.
  tf_impl_no_xla = impl_no_xla.tf_impl_no_xla
  
  # In order to ensure that JAX picks up the proper user-frame for source
  # locations we will register the TensorFlow source path as an internal
  # path with source_info_util. The typical stack when a JAX primitive
  # conversion happens is:
  #    jax2tf.process_primitive  (top of stack)
  #    jax tracing machinery ...
  #    tf.custom_gradient machinery ...
  #    jax2tf.converted_fun
  #    tf function machinery ...
  #    user code invokes the converted function on TF tensors
  #
  # We need to skip over not only JAX internal frames, but TF internal frames
  # also.
  # We register the TensorFlow source path lazily
  _has_registered_tf_source_path = False
  
  class _ThreadLocalState(threading.local):
    def __init__(self):
      self.name_stack = ""
      # XLA is not linked in all environments; when converting a primitive, if this
      # variable is disabled, we try harder to use only standard TF ops if they are
      # applicable to the concrete use case; if the resulting conversion path ends up
      # requiring a TFXLA operation, an exception is thrown instead.
      self.enable_xla = True
  
      # Keep track if we are inside a call_tf. In that context we disable the
      # safety check that we are not inside JAX transformations.
      self.inside_call_tf = False
  
      # Maps dimension variables to TF expressions
      self.shape_env: Sequence[Tuple[str, TfVal]] = ()
  
      # Whether to actually include XLA op metadata in the generated TF ops
      # TODO(b/189306134): implement support for XLA metadata
      self.include_xla_op_metadata = False
  
      # A cache for the tf.convert_to_tensor for constants. We try to preserve
      # sharing for constants, to enable tf.Graph to take advantage of it.
      # See https://github.com/google/jax/issues/7992.
      self.constant_cache = None  # None means that we don't use a cache. We
      # may be outside a conversion scope.
  
  
  _thread_local_state = _ThreadLocalState()
  
  def _get_current_name_stack():
    return _thread_local_state.name_stack
  
  @contextlib.contextmanager
  def inside_call_tf():
    # Set the inside_call_tf flag for a context.
    prev = _thread_local_state.inside_call_tf
    _thread_local_state.inside_call_tf = True
    try:
      yield
    finally:
      _thread_local_state.inside_call_tf = prev
  
  @partial(api_util.api_hook, tag="jax2tf_convert")
  def convert(fun: Callable,
              *,
              polymorphic_shapes=None,
              with_gradient=True,
              enable_xla=True
              ) -> Callable:
    """Transforms `fun` to be executed by TensorFlow.
  
    See
    [README](https://github.com/google/jax/blob/main/jax/experimental/jax2tf/README.md)
    for more details about usage and common problems.
  
    Args:
      fun: Function to be transformed. Its arguments and return value should be
        JAX arrays, or nested standard Python containers (tuple/list/dict) thereof
        (pytrees).
      polymorphic_shapes: Specifies input shapes to be treated polymorphically
        during conversion.
  
        .. warning:: The shape-polymorphic conversion is an experimental feature.
          It is meant to be sound, but it is known to reject some JAX programs
          that are shape polymorphic. The details of this feature can change.
  
        It should be `None` (all arguments are monomorphic), a single PolyShape
        or string (applies to all arguments), or a tuple/list of the same length
        as the function arguments. For each argument the shape specification
        should be `None` (monomorphic argument), or a Python object with the
        same pytree structure as the argument.
        See [how optional parameters are matched to
        arguments](https://jax.readthedocs.io/en/latest/pytrees.html#applying-optional-parameters-to-pytrees).
  
        A shape specification for an array argument should be an object
        `PolyShape(dim0, dim1, ..., dimn)`
        where each `dim` is a dimension specification: a positive integer denoting
        a monomorphic dimension of the given size, or a string denoting a
        dimension variable assumed to range over non-zero dimension sizes, or
        the special placeholder string "_" denoting a monomorphic dimension
        whose size is given by the actual argument. As a shortcut, an Ellipsis
        suffix in the list of dimension specifications stands for a list of "_"
        placeholders.
  
        For convenience, a shape specification can also be given as a string
        representation, e.g.: "batch, ...", "batch, height, width, _", possibly
        with surrounding parentheses: "(batch, ...)".
  
        The conversion fails if it cannot ensure that the it would produce the same
        sequence of TF ops for any non-zero values of the dimension variables.
  
        polymorphic_shapes are only supported for positional arguments; shape
        polymorphism is not supported for keyword arguments.
  
        See [the README](https://github.com/google/jax/blob/main/jax/experimental/jax2tf/README.md#shape-polymorphic-conversion)
        for more details.
  
      in_shapes: DEPRECATED in favor of `polymorphic_shapes`.
      with_gradient: if set (default), add a tf.custom_gradient to the converted
        function, by converting the ``jax.vjp(fun)``. This means that reverse-mode
        TensorFlow AD is supported for the output TensorFlow function, and the
        value of the gradient will be JAX-accurate.
      enable_xla: if set (default), the converter will use the simplest conversion
        and use XLA TF ops when necessary. These ops are known to create issues
        for the TFLite and TFjs converters. For those cases, unset this parameter
        so the converter tries harder to use non-XLA TF ops to convert the
        function and aborts if this is not possible.
  
    Returns:
      A version of `fun` that expects TfVals as arguments (or
      tuple/lists/dicts) thereof, and returns TfVals as outputs, and uses
      only TensorFlow ops.
    """
    api._check_callable(fun)
    fun_name = getattr(fun, "__name__", "unknown")
    name_stack = util.wrap_name(fun_name, "jax2tf") + "/"
    def converted_fun(*args: TfVal, **kwargs: TfVal) -> TfVal:
      # TODO: is there a better way to check if we are inside a transformation?
      if not core.trace_state_clean() and not _thread_local_state.inside_call_tf:
        # It is Ok to nest convert when we are inside a call_tf
        raise ValueError("convert must be used outside all JAX transformations." +
                         f"Trace state: {core.thread_local_state.trace_state.trace_stack}")
  
      # We support kwargs by wrapping the function to take only positional arguments.
      # This is in part because jax.vjp does not support kwargs.
      nr_positional_args = len(args)
      kw_names = kwargs.keys()
      args = tuple(args) + tuple(kwargs[kw] for kw in kw_names)
  
      def fun_no_kwargs(*args_and_kwargs):
        assert len(args_and_kwargs) == nr_positional_args + len(kw_names)
        args = args_and_kwargs[:nr_positional_args]
        kwargs = {kw: args_and_kwargs[nr_positional_args + i]
                  for i, kw in enumerate(kw_names)}
        return fun(*args, **kwargs)
  
      def check_arg(a):
        if not _is_tfval(a):
          msg = (f"Argument {a} of type {type(a)} of jax2tf.convert(f) should "
                 "be NumPy array, scalar, tf.Variable, or tf.Tensor")
          raise TypeError(msg)
  
      tree_util.tree_map(check_arg, args)
  
      args_flat, in_tree = tree_util.tree_flatten((args, {}))
      # May need to cast the arguments to have the type assumed by JAX
      args_and_dtypes_flat = tuple(map(_tfval_to_tensor_jax_dtype, args_flat))
      args_flat, arg_dtypes_flat = util.unzip2(args_and_dtypes_flat)
      # Name input tensors; do this after we have cast the arguments
      def _apply_name(a: TfVal, suffix) -> TfVal:
        return tf.identity(a, f"jax2tf_arg_{suffix}")
      args_flat = tuple(_apply_name(a, i) for i, a in enumerate(args_flat))
  
      if polymorphic_shapes is None:
        polymorphic_shapes_ = (polymorphic_shapes,) * len(args)
      elif isinstance(polymorphic_shapes, (PolyShape, str)):
        polymorphic_shapes_ = (polymorphic_shapes,) * len(args)  # type: ignore
      else:
        if not isinstance(polymorphic_shapes, Sequence) or len(polymorphic_shapes) != len(args) - len(kw_names):
          msg = ("polymorphic_shapes must be a sequence with the same length as the positional argument list "
                 f"({len(args)}). Got polymorphic_shapes={repr(polymorphic_shapes)}.")
          raise TypeError(msg)
        polymorphic_shapes_ = tuple(polymorphic_shapes) + (None,) * len(kw_names)
  
      # Expand the polymorphic_shapes to match the argument pytree
      polymorphic_shapes_flat = tuple(api_util.flatten_axes("jax2tf.convert polymorphic_shapes",
                                                            in_tree.children()[0],
                                                            polymorphic_shapes_))
  
      def fix_tf1_shape(arg: TfVal) -> Sequence[Optional[int]]:
        tf_arg_shape = np.shape(arg)
        return tuple(d.value if isinstance(d, tf.compat.v1.Dimension) else d for d in tf_arg_shape)
      args_shapes_flat = tuple(fix_tf1_shape(a) for a in args_flat)
  
      # Construct the abstract values for the flat arguments, possibly based on
      # the input shapes and the polymorphic_shapes if given. May create new shape
      # variables. May cast the args_flat to JAX types, using JAX's interpretation
      # of types of constants.
      args_avals_flat = shape_poly.args_avals(
          args_shapes_flat, arg_dtypes_flat, polymorphic_shapes_flat)
  
      dim_vars, get_dim_values = shape_poly.prepare_dim_var_env(args_avals_flat)
      dim_values, _ = util.unzip2(_interpret_fun(lu.wrap_init(get_dim_values),
                                                 args_flat, args_avals_flat, ""))
      shape_env = zip(dim_vars, dim_values)
  
      # This function may take pytrees of TfVals. We can only set
      # tf.custom_gradient on functions that take a flat argument list.
      f = lu.wrap_init(fun_no_kwargs)
      # out_tree_thunk() will be the output tree, after running _interpret_fun.
      flat_fun, out_tree_thunk = api_util.flatten_fun(f, in_tree)
      # out_tree_thunk will be ready after _interpret_fun below.
  
      # Prepare the grad_fn for tf.custom_gradient.
      def converted_grad_fn(*out_cts_flat: TfVal,
                            _out_cts_avals: Sequence[core.ShapedArray],
                            variables=None):
        if variables:
          raise ValueError(
              "Unexpected variables used in forward pass. "
              "This should not happen for first-order differentiation. "
              f"variables={variables}")
  
        out_tree = out_tree_thunk()
        if polymorphic_shapes is None:
          vjp_polymorphic_shapes = None
        else:
          args_flat_polymorphic_shapes = polymorphic_shapes_flat
          out_cts_flat_polymorphic_shapes = tuple(str(out_aval.shape)  # Note: may be polynomials, not just DimVar
                                             for out_aval in _out_cts_avals)  # type: ignore
          vjp_polymorphic_shapes = [
              args_flat_polymorphic_shapes, out_cts_flat_polymorphic_shapes
          ]
  
        def fun_vjp_jax(args_flat_jax, out_cts_flat_jax):
          # One may think that we can get the pullback while we are converting
          # the main function in the first place. That is problematic, because the
          # pullback may contain captured tracers from the conversion of the
          # main function. Those tracers will confuse the conversion of the
          # pullback. So, we construct the vjp anew and we convert it separately.
          args_jax, kwargs_jax = tree_util.tree_unflatten(in_tree, args_flat_jax)
          assert not kwargs_jax
          _, pullback_jax = jax.vjp(fun_no_kwargs, *args_jax)
  
          def fix_out_ct(out_ct_jax, out_ct_aval: core.ShapedArray):
            # If the primal function has outputs of integer or bool types, and if we are
            # under a tf.function context, then TF will pass None in _out_cts_flat
            # in place of these values. We should change these to float0 or
            # else JAX gets unhappy. See issue #6975.
            if out_ct_jax is not None:
              return out_ct_jax
            assert core.primal_dtype_to_tangent_dtype(out_ct_aval.dtype) == dtypes.float0, f"out_ct={out_ct_jax}"
            # Note that out_ct_aval.shape contains dimension variable from the
            # primal function scope. It is Ok to use them here because we
            # use the same shape variables for the VJP function.
            return jnp.zeros(out_ct_aval.shape, dtype=_tf_np_dtype_for_float0)
  
          out_cts_fixed_flat = tuple(map(fix_out_ct, out_cts_flat_jax, _out_cts_avals))
  
          out_cts_fixed = tree_util.tree_unflatten(out_tree, out_cts_fixed_flat)
          in_cts_jax = pullback_jax(out_cts_fixed)
  
          in_cts_flat_jax, in_cts_tree = tree_util.tree_flatten(in_cts_jax)
          def fix_in_ct(in_ct, arg_aval: core.ShapedArray):
            if jnp.issubdtype(arg_aval.dtype, jnp.inexact):
              return in_ct
            else:
              assert in_ct.dtype == dtypes.float0
              return jnp.zeros(arg_aval.shape, _tf_np_dtype_for_float0)
  
          in_cts_fixed_flat_jax = tuple(map(fix_in_ct, in_cts_flat_jax, args_avals_flat))
          return in_cts_fixed_flat_jax
  
        # TODO: enable higher-order gradients
        with tf.name_scope("jax2tf_vjp"):
          in_cts_flat = convert(
              fun_vjp_jax,
              with_gradient=False,
              polymorphic_shapes=vjp_polymorphic_shapes)(args_flat, out_cts_flat)
        return in_cts_flat
  
      try:
        assert not _thread_local_state.shape_env, f"Unexpected shape environment {_thread_local_state.shape_env}"
  
        prev_enable_xla = _thread_local_state.enable_xla
        _thread_local_state.enable_xla = enable_xla
  
        prev_include_xla_op_metadata = _thread_local_state.include_xla_op_metadata
        # TODO(b/189306134): implement support for XLA metadata
        _thread_local_state.include_xla_op_metadata = False
  
        _thread_local_state.shape_env = shape_env
        global _has_registered_tf_source_path
        if not _has_registered_tf_source_path:
          source_info_util.register_exclusion(os.path.dirname(tf.__file__))
          _has_registered_tf_source_path = True
  
        if with_gradient:
  
          @tf.custom_gradient
          def converted_fun_flat_with_custom_gradient(*args_flat: TfVal) -> TfVal:
            out_with_avals = _interpret_fun(flat_fun, args_flat, args_avals_flat,
                                            name_stack,
                                            fresh_constant_cache=True)
            outs, out_avals = util.unzip2(out_with_avals)
            return (tuple(outs),
                    partial(converted_grad_fn, _out_cts_avals=tuple(out_avals)))
  
          out_flat = converted_fun_flat_with_custom_gradient(*args_flat)
        else:
          out_with_avals = _interpret_fun(flat_fun, args_flat, args_avals_flat,
                                          name_stack, fresh_constant_cache=True)
          outs, out_avals = util.unzip2(out_with_avals)
          message = ("The jax2tf-converted function does not support gradients. "
                     "Use `with_gradient` parameter to enable gradients")
          # We use PreventGradient, which is propagated through a SavedModel.
          out_flat = [
              tf.raw_ops.PreventGradient(input=o, message=message)
              for o in outs
          ]
      finally:
        _thread_local_state.shape_env = ()
        _thread_local_state.enable_xla = prev_enable_xla
        _thread_local_state.include_xla_op_metadata = prev_include_xla_op_metadata
  
      out_flat = [tf.identity(x, "jax2tf_out") for x in out_flat]
      out = tree_util.tree_unflatten(out_tree_thunk(), out_flat)
      return out
  
    return converted_fun
  
  
  def dtype_of_val(val: TfVal) -> DType:
    """Computes the TensorFlow dtype using JAX's typing rules.
  
    If the value is a tf.Tensor, it starts with its dtype. If the value is a
    constant it uses JAX to infer its dtype. The resulting dtype follows the
    JAX type inference rules, and depends on the value of the
    JAX_ENABLE_X64 flag.
  
    See README.md for how 64-bit values are treated.
    """
    tval, _ = _tfval_to_tensor_jax_dtype(val)
    return tval.dtype
  
  # Internals
  
  @contextlib.contextmanager
  def _extended_name_stack(extra_name_stack: Optional[str]):
    prev_name_stack = _thread_local_state.name_stack
    if extra_name_stack:
      if not prev_name_stack:
        _thread_local_state.name_stack = extra_name_stack
      else:
        _thread_local_state.name_stack = util.extend_name_stack(
            _thread_local_state.name_stack, extra_name_stack)
    try:
      yield
    finally:
      _thread_local_state.name_stack = prev_name_stack
  
  
  def _interpret_fun(
      fun: lu.WrappedFun, in_vals: Sequence[TfVal],
      in_avals: Sequence[core.ShapedArray],
      extra_name_stack: Optional[str],
      fresh_constant_cache: bool = False
  ) -> Sequence[Tuple[TfVal, core.ShapedArray]]:
    with core.new_base_main(TensorFlowTrace) as main:  # type: ignore
      fun = _interpret_subtrace(fun, main, in_avals)
      with _extended_name_stack(extra_name_stack):
        with core.new_sublevel():
          out_vals: Sequence[Tuple[TfVal, core.ShapedArray]] = \
              _call_wrapped_with_new_constant_cache(fun, in_vals,
                                                    fresh_constant_cache=fresh_constant_cache)
  
        del main
  
    return tuple(out_vals)
  
  def _call_wrapped_with_new_constant_cache(fun: lu.WrappedFun,
                                            in_vals: Sequence[TfVal],
                                            fresh_constant_cache: bool = False
                                            ) -> Sequence[Tuple[TfVal, core.ShapedArray]]:
    try:
      prev_constant_cache = _thread_local_state.constant_cache
      prev_constant_cache_keys = set(prev_constant_cache.keys()) if prev_constant_cache is not None else set()
      # Start a new cache, so that we don't share constants across tf.function
      # boundaries.
      if fresh_constant_cache:
        _thread_local_state.constant_cache = {}
  
      out_vals: Sequence[Tuple[TfVal, core.ShapedArray]] = \
          fun.call_wrapped(*in_vals)
    finally:
      if prev_constant_cache is not None and not fresh_constant_cache:
        newly_added_keys = set(prev_constant_cache.keys()) - prev_constant_cache_keys
        # Delete the newly added keys
        for k in newly_added_keys:
          del prev_constant_cache[k]
      _thread_local_state.constant_cache = prev_constant_cache
    return out_vals
  
  def _convert_jax_impl(jax_impl: Callable, *,
                        multiple_results=True,
                        extra_name_stack: Optional[str] = None) -> Callable:
    """Convert the JAX implementation of a primitive.
  
    Args:
      jax_impl: typically the impl-rule for a primitive, with signature
        `(*args: JaxVal, **kwargs) -> Sequence[JaxVal]`. This function implements
          a primitive in terms of other primitives.
      multiple_results: whether `jax_impl` returns a sequence of results.
      extra_name_stack: additional element to add to the name stack for the
        converted ops.
  
    Returns:
       a function with signature `(*args: TfVal, _in_avals, _out_aval, **kwargs)
       -> Sequence[TfVal]`.
    """
  
    def wrapped(*tf_args: TfVal, _in_avals: Sequence[core.ShapedArray],
                _out_aval: core.ShapedArray,
                **kwargs) -> Sequence[TfVal]:
  
      # We wrap the jax_impl under _interpret_fun to abstract the TF values
      # from jax_impl and turn them into JAX abstract values.
      def jax_impl_jax_args(*jax_args):
        jax_results = jax_impl(*jax_args, **kwargs)
        return jax_results if multiple_results else [jax_results]
  
      tf_results_with_avals = _interpret_fun(
          lu.wrap_init(jax_impl_jax_args), tf_args, _in_avals,
          extra_name_stack)
      tf_results, _ = util.unzip2(tf_results_with_avals)
      return tf_results if multiple_results else tf_results[0]
  
    return wrapped
  
  
  @lu.transformation
  def _interpret_subtrace(main: core.MainTrace,
                          in_avals: Sequence[core.ShapedArray],
                          *in_vals: TfVal):
    trace = TensorFlowTrace(main, core.cur_sublevel())
    in_tracers = tuple(
        TensorFlowTracer(trace, val, aval)
        for val, aval in zip(in_vals, in_avals))
    # The outs may be core.unit, see comment in TensorFlowTrace.pure.
    outs = yield in_tracers, {}  # type: Sequence[Union[TfVal, core.Unit]]
    out_tracers: Iterable[TensorFlowTracer] = (
        map(trace.full_raise, outs))  # type: ignore
    out_vals_with_avals: Sequence[Tuple[TfVal, core.ShapedArray]] = (
        tuple((t.val, t.aval) for t in out_tracers))
    yield out_vals_with_avals
  
  
  def _interpret_jaxpr(jaxpr: core.ClosedJaxpr, *args: TfVal,
                       extra_name_stack: Optional[str]) -> Sequence[TfVal]:
    """Evaluates a Jaxpr with tf.Tensor arguments.
  
    The output is a sequence of TfVal (no `core.unit`), suitable for use with TF.
    """
    fun: lu.WrappedFun = lu.wrap_init(core.jaxpr_as_fun(jaxpr))
    out_with_avals = _interpret_fun(fun, args, jaxpr.in_avals, extra_name_stack)
    return tuple(v for v, _ in out_with_avals)
  
  
  def _aval_to_tf_shape(aval: core.ShapedArray) -> Tuple[Optional[int], ...]:
    """Generate a TF shape, possibly containing None for polymorphic dimensions."""
    return tuple(map(lambda d: None if shape_poly.is_poly_dim(d) else d,
                     aval.shape))  # type: ignore[attr-defined]
  
  # In the TF world, we represent float0 as zeros of this type.
  _tf_np_dtype_for_float0 = np.int32
  
  def _to_tf_dtype(jax_dtype):
    # Note that converting _to_tf_dtype and _to_jax_dtype are not inverses,
    # due to float0 and 64-bit behavior.
    if jax_dtype == dtypes.float0:
      jax_dtype = _tf_np_dtype_for_float0
    return tf.dtypes.as_dtype(jax_dtype)
  
  
  def _to_jax_dtype(tf_dtype):
    # Note that converting _to_tf_dtype and _to_jax_dtype are not inverses,
    # due to float0 and 64-bit behavior.
    return dtypes.canonicalize_dtype(tf_dtype.as_numpy_dtype)
  
  
  def _tfval_to_tensor_jax_dtype(val: TfVal,
                                 jax_dtype: Optional[DType] = None,
                                 memoize_constants=False) -> Tuple[TfVal, DType]:
    """Converts a scalar, ndarray, or tf.Tensor to a tf.Tensor with proper type.
  
    If `jax_dtype` is missing, uses JAX typing rules.
    See README.md for details regarding 64-bit values.
  
    Args:
      val: a scalar, ndarray, tf.Tensor, or tf.Variable
      jax_dtype: an optional dtype to use. If missing, uses JAX type inference
        rules for constants.
      memoize_constants: whether to memoize TF constants. We can't do this
        everywhere, we may be outside of a conversion scope.
  
    Returns:
      a tuple with a tf.Tensor with the type as needed by JAX, and the JAX type.
    """
    if isinstance(val, (tf.Tensor, tf.Variable)):
      jax_dtype = jax_dtype or _to_jax_dtype(val.dtype)  # Give JAX a chance to pick the type
      conversion_dtype = _to_tf_dtype(jax_dtype)
      if conversion_dtype != val.dtype:
        return tf.cast(val, conversion_dtype), jax_dtype
      else:
        return val, jax_dtype
    else:  # A constant
      jax_dtype = jax_dtype or xla.abstractify(val).dtype
      # TODO(document): We assume that the value of a constant does not
      # change through the scope of the function. But it may be an ndarray, ...
      # JAX has the same problem when generating HLO.
      const_key = (id(val), jax_dtype)
      # Since we use id(val) as a cache key, we have to make sure that we keep
      # the previous `val` alive. Otherwise, for an ndarray, it can get garbage
      # collected and reused for a different value, which would create correctness
      # issues. We keep the `val` alive by storing in the cache the pair
      # `(val, tf_val)`.
      do_memoize = (memoize_constants and np.shape(val) and _thread_local_state.constant_cache is not None)
      if do_memoize:
        _, tf_val = _thread_local_state.constant_cache.get(const_key, (None, None))
      else:
        tf_val = None
      if tf_val is None:
        conversion_dtype = _to_tf_dtype(jax_dtype)
        # The float0 type is not known to TF.
        if jax_dtype == dtypes.float0:
          val = np.zeros(np.shape(val), conversion_dtype.as_numpy_dtype)
        tf_val = tf.convert_to_tensor(val, dtype=conversion_dtype)
        if do_memoize:
          _thread_local_state.constant_cache[const_key] = (val, tf_val)
      return tf_val, jax_dtype
  
  
  def _eval_shape(shape: Sequence[shape_poly.DimSize]) -> Sequence[TfVal]:
    assert all(map(lambda x: x is not None, shape)), (
        f"Argument shape should be a valid JAX shape but got {shape}")
    dim_vars, dim_values = util.unzip2(_thread_local_state.shape_env)
    eval_shape, dim_avals = shape_poly.get_shape_evaluator(dim_vars, shape)
    shape_values, _ = util.unzip2(_interpret_fun(lu.wrap_init(eval_shape),
                                                 dim_values, dim_avals, ""))  # type: ignore
    return shape_values
  
  
  # TODO(b/26854495): pylint doesn't understand slots and inheritance.
  # pylint: disable=assigning-non-slot
  
  
  class TensorFlowTracer(core.Tracer):
    """Tracer class that boxes a TF value and a JAX abstract value.
  
    In addition to the TF value we carry the JAX abstract value because there are
    two cases when it cannot be recovered from the value: (a) when the abstract
    value is core.abstract_unit, in which case the value is tf.nan; (b) when we
    are converting with polymorphic shapes, in which case the shape of the value
    may have dimensions set to `None`, which the JAX abstract value may contain
    more precise information.
  
    When the value has a partially-known shape, the dimensions marked as `None`
    must correspond to non-constant dimensions in the abstract value.
  
    See README.md for details.
    """
    # val: TfVal
    # _aval: core.ShapedArray
    __slots__ = ["val", "_aval"]
  
    def __init__(self, trace: "TensorFlowTrace", val: TfVal,
                 aval: core.AbstractValue):
      self._trace = trace
      self._aval = aval
      if aval is core.abstract_unit:
        self.val = val
        return
  
      if isinstance(val, (tf.Tensor, tf.Variable)):
        val_shape = val.shape
  
        if config.jax_enable_checks:
          assert len(self._aval.shape) == len(val_shape), f"_aval.shape={self._aval.shape} different rank than val_shape={val_shape}"
          # To compare types, we must handle float0 in JAX and x64 in TF
          if self._aval.dtype == dtypes.float0:
            assert _to_tf_dtype(self._aval.dtype) == val.dtype, f"expected {self._aval.dtype} == {val.dtype}"
          else:
            assert self._aval.dtype == _to_jax_dtype(val.dtype), f"expected {self._aval.dtype} == {val.dtype}"
  
          for aval_dim, val_dim in zip(self._aval.shape, val_shape):  # type: ignore[attr-defined]
            if val_dim is None:
              assert shape_poly.is_poly_dim(aval_dim), f"expected {self._aval.shape} == {val_shape}"  # type: ignore[attr-defined]
            elif not shape_poly.is_poly_dim(aval_dim):
              assert aval_dim == val_dim, f"expected {self._aval.shape} == {val_shape}"  # type: ignore[attr-defined]
            else:
              # We have a TF value with known shape, and the abstract shape is a shape variable.
              try:
                aval_int = int(_eval_shape([aval_dim]))  # type: ignore
              except (TypeError, KeyError):
                continue
              assert aval_int == val_dim, f"expected {self._aval.shape} == {val_shape}. Found {aval_int} != {val_dim}."  # type: ignore
  
      self.val = _tfval_to_tensor_jax_dtype(val,
                                            self._aval.dtype,
                                            memoize_constants=True)[0]  # type: ignore[attr-defined]
  
    @property
    def aval(self):
      return self._aval
  
    def full_lower(self):
      return self
  
  
  class TensorFlowTrace(core.Trace):
    """Trace class that underlies the jax2tf transformation.
  
    We are going to ensure that jax2tf.convert is never nested inside other
    transformations. This is sufficient for intended use cases (converting
    fully-transformed JAX code). It also simplifies our job because we do not have
    to handle situations where we apply primitives on a mix of TF values and
    JAX tracers from an outer transformation. E.g., for addition both the TF
    values
    and the JAX tracers have an override and they get confused if they see values
    from the other world.
  
    Hence a TFT trace does not interact with non-TFT traces at lower-level. For
    higher-order control-flow primitives we invoke recursively
    _interpret_fun on the body of the conditional, which will create a nested TFT.
  
    We do want to allow transformations nested inside a TensorFlowTrace (TFT), but
    those will introduce their own MainTrace, and any operations involving those
    will be done on those traces, i.e., not a concern for TFT.
    """
    def pure(self, val: Union[TfVal, core.Unit]) -> TensorFlowTracer:
      """Lifts a non-Tracer into the TensorFlowTracer.
  
      This function may be called by way of trace.full_raise.
  
      The value may be a core.unit. During JAX transformations we sometimes
      produce a Jaxpr that has arguments of abstract value core.abstract_unit
      and results equal to core.unit. These are arguments and results that are
      not used in the computation.
  
      In TF world, we represent core.unit as NaN. This is safe, as these values
      should never be used.
      """
      if val is core.unit:
        return TensorFlowTracer(self, tf.constant(np.nan, tf.float32),
                                core.abstract_unit)
      else:
        tf_val, jax_dtype = _tfval_to_tensor_jax_dtype(val, memoize_constants=True)
        return TensorFlowTracer(
          self, val, core.ShapedArray(tf_val.shape, jax_dtype,
                                      weak_type=dtypes.is_weakly_typed(val)))
  
    def lift(self, val: core.Tracer) -> TensorFlowTracer:
      # This would be called when we need to raise a tracer from a lower-level
      # main into the TensorFlowTrace. Since the TensorFlowTrace is never nested
      # inside another transform, there are no lower-level main traces.
      assert False
  
    def sublift(self, val: TensorFlowTracer) -> TensorFlowTracer:
      # This is called when we need to raise a tracer from the same main,
      # but a lower sublevel. This could come from a nested jit.
      return TensorFlowTracer(self, val.val, val._aval)
  
    def process_primitive(self, primitive: core.Primitive,
                          tracers: Sequence[TensorFlowTracer],
                          params) -> TensorFlowTracer:
      impl, impl_needs_avals = self.get_primitive_impl(primitive)
      args_avals: Sequence[core.ShapedArray] = tuple(t.aval for t in tracers)
      # This is a bit conservative, doing abstract_eval even in op-by-op execution
      # but we needed it for, e.g., shape_polymorphism where only JAX's
      # abstract evaluation rules can properly track polymorphic shapes.
      # Unfortunately under op-by-op execution this is a rare occasion where we
      # need abstract evaluation.
      out_aval = primitive.abstract_eval(*args_avals, **params)
      args_tf: Sequence[TfVal] = [t.val for t in tracers]
      def invoke_impl() -> TfVal:
        if impl_needs_avals:
          return impl(
              *args_tf,
              _in_avals=args_avals,  # type: ignore
              _out_aval=out_aval,
              **params)
        else:
          return impl(*args_tf, **params)
  
      if _thread_local_state.include_xla_op_metadata:
        op_metadata = xla.make_op_metadata(primitive, params,
                                           name_stack=_get_current_name_stack(),
                                           source_info=source_info_util.current())
        op_metadata_proto = xla_data_pb2.OpMetadata(
            op_type=op_metadata.op_type,
            op_name=op_metadata.op_name,
            source_file=op_metadata.source_file,
            source_line=op_metadata.source_line
        )
        with tf_ops.get_default_graph()._attr_scope(
            {"_XlaOpMetadata": attr_value_pb2.AttrValue(
                s=op_metadata_proto.SerializeToString())}):
          val_out = invoke_impl()
      else:
        val_out = invoke_impl()
  
      if primitive.multiple_results:
        out = [
            TensorFlowTracer(self, v, a)
            for v, a in zip(val_out, out_aval)
        ]  # type: ignore
      else:
        out = TensorFlowTracer(self, val_out, out_aval)  # type: ignore
  
      # Check that the impl rule returned a value of expected shape and dtype
      # TODO: adapt this to match polymorphic shapes
      if config.jax_enable_checks:
        if primitive.multiple_results:
          for o, expected_aval in zip(out, out_aval):  # type: ignore
            assert o.aval.strip_weak_type() == expected_aval.strip_weak_type(), (
                f"{primitive}: out.aval = {o.aval}; expected {expected_aval}")
        else:
          assert out.aval == out_aval, (  # type: ignore
              f"{primitive}: out.aval = {out.aval}; expected {out_aval}"
          )  # type: ignore
      return out  # type: ignore
  
    def process_call(self, call_primitive: core.Primitive, fun: lu.WrappedFun,
                     tracers: Sequence[TensorFlowTracer], params):
      assert call_primitive.multiple_results
      vals: Sequence[TfVal] = [t.val for t in tracers]
      avals: Sequence[core.ShapedArray] = tuple(t.aval for t in tracers)
      interpreted_fun = _interpret_subtrace(fun, self.main, avals)
      extra_name_stack = None
      if call_primitive == core.named_call_p:
        extra_name_stack = util.wrap_name(params["name"], "named")
      elif call_primitive == xla.xla_call_p:
        extra_name_stack = util.wrap_name(params["name"], "jit")
      with _extended_name_stack(extra_name_stack):
        with core.new_sublevel():
          if call_primitive == core.named_call_p:
            with tf.name_scope(_sanitize_scope_name(params["name"])):
              vals_out: Sequence[Tuple[TfVal, core.ShapedArray]] = \
                  interpreted_fun.call_wrapped(*vals)
          elif call_primitive == xla.xla_call_p:
            if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
              # Make a nested tf.function(jit_compile=True)
              store_tf_res_avals = None
              def f_tf(*tf_args):
                nonlocal store_tf_res_avals
                tf_res_out: Sequence[Tuple[TfVal, core.ShapedArray]] = \
                  _call_wrapped_with_new_constant_cache(interpreted_fun, tf_args,
                                                        fresh_constant_cache=False)
                tf_res_vals, tf_res_avals = util.unzip2(tf_res_out)
                store_tf_res_avals = tf_res_avals
                return tf_res_vals
              tf_vals_out = tf.function(f_tf, autograph=False, jit_compile=True)(*vals)
              vals_out = zip(tf_vals_out, store_tf_res_avals)
            else:
              vals_out = interpreted_fun.call_wrapped(*vals)
          else:
            vals_out = interpreted_fun.call_wrapped(*vals)
      return [TensorFlowTracer(self, v, a) for v, a in vals_out]
  
    def post_process_call(self, call_primitive: core.Primitive,
                          out_tracers: Sequence[TensorFlowTracer], params):
      # We encountered a call primitive, e.g., remat_call_p, whose result
      # (out_tracers) include TensorFlowTracer that were not passed through
      # its arguments (captured from the environment).
      vals = tuple(t.val for t in out_tracers)
      main = self.main
  
      def todo(vals: Sequence[TfVal]):
        # TODO: is name_stack correct?
        trace = TensorFlowTrace(main, core.cur_sublevel())
        return [
            TensorFlowTracer(trace, v, out_tracer.aval)
            for v, out_tracer in zip(vals, out_tracers)
        ]
  
      return vals, todo
  
    def process_map(self, map_primitive, f, tracers, params):
      raise NotImplementedError("process_map")
  
    def post_process_map(self, map_primitive, out_tracers, params):
      raise NotImplementedError("post_process_map")
  
    def process_custom_jvp_call(self, prim, fun, jvp, tracers):
      # Drop the custom differentiation rule and act like a call primitive. This
      # behavior is desirable because jax2tf stages code out of the JAX system, so
      # there are no more JAX differentiation transformations to be applied.
      del jvp  # Unused.
      return self.process_call(core.call_p, fun, tracers, {})
  
    def post_process_custom_jvp_call(self, out_tracers, _):
      assert False  # unreachable assuming jax2tf runs with clean trace state
  
    def process_custom_vjp_call(self, prim, fun, fwd, bwd, tracers, out_trees):
      # Drop the custom differentiation rule and act like a call primitive. This
      # behavior is desirable because jax2tf stages code out of the JAX system, so
      # there are no more JAX differentiation transformations to be applied.
      del fwd, bwd, out_trees  # Unused.
      return self.process_call(core.call_p, fun, tracers, {})
  
    def post_process_custom_vjp_call(self, out_tracers, _):
      assert False  # unreachable assuming jax2tf runs with clean trace state
  
    def post_process_custom_vjp_call_fwd(self, *_, **__):
      assert False  # unreachable assuming jax2tf runs with clean trace state
  
    def get_primitive_impl(self, p: core.Primitive) -> Tuple[Callable, bool]:
      # Returns the primitive implementation and whether the implementation
      # takes abstract values (see definition of tf_impl_with_avals)
      if not _thread_local_state.enable_xla:
        try:
          return tf_impl_no_xla[p], True  # Always require avals.
        except KeyError:
          pass
      try:
        return tf_impl[p], False
      except KeyError:
        try:
          return tf_impl_with_avals[p], True
        except KeyError as err:
          msg = "TensorFlow interpretation rule for '{}' not implemented"
          raise NotImplementedError(msg.format(p)) from err
  
  def _unexpected_primitive(p: core.Primitive, *args, **kwargs):
    assert False, f"Encountered unexpected primitive {p}"
  
  
  # Call primitives are inlined
  for unexpected in [core.call_p, core.named_call_p, xla.xla_call_p,
                     partial_eval.remat_call_p, maps.xmap_p]:
    tf_impl[unexpected] = partial(_unexpected_primitive, unexpected)
  
  # Primitives that are not yet implemented must be explicitly declared here.
  tf_not_yet_impl = [
      "clz",
      "igamma_grad_a",
      "random_gamma_grad",
      "reduce_precision",
      "schur",
      "name",
      "optimization_barrier",
      "unreachable",
  
      # Not high priority?
      "after_all",
      "all_to_all",
      "approx_top_k",
      "create_token",
      "custom_transpose_call",
      "custom_vmap_call",
      "infeed",
      "linear_call",
      "outfeed",
      "pmax_p",
      "pmin",
      "ppermute",
      "psum",
      "pmax",
      "pgather",
      "reduce_scatter",
      "axis_index",
      "pdot",
      "all_gather",
      "lu_pivots_to_permutation",
      "xla_pmap",
  ]
  
  tf_impl[ad_util.stop_gradient_p] = tf.stop_gradient
  tf_impl[ad_util.zeros_like_p] = tf.zeros_like
  
  
  def _add(x: TfVal, y: TfVal) -> TfVal:
    return tf.raw_ops.AddV2(x=x, y=y)
  
  
  tf_impl[ad_util.add_jaxvals_p] = _add
  tf_impl[dispatch.device_put_p] = lambda x, device=None: x
  tf_impl[lax_internal.copy_p] = lambda x: x
  
  def _neg(x: TfVal) -> TfVal:
    if x.dtype.is_unsigned:
      signed_dtype = _UNSIGNED_TO_SIGNED_TABLE[x.dtype]
      x_signed = tf.cast(x, signed_dtype)
      res_signed = tf.math.negative(x_signed)
      return tf.cast(res_signed, x.dtype)
    else:
      return tf.math.negative(x)
  
  tf_impl[lax.neg_p] = _neg
  
  
  def _sign(x: TfVal) -> TfVal:
    if x.dtype.is_unsigned:
      # TF and XLA do not support tf.math.sign for unsigned types.
      return tf.where(
          tf.math.equal(x, 0), tf.constant(0, dtype=x.dtype),
          tf.constant(1, dtype=x.dtype))
    else:
      return tf.math.sign(x)
  
  
  tf_impl[lax.sign_p] = _sign
  tf_impl[lax.floor_p] = tf.math.floor
  tf_impl[lax.ceil_p] = tf.math.ceil
  
  
  def _round(operand, *, rounding_method,
             _in_avals: Sequence[core.ShapedArray],
             _out_aval: core.ShapedArray):
    if rounding_method is lax.RoundingMethod.AWAY_FROM_ZERO:
      # JAX uses a single HLO op Round here
      sign = _sign(operand)
      operand *= sign
      floor = tf.math.floor(operand)
      operand -= floor
      cond = tf.math.equal(operand, tf.constant(np.array(0.5), operand.dtype))
      return sign * (
          tf.where(cond, tf.constant(np.array(1), operand.dtype),
                   tf.math.round(operand)) + floor)
    else:  # rounding_method is RoundingMethod.TO_NEAREST_EVEN
      rounding_fun = _convert_jax_impl(
          lax_internal._round_to_nearest_even, multiple_results=False)
      return rounding_fun(operand, _in_avals=_in_avals, _out_aval=_out_aval)
  
  tf_impl_with_avals[lax.round_p] = _round
  tf_impl[lax.nextafter_p] = tf.math.nextafter
  
  
  def _population_count(x):
    orig_dtype = x.dtype
    return tf.cast(tf.raw_ops.PopulationCount(x=x), orig_dtype)
  
  
  tf_impl[lax.population_count_p] = _population_count
  tf_impl[lax.is_finite_p] = tf.math.is_finite
  
  
  def _abs(x: TfVal) -> TfVal:
    # TF and XLA do not support tf.math.abs for unsigned types.
    return tf.math.abs(x) if not x.dtype.is_unsigned else x
  
  
  tf_impl[lax.abs_p] = _abs
  tf_impl[lax.pow_p] = tf.math.pow
  
  
  def _integer_pow(x, *, y: int, _in_avals: Sequence[core.ShapedArray],
                   _out_aval: core.ShapedArray):
    # Follows the implementation in lax._integer_pow_translation_rule
    if y == 0:
      return tf.broadcast_to(
          tf.constant(1, dtype=x.dtype, shape=()), _eval_shape(_out_aval.shape))
    is_reciprocal = y < 0
    if is_reciprocal:
      y = -y
    acc = None
    while y > 0:
      if y & 1:
        acc = x if acc is None else tf.math.multiply(acc, x)
      y >>= 1
      if y > 0:
        x = tf.math.multiply(x, x)
    return tf.math.reciprocal(acc) if is_reciprocal else acc
  
  
  tf_impl_with_avals[lax.integer_pow_p] = _integer_pow
  tf_impl[lax.exp_p] = tf.math.exp
  tf_impl[lax.expm1_p] = tf.math.expm1
  tf_impl[lax.log_p] = tf.math.log
  tf_impl[lax.log1p_p] = tf.math.log1p
  tf_impl[lax.tan_p] = tf.math.tan
  tf_impl[lax.tanh_p] = tf.math.tanh
  tf_impl[lax.sin_p] = tf.math.sin
  tf_impl[lax.sinh_p] = tf.math.sinh
  tf_impl[lax.cos_p] = tf.math.cos
  tf_impl[lax.cosh_p] = tf.math.cosh
  tf_impl_with_avals[lax.acos_p] = _convert_jax_impl(
      lax_internal.acos_impl, multiple_results=False)
  tf_impl_with_avals[lax.asin_p] = _convert_jax_impl(
      lax_internal.asin_impl, multiple_results=False)
  tf_impl_with_avals[lax.atan_p] = _convert_jax_impl(
      lax_internal.atan_impl, multiple_results=False)
  
  def _atan2(y, x, **kwargs):
    if x.dtype.is_complex or y.dtype.is_complex:
      complex_component_dtype = {
        tf.complex64: tf.float32,
        tf.complex128: tf.float64
      }.get(y.dtype)
      zero = tf.constant(0, complex_component_dtype)
      one = tf.constant(1, complex_component_dtype)
      i = tf.complex(zero, one)
      return -i * tf.math.log((x + i * y)/tf.math.sqrt(x * x + y * y))
    else:
      return tf.math.atan2(y, x)
  
  
  tf_impl[lax.atan2_p] = _atan2
  tf_impl[lax.acosh_p] = tf.math.acosh
  tf_impl[lax.atanh_p] = tf.math.atanh
  tf_impl[lax.asinh_p] = tf.math.asinh
  
  tf_impl[lax.sqrt_p] = tf.math.sqrt
  tf_impl[lax.rsqrt_p] = tf.math.rsqrt
  
  def _cbrt(x):
    return tf.math.sign(x) * tf.math.pow(tf.math.abs(x), 1/3)
  
  tf_impl[lax.cbrt_p] = _cbrt
  
  tf_impl[lax.lgamma_p] = tf.math.lgamma
  tf_impl[lax.digamma_p] = tf.math.digamma
  tf_impl[lax.igamma_p] = tf.math.igamma
  tf_impl[lax.igammac_p] = tf.math.igammac
  tf_impl[lax.regularized_incomplete_beta_p] = tf.math.betainc
  tf_impl[lax.erf_p] = tf.math.erf
  tf_impl[lax.erfc_p] = tf.math.erfc
  tf_impl[lax.erf_inv_p] = tf.math.erfinv
  tf_impl[lax.bessel_i0e_p] = tf.math.bessel_i0e
  tf_impl[lax.bessel_i1e_p] = tf.math.bessel_i1e
  
  tf_impl[lax.complex_p] = tf.complex
  
  
  def _conj(x, **kwargs):
    # The only dtypes that are allowed are: float32, float64, complex64, and
    # complex128.
    if x.dtype == tf.float32:
      return tf.cast(x, tf.complex64)
    elif x.dtype == tf.float64:
      return tf.cast(x, tf.complex128)
    else:
      return tf.math.conj(x)
  
  
  tf_impl[lax.conj_p] = _conj
  tf_impl[lax.real_p] = tf.math.real
  tf_impl[lax.imag_p] = tf.math.imag
  
  tf_impl[lax.add_p] = _add
  tf_impl[lax.sub_p] = tf.math.subtract
  tf_impl[lax.mul_p] = tf.math.multiply
  
  
  def _iota(*, dtype, shape, dimension):
    dtype = _to_tf_dtype(dtype)
    # Some dtypes are unsupported, like uint32, so we just fall back to int32.
    # TODO(mattjj, necula): improve tf.range dtype handling
    shape_tf = _eval_shape(shape)
    vec = tf.range(tf.cast(shape_tf[dimension], tf.int32), dtype=tf.int32)
    vec_shape = [-1 if i == dimension else 1 for i in range(len(shape))]
    return tf.cast(tf.broadcast_to(tf.reshape(vec, vec_shape), shape_tf), dtype)
  
  
  tf_impl[lax.iota_p] = _iota
  
  
  def _div(lhs, rhs):
    if lhs.dtype.is_integer:
      quotient = tf.math.floordiv(lhs, rhs)
      select = tf.math.logical_and(
          tf.not_equal(_sign(lhs), _sign(rhs)),
          tf.not_equal(tf.math.floormod(lhs, rhs), 0))
      return tf.where(select, quotient + 1, quotient)
    else:
      return tf.math.truediv(lhs, rhs)
  
  
  def _rem(lhs, rhs):
    return _sign(lhs) * tf.math.floormod(_abs(lhs), _abs(rhs))
  
  
  tf_impl[lax.div_p] = _div
  tf_impl[lax.rem_p] = _rem
  
  
  def _minmax(x: TfVal, y: TfVal, *, is_min: bool,
              _in_avals: Sequence[core.ShapedArray],
              _out_aval: core.ShapedArray,) -> TfVal:
    # For complex numbers use lexicographic ordering, like JAX
    if dtypes.issubdtype(x.dtype.as_numpy_dtype, np.complexfloating):
      return _convert_jax_impl(
          partial(lax_internal._minmax_complex_lowering,
                  lax_cmp_pick_x=lax.lt if is_min else lax.gt),
          multiple_results=False)(x, y, _in_avals=_in_avals, _out_aval=_out_aval)
    elif x.dtype.as_numpy_dtype == np.bool_:
      return (tf.math.logical_and if is_min else tf.math.logical_or)(x, y)
    else:
      return (tf.math.minimum if is_min else tf.math.maximum)(x, y)
  
  def _minmax_scalar(x: TfVal, y: TfVal, *, is_min: bool) -> TfVal:
    # For reducers we will need min/max for scalars only. In that case we
    # can construct the AbstractValues outselves, even in the presence of
    # shape polymorphism.
    assert len(x.shape) == 0 and len(y.shape) == 0, f"x: {x.shape}, y: {y.shape}"
    aval = core.ShapedArray((), _to_jax_dtype(x.dtype))
    return _minmax(x, y, is_min=is_min,
                   _in_avals=[aval, aval], _out_aval=aval)
  
  tf_impl_with_avals[lax.max_p] = partial(_minmax, is_min=False)
  tf_impl_with_avals[lax.min_p] = partial(_minmax, is_min=True)
  
  # Map from TF signed types to TF unsigned types.
  _SIGNED_TO_UNSIGNED_TABLE = {
      tf.int8: tf.uint8,
      tf.int16: tf.uint16,
      tf.int32: tf.uint32,
      tf.int64: tf.uint64,
  }
  
  # Map from TF unsigned types to TF signed types.
  _UNSIGNED_TO_SIGNED_TABLE = {u: s for s, u in _SIGNED_TO_UNSIGNED_TABLE.items()}
  
  
  # Note: Bitwise operations only yield identical results on unsigned integers!
  # pylint: disable=protected-access
  def _shift_right_arithmetic_raw(x, y):
    if x.dtype.is_unsigned:
      assert x.dtype == y.dtype
      orig_dtype = x.dtype
      signed_dtype = _UNSIGNED_TO_SIGNED_TABLE[orig_dtype]
      x = tf.cast(x, signed_dtype)
      y = tf.cast(y, signed_dtype)
      res = tf.bitwise.right_shift(x, y)
      return tf.cast(res, orig_dtype)
    else:
      return tf.bitwise.right_shift(x, y)
  
  
  def _shift_right_arithmetic(x, y):
    # TF shift is "implementation defined" if the shift amount is negative
    # or larger or equal to the size of the value. We implement the XLA
    # semantics to return the shift by the max value (x_bits - 1).
    # TODO: it is likely better to add XlaOps for shifts
    x_bits = 8 * x.dtype.size
    clamp_y = tf.where(_shift_in_bounds(x, y), y, x_bits - 1)
    return _shift_right_arithmetic_raw(x, clamp_y)
  
  
  tf_impl[lax.shift_right_arithmetic_p] = _shift_right_arithmetic
  
  
  def _shift_right_logical_raw(x, y):
    if x.dtype.is_unsigned:
      return tf.bitwise.right_shift(x, y)
    else:
      assert x.dtype == y.dtype
      orig_dtype = x.dtype
      unsigned_dtype = _SIGNED_TO_UNSIGNED_TABLE[orig_dtype]
      x = tf.cast(x, unsigned_dtype)
      y = tf.cast(y, unsigned_dtype)
      res = tf.bitwise.right_shift(x, y)
      return tf.cast(res, orig_dtype)
  
  
  def _shift_right_logical(x, y):
    # TF shift is "implementation defined" if the shift amount is negative
    # or larger or equal to the size of the value. We implement the XLA semantics
    # to return 0.
    # TODO: it is likely better to add XlaOps for shifts
    return tf.where(
        _shift_in_bounds(x, y), _shift_right_logical_raw(x, y), tf.zeros_like(x))
  
  
  tf_impl[lax.shift_right_logical_p] = _shift_right_logical
  
  
  def _shift_left(x, y):
    # TF shift is "implementation defined" if the shift amount is negative
    # or larger or equal to the size of the value. We implement the XLA semantics
    # to return 0.
    # TODO: it is likely better to add XlaOps for shifts
    return tf.where(
        _shift_in_bounds(x, y), tf.bitwise.left_shift(x, y), tf.zeros_like(x))
  
  
  tf_impl[lax.shift_left_p] = _shift_left
  
  
  def _shift_in_bounds(x: TfVal, y: TfVal) -> TfVal:
    # Return the TF expression for when y is within bounds (0 <= y < |x|)
    x_bits = 8 * x.dtype.size
    # TF does not have comparisons for uint16 and uint32 (despite what the
    # documentation says)
    y_comp = tf.cast(
        y, _UNSIGNED_TO_SIGNED_TABLE[y.dtype]) if y.dtype.is_unsigned else y
    y_lt_x_bits = tf.math.less(y_comp, x_bits)
    y_ge_0 = tf.math.greater_equal(y_comp, 0)
    return tf.logical_and(y_lt_x_bits, y_ge_0)
  
  
  def _not(x):
    """Computes bitwise not with support for booleans.
  
    Numpy and JAX support bitwise not for booleans by applying a logical not!
    This means that applying bitwise_not yields an unexpected result:
      jnp.bitwise_not(jnp.array([True, False]))
      >> DeviceArray([False,  True], dtype=bool)
  
    if you assume that booleans are simply casted to integers.
      jnp.bitwise_not(jnp.array([True, False]).astype(np.int32)).astype(bool)
      >> DeviceArray([True,  True], dtype=bool)
    """
    if x.dtype == tf.bool:
      return tf.logical_not(x)
    else:
      return tf.bitwise.invert(x)
  
  
  tf_impl[lax.not_p] = _not
  
  
  def handle_boolean_args(f, argnums: Sequence[int], boolean_f=None):
    """Computes functions with some bool args and bool results using int8.
  
    This is needed because some TF ops do not work for bool args, e.g.,
    inequalities, min/max.
  
    Args:
      f: a TF callable to wrap. It will be called with non-boolean arguments.
      argnums: the positional arguments that may be booleans.
      boolean_f: [Optional] a TF callable compatible with boolean
        arguments.
  
    Returns: a TF callable that can take a mix of boolean positional arguments
      (in the positions specified by `argnums`) and some non-boolean positional
      arguments. If there are no boolean arguments, just calls `f`. Otherwise,
      it calls `boolean_f` if defined. Otherwise, casts the boolean
      arguments to `int8`, calls `f`, then casts the result to `bool`.
    """
    argnums = tf.nest.flatten(argnums)
  
    def wrapper(*args: TfVal, **kwargs):
      argnum_types = {args[i].dtype for i in argnums}
      if tf.bool not in argnum_types:
        return f(*args, **kwargs)
      else:
        # All argnums should be boolean
        assert len(argnum_types) == 1, argnum_types
        if boolean_f != None:
          return boolean_f(*args, **kwargs)
        else:
          args_cast = [(tf.cast(a, tf.int8) if i in argnums else a)
                      for i, a in enumerate(args)]
          if "_in_avals" in kwargs:
  
            def cast_aval(aval):
              assert aval.dtype == np.bool_
              return core.ShapedArray(aval.shape, np.int8)
  
            _in_avals_cast = [
                cast_aval(aval) if i in argnums else aval
                for i, aval in enumerate(kwargs["_in_avals"])
            ]
            _out_aval_cast = tf.nest.map_structure(cast_aval, kwargs["_out_aval"])
            kwargs = dict(
                kwargs, _in_avals=_in_avals_cast, _out_aval=_out_aval_cast)
          out = f(*args_cast, **kwargs)
          return tf.nest.map_structure(lambda o: tf.cast(o, tf.bool), out)
  
    return wrapper
  
  
  tf_impl[lax.or_p] = handle_boolean_args(tf.bitwise.bitwise_or, argnums=(0, 1), boolean_f=tf.logical_or)
  tf_impl[lax.and_p] = handle_boolean_args(tf.bitwise.bitwise_and, argnums=(0, 1), boolean_f=tf.logical_and)
  tf_impl[lax.xor_p] = handle_boolean_args(tf.bitwise.bitwise_xor, argnums=(0, 1), boolean_f=tf.math.logical_xor)
  
  tf_impl[lax.eq_p] = tf.math.equal
  tf_impl[lax.ne_p] = tf.math.not_equal
  
  boolean_greater = lambda x,y: tf.logical_and(x, tf.logical_not(y)) # Only one combo: T,F -> T
  boolean_less = lambda x,y: tf.logical_and(tf.logical_not(x), y) # Only one combo: F,T -> T
  boolean_greater_or_equal = lambda x, y: tf.logical_not(boolean_less(x,y)) # All cases except F,T
  boolean_less_or_equal = lambda x, y: tf.logical_not(boolean_greater(x,y)) # All cases except T,F
  
  tf_impl[lax.gt_p] = handle_boolean_args(tf.math.greater, argnums=(0, 1), boolean_f=boolean_greater)
  tf_impl[lax.lt_p] = handle_boolean_args(tf.math.less, argnums=(0, 1), boolean_f=boolean_less)
  tf_impl[lax.ge_p] = handle_boolean_args(tf.math.greater_equal, argnums=(0, 1), boolean_f=boolean_greater_or_equal)
  tf_impl[lax.le_p] = handle_boolean_args(tf.math.less_equal, argnums=(0, 1), boolean_f=boolean_less_or_equal)
  
  tf_impl[lax.linalg.cholesky_p] = tf.linalg.cholesky
  
  
  def _convert_element_type(operand, *, new_dtype, weak_type=False):
    old_dtype = operand.dtype.as_numpy_dtype
    if (dtypes.issubdtype(old_dtype, np.complexfloating) and
        not dtypes.issubdtype(new_dtype, np.complexfloating)):
      operand = tf.math.real(operand)
    if (dtypes.issubdtype(old_dtype, np.floating) and
        not (dtypes.issubdtype(new_dtype, np.floating) or dtypes.issubdtype(
            new_dtype, np.complexfloating) or new_dtype == np.bool_)):
      sign = _sign(operand)
      operand = sign * tf.math.floor(sign * operand)
    return tf.dtypes.cast(operand, _to_tf_dtype(new_dtype))
  
  
  tf_impl[lax.convert_element_type_p] = _convert_element_type
  
  
  def _bitcast_convert_type(operand, new_dtype):
    if operand.dtype == new_dtype:
      return operand
    return tf.bitcast(operand, _to_tf_dtype(new_dtype))
  
  
  tf_impl[lax.bitcast_convert_type_p] = _bitcast_convert_type
  
  
  def _clamp(minval, operand, maxval, *, _in_avals, _out_aval):
    # The below permits mirroring the behavior of JAX when maxval < minval
    op_shape_tf_val = _eval_shape(_in_avals[1].shape)
    maxval = tf.broadcast_to(maxval, op_shape_tf_val)
    minval = tf.math.minimum(tf.broadcast_to(minval, op_shape_tf_val), maxval)
    return tf.clip_by_value(operand, minval, maxval)
  
  
  tf_impl_with_avals[lax.clamp_p] = _clamp
  
  
  def _concatenate(*operands, dimension):
    return tf.concat(operands, axis=dimension)
  
  
  tf_impl[lax.concatenate_p] = _concatenate
  
  
  def _conv_general_dimension_numbers_proto(dimension_numbers):
    """Converts a ConvDimensionNumbers to an XLA ConvolutionDimensionNumbers."""
    assert isinstance(dimension_numbers, lax.ConvDimensionNumbers)
    lhs_spec, rhs_spec, out_spec = dimension_numbers
    proto = xla_data_pb2.ConvolutionDimensionNumbers()
    proto.input_batch_dimension = lhs_spec[0]
    proto.input_feature_dimension = lhs_spec[1]
    proto.output_batch_dimension = out_spec[0]
    proto.output_feature_dimension = out_spec[1]
    proto.kernel_output_feature_dimension = rhs_spec[0]
    proto.kernel_input_feature_dimension = rhs_spec[1]
    proto.input_spatial_dimensions.extend(lhs_spec[2:])
    proto.kernel_spatial_dimensions.extend(rhs_spec[2:])
    proto.output_spatial_dimensions.extend(out_spec[2:])
    return proto
  
  
  def _precision_config_proto(precision: Optional[Tuple[PrecisionType,
                                                        PrecisionType]]):
    """Convert an integer to an XLA.PrecisionConfig."""
    if precision is None:
      return None
  
    proto = xla_data_pb2.PrecisionConfig()
    proto.operand_precision.append(int(precision[0]))
    proto.operand_precision.append(int(precision[1]))
    return proto
  
  
  def _conv_general_dilated(lhs, rhs, *,
                            window_strides, padding, lhs_dilation,
                            rhs_dilation,
                            dimension_numbers: lax.ConvDimensionNumbers,
                            feature_group_count: int,
                            batch_group_count: int,
                            lhs_shape: Sequence[int],
                            rhs_shape: Sequence[int],
                            precision: Optional[Tuple[PrecisionType, PrecisionType]],
                            preferred_element_type: Optional[DType],
                            _in_avals: Sequence[core.ShapedArray],
                            _out_aval: core.ShapedArray):
    """Implementation of lax.conv_general_dilated_p using XlaConv."""
    out_tf_shape = _aval_to_tf_shape(_out_aval)
    dnums_proto = _conv_general_dimension_numbers_proto(dimension_numbers)
    precision_config_proto = _precision_config_proto(precision)
  
    def gen_conv(lhs, rhs, preferred_element_type: Optional[DType]):
      tf_version = tuple(int(v) for v in tf.__version__.split(".")[:2])
      if tf_version >= (2, 8):
        # TODO(necula): remove when 2.8.0 is the stable TF version (and supports
        # batch_group_count.
        out = tfxla.conv(
            lhs, rhs, window_strides, padding, lhs_dilation, rhs_dilation,
            dnums_proto,
            feature_group_count=feature_group_count,
            batch_group_count=batch_group_count,
            precision_config=precision_config_proto,
            preferred_element_type=preferred_element_type,
            use_v2=True)
      else:
        if batch_group_count != 1:
          raise ValueError(
              "The batch_group_count parameter for conv requires TF version "
              "at least 2.8.0. You may want to use tf-nightly.")
        out = tfxla.conv(
            lhs, rhs, window_strides, padding, lhs_dilation, rhs_dilation,
            dnums_proto,
            feature_group_count=feature_group_count,
            precision_config=precision_config_proto,
            preferred_element_type=preferred_element_type,
            use_v2=True)
      # TODO: implement shape inference for XlaConv
      out.set_shape(out_tf_shape)
      if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
        out = tf.stop_gradient(out)  # See #7839
      return out
  
    # Follow the lowering for complex convolutions from
    # lax._conv_general_dilated_translation. We can use the same conversion on all
    # platforms because on XLA:TPU the compiler does the same as a rewrite.
    preferred_float_et: Optional[Any]
    if np.issubdtype(_in_avals[0].dtype, np.complexfloating):
      if preferred_element_type is not None:
        # Convert complex dtype to types used for real and imaginary parts
        assert np.issubdtype(preferred_element_type, np.complexfloating)
        preferred_float_et = (
            np.float64 if preferred_element_type == np.complex128 else np.float32)
      else:
        preferred_float_et = None
      lhs_real, lhs_imag = tf.math.real(lhs), tf.math.imag(lhs)
      rhs_real, rhs_imag = tf.math.real(rhs), tf.math.imag(rhs)
      k1 = gen_conv(_add(lhs_real, lhs_imag), rhs_real, preferred_float_et)
      k2 = gen_conv(lhs_real, tf.math.subtract(rhs_imag, rhs_real),
                    preferred_float_et)
      k3 = gen_conv(lhs_imag, _add(rhs_real, rhs_imag), preferred_float_et)
      return tf.complex(tf.math.subtract(k1, k3), _add(k1, k2))
    else:
      return gen_conv(lhs, rhs, preferred_element_type)
  
  
  tf_impl_with_avals[lax.conv_general_dilated_p] = _conv_general_dilated
  
  
  def _dot_general(lhs, rhs, *, dimension_numbers,
                   precision: Optional[Tuple[PrecisionType, PrecisionType]],
                   preferred_element_type: Optional[DType],
                   _in_avals: Sequence[core.ShapedArray],
                   _out_aval: core.ShapedArray):
    """Implementation of lax.dot_general_p in terms of tf.linalg.einsum."""
    (lhs_contracting, rhs_contracting), (lhs_batch, rhs_batch) = dimension_numbers
    dnums_proto = xla_data_pb2.DotDimensionNumbers()
    dnums_proto.lhs_contracting_dimensions.extend(lhs_contracting)
    dnums_proto.rhs_contracting_dimensions.extend(rhs_contracting)
    dnums_proto.lhs_batch_dimensions.extend(lhs_batch)
    dnums_proto.rhs_batch_dimensions.extend(rhs_batch)
    precision_config_proto = _precision_config_proto(precision)
    res = tfxla.dot_general(
        lhs,
        rhs,
        dnums_proto,
        precision_config_proto,
        preferred_element_type=preferred_element_type,
        use_v2=True)
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      res = tf.stop_gradient(res)  # See #7839
    return res
  
  
  tf_impl_with_avals[lax.dot_general_p] = _dot_general
  
  
  def _broadcast_in_dim(operand, *, shape, broadcast_dimensions,
                        _in_avals: Sequence[core.ShapedArray],
                        _out_aval: core.ShapedArray):
    # for i in range(len(operand.shape)):
    #   result.shape[bcast_dims[i]] <- operand.shape[i]
    # bcast_dims must be strictly increasing.
    # len(bcast_dims) == len(operand.shape)
    op_shape = _in_avals[0].shape
    add_1s_shape = [1] * len(shape)
    for i, broadcast_dim_i in enumerate(broadcast_dimensions):
      add_1s_shape[broadcast_dim_i] = op_shape[i]
    with_1s = tf.reshape(operand, _eval_shape(add_1s_shape))
    return tf.broadcast_to(with_1s, _eval_shape(shape))
  
  
  tf_impl_with_avals[lax.broadcast_in_dim_p] = _broadcast_in_dim
  
  
  def _reshape(operand, *, new_sizes, dimensions):
    if dimensions is None:
      dimensions = tf.range(tf.rank(operand))
    new_sizes_tf = _eval_shape(new_sizes)
    return tf.reshape(tf.transpose(operand, dimensions), new_sizes_tf)
  
  
  tf_impl[lax.reshape_p] = _reshape
  
  
  def _squeeze(operand, *, dimensions, _in_avals, _out_aval):
    op_shape = _in_avals[0].shape
    new_shape = tuple(d for i, d in enumerate(op_shape) if i not in dimensions)
    new_shape_tf = _eval_shape(new_shape)
    return tf.reshape(operand, new_shape_tf)
  
  
  tf_impl_with_avals[lax.squeeze_p] = _squeeze
  
  
  def _pad(operand, padding_value, *, padding_config,
           _in_avals: Sequence[core.ShapedArray],
           _out_aval: core.ShapedArray):
    low, high, interior = util.unzip3(padding_config)
    out = tfxla.pad(operand, padding_value, low, high, interior)
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      out = tf.stop_gradient(out)  # See #7839
    return out
  
  
  tf_impl_with_avals[lax.pad_p] = _pad
  
  
  def _rev(operand, *, dimensions):
    return tf.reverse(operand, dimensions)
  
  
  tf_impl[lax.rev_p] = _rev
  
  
  def _where(which, *cases):
    if which.dtype == tf.bool:
      assert len(cases) <= 2
      return cases if len(cases) == 1 else tf.where(which, cases[1], cases[0])
  
    def _select(offset, cases):
      assert len(cases) > 0
      if len(cases) == 1:
        return cases[0]
      mid = len(cases) // 2
      return tf.where(tf.less(which, offset + mid),
                      _select(offset, cases[:mid]),
                      _select(mid, cases[mid:]))
  
    return _select(0, cases)
  
  
  tf_impl[lax.select_n_p] = _where
  
  
  def _transpose(operand, *, permutation):
    return tf.transpose(operand, perm=permutation)
  
  
  tf_impl[lax.transpose_p] = _transpose
  
  axes_to_axis = lambda func: lambda operand, axes: func(operand, axis=axes)
  
  # reduce_sum and reduce_prod are not supported for bool
  tf_impl[lax.reduce_sum_p] = axes_to_axis(tf.reduce_sum)
  tf_impl[lax.reduce_prod_p] = axes_to_axis(tf.reduce_prod)
  tf_impl[lax.reduce_max_p] = handle_boolean_args(
    axes_to_axis(tf.reduce_max), argnums=[0],
    boolean_f=axes_to_axis(tf.reduce_any)) # Max is T if any one is T
  tf_impl[lax.reduce_min_p] = handle_boolean_args(
    axes_to_axis(tf.reduce_min), argnums=[0],
    boolean_f=axes_to_axis(tf.reduce_all)) # Min is F if not all are T
  tf_impl[lax.reduce_or_p] = axes_to_axis(tf.reduce_any)
  tf_impl[lax.reduce_and_p] = axes_to_axis(tf.reduce_all)
  
  
  def _argminmax(is_min: bool, operand: TfVal, axes: Sequence[int],
                 index_dtype: DType,
                 _in_avals: Sequence[core.ShapedArray],
                 _out_aval: core.ShapedArray):
    # Follow the JAX implementation, using a XlaReduce with a custom comparator
    if is_min:
      extra_name_stack = "argmin"
      value_comparator = lax.lt
      get_identity = lax_internal._get_min_identity
    else:
      extra_name_stack = "argmax"
      value_comparator = lax.gt
      get_identity = lax_internal._get_max_identity
  
    res = _convert_jax_impl(
        partial(lax_internal._compute_argminmax, value_comparator, get_identity),
        multiple_results=False,
        extra_name_stack=extra_name_stack)(
            operand,
            index_dtype=index_dtype,
            axes=axes,
            _in_avals=_in_avals,
            _out_aval=_out_aval)
    return res
  
  
  tf_impl_with_avals[lax.argmin_p] = partial(_argminmax, True)
  tf_impl_with_avals[lax.argmax_p] = partial(_argminmax, False)
  
  
  _add_fn = tf.function(_add, autograph=False)
  _ge_fn = tf.function(tf.math.greater_equal, autograph=False)
  
  
  def _select_and_gather_add(
      tangents: TfVal, operand: TfVal, select_prim: core.Primitive,
      window_dimensions: Sequence[int], window_strides: Sequence[int],
      base_dilation: Sequence[int], window_dilation: Sequence[int],
      padding: Sequence[Tuple[int, int]], _in_avals: Sequence[core.ShapedArray],
      _out_aval: core.ShapedArray):
    # Note: this function follows the pattern in
    # jax.lax._select_and_gather_add_translation.
    dtype = operand.dtype
    nbits = dtypes.finfo(dtype.as_numpy_dtype).bits
  
    # Specializing the function for 64 bits. Only up to 32 bits are supported on TPU,
    # we thus intend to let the code throw a different exception on this platform.
    max_bits = 64
  
    assert nbits <= max_bits
    double_word_reduction = nbits * 2 <= max_bits
  
    const = lambda dtype, x: tf.constant(np.array(x), dtype)
  
    if double_word_reduction:
      word_dtype = lax_internal._UINT_DTYPES[nbits]
      double_word_dtype = lax_internal._UINT_DTYPES[nbits * 2]
  
      # Packs two values into a tuple.
      def pack(a, b):
        a = _bitcast_convert_type(a, word_dtype)
        b = _bitcast_convert_type(b, word_dtype)
        a = _convert_element_type(a, new_dtype=double_word_dtype)
        b = _convert_element_type(b, new_dtype=double_word_dtype)
        a = tf.bitwise.left_shift(a, const(double_word_dtype, nbits))
        return tf.bitwise.bitwise_or(a, b)
  
      # Unpacks the first element of a tuple.
      def fst(t):
        assert t.dtype == double_word_dtype
        st = _shift_right_logical(t, const(double_word_dtype, nbits))
        return _bitcast_convert_type(
            _convert_element_type(st, new_dtype=word_dtype), dtype)
  
      # Unpacks the second element of a tuple.
      def snd(t):
        return _bitcast_convert_type(
            _convert_element_type(t, new_dtype=word_dtype), dtype)
  
    else:
      raise NotImplementedError(
          f"TODO: need to pack {nbits * 2} bits but this platform can only go up to {max_bits} bits."
      )
  
    assert select_prim is lax.ge_p or select_prim is lax.le_p, select_prim
  
    def reducer(x, y):
      which = tf_impl[select_prim]
      return tf_impl[lax.select_n_p](which(fst(x), fst(y)), y, x)
  
    init = -np.inf if select_prim is lax.ge_p else np.inf
    init_identity = lambda x: pack(const(dtype, init), const(dtype, 0))
  
    out = _specialized_reduce_window(
        reducer,
        init_identity,
        pack(operand, tangents),
        window_dimensions=window_dimensions,
        window_strides=window_strides,
        padding=padding,
        base_dilation=base_dilation,
        window_dilation=window_dilation,
        _in_avals=_in_avals,
        _out_aval=_out_aval)
  
    return snd(out)
  
  
  tf_impl_with_avals[lax.select_and_gather_add_p] = _select_and_gather_add
  
  
  def _get_shape_from_tensor_or_array(x):
    if isinstance(x.shape, tf.TensorShape):
      return tuple(x.shape.as_list())
    return tuple(x.shape)
  
  
  def _common_reduce_window(operand, init_val, reducer, window_dimensions,
                            window_strides, padding, base_dilation,
                            window_dilation, _in_avals, _out_aval):
    o_spec = tf.TensorSpec((), dtype=operand.dtype)
    reducer_fn = tf.function(
        reducer, autograph=False).get_concrete_function(o_spec, o_spec)
  
    if not isinstance(init_val, (tf.Tensor, tf.Variable)):
      init_val = tf.constant(init_val, operand.dtype)
    out = tfxla.reduce_window(
        operand,
        init_val,
        reducer_fn,
        window_dimensions,
        window_strides,
        base_dilations=base_dilation,
        window_dilations=window_dilation,
        padding=padding)
    # TODO: implement shape inference for XlaReduceWindow
    out.set_shape(_aval_to_tf_shape(_out_aval))
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      out = tf.stop_gradient(out)  # See #7839
    return out
  
  
  def _reduce_window(*args, jaxpr, consts, window_dimensions,
                     window_strides, padding, base_dilation, window_dilation,
                     _in_avals, _out_aval):
    """TensorFlow implementation of reduce_window.
  
    Args:
      operands: N dimensional arrays containing elements of type T
      init_values: starting values of the reduction
      jaxpr: the jaxpr corresponding to the reduction function
      consts: the constants associated with jaxpr.
      window_dimensions: array of integers for window dimension values
      window_strides: array of integers for window stride values
      padding: array of pairs of integers for padding values
      base_dilation: array of integers for base dilation values
      window_dilation: array of integers for window dilation values
  
    Returns:
      The reduced operand.
    """
    assert len(consts) == 0, "Reduction computation cannot have constants"
    operands, init_values = util.split_list(args, [len(args) // 2])
  
    if len(operands) != 1:
      raise NotImplementedError("jax2tf does not support variadic reduce_window")
  
    def reducer(arg1: TfVal, arg2: TfVal) -> TfVal:
      closed_jaxpr = core.ClosedJaxpr(jaxpr, consts)
      res, = _interpret_jaxpr(closed_jaxpr, arg1, arg2, extra_name_stack=None)
      return res
  
    return (_common_reduce_window(operands[0], init_values[0], reducer,
                                  window_dimensions, window_strides, padding,
                                  base_dilation, window_dilation, _in_avals,
                                  _out_aval[0]),)
  
  
  
  def _specialized_reduce_window(reducer,
                                 identity,
                                 operand,
                                 *,
                                 window_dimensions,
                                 window_strides,
                                 padding,
                                 base_dilation,
                                 window_dilation,
                                 _in_avals,
                                 _out_aval,
                                 name=None):
    """Wraps the TensorFlow reduce window operation based on a reducer and an
  
    identity function defining the initial value of the reduction depending on
    the dtype of the operand.
  
    Args:
      reducer: reduction function of type TfVal -> TfVal -> TfVal
      identity: function that takes a TensorFlow dtype as a parameter and returns
        the starting value of the reduction.
      operand: N dimensional array containing elements of type T
      window_dimensions: array of integers for window dimension values
      window_strides: array of integers for window stride values
      padding: array of pairs of integers for padding values
      base_dilation: array of integers for base dilation values
      window_dilation: array of integers for window dilation values
      name: the name of the specialized reduce window primitive for which this
        conversion function is called. This information may help to choose a
        different conversion path (optional)
  
    Returns:
      The reduced operand.
    """
    return _common_reduce_window(operand, identity(operand.dtype), reducer,
                                 window_dimensions, window_strides, padding,
                                 base_dilation, window_dilation, _in_avals,
                                 _out_aval)
  
  
  def _get_max_identity(tf_dtype):
    numpy_tf_dtype = tf_dtype.as_numpy_dtype
    if tf_dtype == tf.bfloat16 or dtypes.issubdtype(numpy_tf_dtype, np.inexact):
      return numpy_tf_dtype(-np.inf)
    elif dtypes.issubdtype(numpy_tf_dtype, np.integer):
      return dtypes.iinfo(numpy_tf_dtype).min
    else:
      assert dtypes.issubdtype(
          numpy_tf_dtype, np.bool_), (f"{tf_dtype} has no defined max identity")
      return False
  
  
  def _get_min_identity(tf_dtype):
    numpy_tf_dtype = tf_dtype.as_numpy_dtype
    if tf_dtype == tf.bfloat16 or dtypes.issubdtype(numpy_tf_dtype, np.inexact):
      return numpy_tf_dtype(np.inf)
    elif dtypes.issubdtype(numpy_tf_dtype, np.integer):
      return dtypes.iinfo(numpy_tf_dtype).max
    else:
      assert dtypes.issubdtype(
          numpy_tf_dtype, np.bool_), (f"{tf_dtype} has no defined min identity")
      return True
  
  
  # pylint: disable=protected-access
  tf_impl_with_avals[lax.reduce_window_sum_p] = (
      partial(_specialized_reduce_window, _add, lambda x: 0,
              name="reduce_window_sum"))
  tf_impl_with_avals[lax.reduce_window_min_p] = (
      partial(_specialized_reduce_window,
              partial(_minmax_scalar, is_min=True),
              _get_min_identity,
              name="reduce_window_min"))
  tf_impl_with_avals[lax.reduce_window_max_p] = (
      partial(_specialized_reduce_window,
              partial(_minmax_scalar, is_min=False),
              _get_max_identity,
              name="reduce_window_max"))
  tf_impl_with_avals[lax.reduce_window_p] = _reduce_window
  # pylint: enable=protected-access
  
  def _reduce(*operands: TfVal,
              computation: Callable,
              jaxpr: core.Jaxpr,
              consts:  Sequence[Any],
              dimensions: Sequence[int],
              _in_avals: Sequence[core.ShapedArray],
              _out_aval: core.ShapedArray) -> Sequence[TfVal]:
    del computation
    assert not consts
    assert len(operands) % 2 == 0
    # operands: op1, op2, ..., init_val1, init_val2, ...
    # reducer takes op1[i], op2[i], ..., init_val1, init_val2, ...
    nr_operands = len(operands) // 2
    init_vals = operands[nr_operands:]
    operands = operands[0:nr_operands]
  
    reducer_arg_spec = tuple([tf.TensorSpec((), op.dtype) for op in init_vals] * 2)
  
    def reducer_computation(*args: TfVal) -> TfVal:
      closed_jaxpr = core.ClosedJaxpr(jaxpr, consts)
      res = _interpret_jaxpr(closed_jaxpr, *args, extra_name_stack=None)
      return res
  
    xla_reducer_computation = (
        tf.function(reducer_computation,
                    autograph=False).get_concrete_function(*reducer_arg_spec))
  
    outs = tfxla.variadic_reduce(operands, init_vals,
                                 dimensions_to_reduce=dimensions,
                                 reducer=xla_reducer_computation)
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      outs = tuple(tf.stop_gradient(out) for out in outs)  # See #7839
    return outs
  
  tf_impl_with_avals[lax.reduce_p] = _reduce
  
  
  # We use lax._cumred_tpu_translation_rule to convert cummax,
  # cummin, cumsum and cumprod. This is efficient on TPU, but the complexity is
  # O(n^2) on other backends. This may be implemented using associative_scan
  # instead to favor different backends.
  def _cumred(lax_reduce_fn: Callable,
              lax_reduce_window_fn: Callable,
              extra_name_stack: str):
    if config.jax2tf_associative_scan_reductions:
      return _convert_jax_impl(partial(lax_control_flow.associative_scan,
                                       lax_reduce_fn),
                               multiple_results=False,
                               extra_name_stack=extra_name_stack)
    else:
      return _convert_jax_impl(partial(lax_control_flow._cumred_tpu_translation_rule,
                                       lax_reduce_window_fn),
                               multiple_results=False,
                               extra_name_stack=extra_name_stack)
  
  
  tf_impl_with_avals[lax.cummax_p] = _cumred(
      lax_reduce_window_fn=lax_windowed_reductions._reduce_window_max,
      lax_reduce_fn=lax.max,
      extra_name_stack="cummax")
  tf_impl_with_avals[lax.cummin_p] = _cumred(
      lax_reduce_window_fn=lax_windowed_reductions._reduce_window_min,
      lax_reduce_fn=lax.min,
      extra_name_stack="cummin")
  tf_impl_with_avals[lax.cumsum_p] = _cumred(
      lax_reduce_window_fn=lax_windowed_reductions._reduce_window_sum,
      lax_reduce_fn=lax.add,
      extra_name_stack="cumsum")
  tf_impl_with_avals[lax.cumprod_p] = _cumred(
      lax_reduce_window_fn=lax_windowed_reductions._reduce_window_prod,
      lax_reduce_fn=lax.mul,
      extra_name_stack="cumprod")
  
  
  def _select_and_scatter(operand, source, init_value, select_jaxpr,
                          select_consts, scatter_jaxpr, scatter_consts,
                          window_dimensions, window_strides, padding):
    raise NotImplementedError("TODO: jax2tf can not convert _select_and_scatter")
  
  
  tf_impl[lax.select_and_scatter_p] = _select_and_scatter
  
  
  @partial(handle_boolean_args, argnums=(0, 1))
  def _select_and_scatter_add(source, operand, *, select_prim, window_dimensions,
                              window_strides, padding, _in_avals, _out_aval):
    init_value = tf.zeros((), operand.dtype)
    select_fn = (
        tf.function(tf_impl[select_prim], autograph=False).get_concrete_function(
            init_value, init_value))
    scatter_fn = _add_fn.get_concrete_function(init_value, init_value)
    out = tfxla.select_and_scatter(operand, window_dimensions, window_strides,
                                   padding, source, init_value, select_fn,
                                   scatter_fn)
    out.set_shape(_aval_to_tf_shape(_out_aval))
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      out = tf.stop_gradient(out)  # See #7839
    return out
  
  
  tf_impl_with_avals[lax.select_and_scatter_add_p] = _select_and_scatter_add
  
  
  def _threefry2x32_jax_impl(*args: TfVal, _in_avals, _out_aval):
    res = _convert_jax_impl(
        partial(jax._src.prng._threefry2x32_lowering, use_rolled_loops=False),
        multiple_results=True, extra_name_stack="threefry")(
            *args, _in_avals=_in_avals, _out_aval=_out_aval)
    return res
  
  
  tf_impl_with_avals[jax._src.prng.threefry2x32_p] = _threefry2x32_jax_impl
  
  # Use the vmap implementation, otherwise on TPU the performance is really bad
  # With use_vmap=True on, we get about the same performance for JAX and jax2tf.
  tf_impl_with_avals[random.random_gamma_p] = _convert_jax_impl(
      partial(jax._src.random._gamma_impl, use_vmap=True),
      multiple_results=False, extra_name_stack="random_gamma")
  
  
  def _rng_bit_generator(key: TfVal, *, shape, dtype, algorithm) -> Sequence[TfVal]:
    is_uint32_key = key.dtype == _to_tf_dtype(jnp.uint32)
    if is_uint32_key:
      key = tf.reshape(key, (2, 2))
      key = tfxla.bitcast_convert_type(key, _to_tf_dtype(jnp.uint64))
    shape_tf = _eval_shape(shape)
    # JAX uses XLA algorithm enums; tfxla uses tf.random.Algorithm
    if algorithm == lax.RandomAlgorithm.RNG_THREE_FRY:
      algorithm_tf = tf.random.Algorithm.THREEFRY
    elif algorithm == lax.RandomAlgorithm.RNG_PHILOX:
      algorithm_tf = tf.random.Algorithm.PHILOX
    elif algorithm == lax.RandomAlgorithm.RNG_DEFAULT:
      algorithm_tf = tf.random.Algorithm.AUTO_SELECT
    else:
      assert False
    (new_key, res) = tfxla.rng_bit_generator(algorithm_tf.value, key, shape_tf,
                                             dtype=_to_tf_dtype(dtype))
    if is_uint32_key:
      new_key = tfxla.bitcast_convert_type(new_key, _to_tf_dtype(jnp.uint32))
      new_key = tf.reshape(new_key, (4,))
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      # See #7839
      new_key = tf.stop_gradient(new_key)
      res = tf.stop_gradient(res)
    return new_key, res
  
  
  tf_impl[lax.rng_bit_generator_p] = _rng_bit_generator
  
  
  def _rng_uniform(minval: TfVal, maxval: TfVal, *, shape) -> TfVal:
    shape_tf = _eval_shape(shape)
    return tf.random.uniform(shape_tf, minval=minval, maxval=maxval, dtype=minval.dtype)
  
  tf_impl[lax.rng_uniform_p] = _rng_uniform
  
  
  def _gather_dimensions_proto(indices_shape, dimension_numbers):
    proto = xla_data_pb2.GatherDimensionNumbers()
    proto.offset_dims.extend(dimension_numbers.offset_dims)
    proto.collapsed_slice_dims.extend(dimension_numbers.collapsed_slice_dims)
    proto.start_index_map.extend(dimension_numbers.start_index_map)
    assert indices_shape
    proto.index_vector_dim = len(indices_shape) - 1
    return proto
  
  
  @partial(handle_boolean_args, argnums=[0])
  def _gather(operand, start_indices, *, dimension_numbers, slice_sizes: core.Shape,
              indices_are_sorted, unique_indices, mode, fill_value,
              _in_avals: Sequence[core.ShapedArray],
              _out_aval: core.ShapedArray):
    """Tensorflow implementation of gather."""
    if mode == lax.GatherScatterMode.FILL_OR_DROP:
      gather_fill_fn = _convert_jax_impl(lax_slicing._gather_fill,
                                         multiple_results=False)
      return gather_fill_fn(
          operand, start_indices, dimension_numbers=dimension_numbers,
          slice_sizes=slice_sizes, unique_indices=unique_indices,
          indices_are_sorted=indices_are_sorted, fill_value=fill_value,
          output_shape=_out_aval.shape, _in_avals=_in_avals, _out_aval=_out_aval)
  
    proto = _gather_dimensions_proto(start_indices.shape, dimension_numbers)
    slice_sizes_tf = _eval_shape(slice_sizes)
    out = tfxla.gather(operand, start_indices, proto, slice_sizes_tf,
                       indices_are_sorted)
    out.set_shape(_aval_to_tf_shape(_out_aval))
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      out = tf.stop_gradient(out)  # See #7839
    return out
  
  
  tf_impl_with_avals[lax.gather_p] = _gather
  
  
  def _slice(operand, start_indices, limit_indices, strides, _in_avals,
             _out_aval):
    if strides is None:
      strides = [1] * len(start_indices)
    slices = tuple(
        map(slice, _eval_shape(start_indices), _eval_shape(limit_indices),
            _eval_shape(strides)))
    out = operand[slices]
    # TODO(b/184503314): improve shape inference for __getitem__
    # E.g., operand.shape=(b, 5, 3), start_indices=(0, 1, 1), limit_indices=(b, 5, 3), strides=(1, 2, 1)
    out.set_shape(_aval_to_tf_shape(_out_aval))
    return out
  
  
  tf_impl_with_avals[lax.slice_p] = _slice
  
  
  def _dynamic_slice(operand, *start_indices, slice_sizes: core.Shape,
                     _in_avals: Sequence[core.ShapedArray],
                     _out_aval: core.ShapedArray):
    start_indices = tf.stack(start_indices)
    slice_sizes_tf = _eval_shape(slice_sizes)
  
    res = tfxla.dynamic_slice(operand, start_indices, size_indices=slice_sizes_tf)
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      res = tf.stop_gradient(res)  # See #7839
    return res
  
  
  tf_impl_with_avals[lax.dynamic_slice_p] = _dynamic_slice
  
  
  def _dynamic_update_slice(operand, update, *start_indices,
                            _in_avals: Sequence[core.ShapedArray],
                            _out_aval: core.ShapedArray):
    out = tfxla.dynamic_update_slice(operand, update, tf.stack(start_indices))
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      out = tf.stop_gradient(out)  # See #7839
    return out
  
  
  tf_impl_with_avals[lax.dynamic_update_slice_p] = _dynamic_update_slice
  
  
  def _scatter_dimensions_proto(indices_shape, dimension_numbers):
    proto = xla_data_pb2.ScatterDimensionNumbers()
    proto.update_window_dims.extend(dimension_numbers.update_window_dims)
    proto.inserted_window_dims.extend(dimension_numbers.inserted_window_dims)
    proto.scatter_dims_to_operand_dims.extend(
        dimension_numbers.scatter_dims_to_operand_dims)
    assert indices_shape
    proto.index_vector_dim = len(indices_shape) - 1
    return proto
  
  
  def _scatter(operand, scatter_indices, updates, *, update_jaxpr, update_consts,
               dimension_numbers, indices_are_sorted, unique_indices, mode,
               _in_avals: Sequence[core.ShapedArray],
               _out_aval: core.ShapedArray):
    del unique_indices
  
    if mode == lax.GatherScatterMode.CLIP:
      clip_fn = _convert_jax_impl(lax_slicing._clamp_scatter_indices,
                                  multiple_results=False)
      scatter_indices = clip_fn(
          operand, scatter_indices, updates, dnums=dimension_numbers,
          _in_avals=_in_avals, _out_aval=_in_avals[1])
  
    assert len(update_consts) == 0, "Update computation cannot have constants"
  
    proto = _scatter_dimensions_proto(scatter_indices.shape, dimension_numbers)
  
    def update_computation(arg1: TfVal, arg2: TfVal) -> TfVal:
      closed_jaxpr = core.ClosedJaxpr(update_jaxpr, update_consts)
      res, = _interpret_jaxpr(closed_jaxpr, arg1, arg2, extra_name_stack=None)
      return res
  
    o_spec = tf.TensorSpec((), dtype=operand.dtype)
    xla_update_computation = (
        tf.function(update_computation,
                    autograph=False).get_concrete_function(o_spec, o_spec))
    out = tfxla.scatter(
        operand,
        scatter_indices,
        updates,
        xla_update_computation,
        proto,
        indices_are_sorted=indices_are_sorted)
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      out = tf.stop_gradient(out)  # See #7839
    return out
  
  
  tf_impl_with_avals[lax.scatter_p] = _scatter
  tf_impl_with_avals[lax.scatter_min_p] = _scatter
  tf_impl_with_avals[lax.scatter_max_p] = _scatter
  tf_impl_with_avals[lax.scatter_mul_p] = _scatter
  tf_impl_with_avals[lax.scatter_add_p] = _scatter
  
  
  def _cond(index: TfVal, *operands: TfVal, branches: Sequence[core.ClosedJaxpr],
            linear: Sequence[bool]) -> Sequence[TfVal]:
    del linear
    # tf.cond needs lambdas with no arguments.
    branches_tf = [
        partial(_interpret_jaxpr, jaxpr, *operands,
                # Same name stack as the XLA translation of cond_p
                extra_name_stack=f"branch_{i}_fun")
        for jaxpr in branches
        for i, jaxpr in enumerate(branches)
    ]
    return tf.switch_case(index, branches_tf)
  
  
  tf_impl[lax.cond_p] = _cond
  
  
  def _while(*args: TfVal, cond_nconsts: int, cond_jaxpr: core.ClosedJaxpr,
             body_nconsts: int, body_jaxpr: core.ClosedJaxpr) -> Sequence[TfVal]:
    cond_consts, body_consts, init_carry = util.split_list(
        args, [cond_nconsts, body_nconsts])
    if cond_jaxpr.out_avals[0].shape:  # type: ignore[attr-defined]
      # The conditional is not a scalar, this must be a batched while
      return _batched_cond_while(
          *args,
          cond_nconsts=cond_nconsts,
          cond_jaxpr=cond_jaxpr,
          body_nconsts=body_nconsts,
          body_jaxpr=body_jaxpr)
  
    # The conditional must return a single value to TF
    def cond_tf_func(*args: TfVal) -> TfVal:
      pred, = _interpret_jaxpr(cond_jaxpr, *cond_consts, *args,
                               # Same name stack as the XLA translation of while_p
                               extra_name_stack="while/cond")
      return pred
  
    body_tf_func = partial(_interpret_jaxpr, body_jaxpr, *body_consts,
                                     extra_name_stack="while/body")
    return tf.while_loop(cond_tf_func, body_tf_func, init_carry)
  
  
  def _batched_cond_while(*args: TfVal, cond_nconsts: int,
                          cond_jaxpr: core.ClosedJaxpr, body_nconsts: int,
                          body_jaxpr: core.ClosedJaxpr) -> Sequence[TfVal]:
    """Interprets a while_loop with a batched condition.
  
    A batched while has a conditional that returns a tensor of booleans, and
    a body that returns a list of tensors whose leading dimensions match those
    of the conditional tensor.
  
    We need to turn it into a while with scalar boolean conditional. We will
    expand the loop carry to include a prefix with the current tensor boolean
    condition. We prepend to the loop the first calculation of the tensor boolean
    condition. The loop condition will use a "reduce_any" to calculate a scalar
    boolean from the tensor boolean condition. The end of the loop body will
    compute the new carry using a "tf.where", and we compute the new tensor
    boolean condition.
    """
    cond_consts, body_consts, init_carry = util.split_list(
        args, [cond_nconsts, body_nconsts])
    # Initial computation of batched condition
    init_pred_b, = _interpret_jaxpr(cond_jaxpr, *cond_consts, *init_carry,
                                    extra_name_stack="while/body_pred")
    assert init_pred_b is not core.unit
  
    def new_cond_tf_func(pred_b: TfVal, *carry: TfVal) -> TfVal:
      pred = tf.reduce_any(pred_b, axis=list(range(len(pred_b.shape))))
      return pred
  
    def new_body_tf_func(pred_b: TfVal, *carry: TfVal) -> Sequence[TfVal]:
      new_carry: Sequence[TfVal] = _interpret_jaxpr(body_jaxpr, *body_consts,
                                                    *carry,
                                                    extra_name_stack="while/body")
      # We repeat those carries for which the loop termination condition is false
      def select_one_carry(new_c: TfVal, c: TfVal, c_aval: core.ShapedArray) -> TfVal:
        pred_b_bcast = _broadcast_in_dim(
            pred_b,
            shape=c_aval.shape,  # a JAX shape
            broadcast_dimensions=list(range(len(pred_b.shape))),
            _in_avals=cond_jaxpr.out_avals,
            _out_aval=core.ShapedArray(c_aval.shape, np.bool_))
        return tf.where(pred_b_bcast, new_c, c)
  
      selected_carry: Sequence[TfVal] = list(map(select_one_carry, new_carry, carry, body_jaxpr.out_avals))
      next_pred_b, = _interpret_jaxpr(cond_jaxpr, *cond_consts, *selected_carry,
                                      extra_name_stack="body_pred")
      return (next_pred_b, *selected_carry)
  
    _, *res_carry = tf.while_loop(new_cond_tf_func, new_body_tf_func,
                                  (init_pred_b, *init_carry))
    return res_carry
  
  
  tf_impl[lax.while_p] = _while
  
  # We use the scan impl rule to rewrite in terms of while.
  tf_impl_with_avals[lax.scan_p] = _convert_jax_impl(
      lax_control_flow._scan_impl,
      extra_name_stack="scan")
  
  tf_impl_with_avals[ad_checkpoint.remat_p] = \
    _convert_jax_impl(partial(lax_control_flow._remat_translation_rule,
                              # TODO: jax2tf cannot discriminate by platform
                              platform="cpu"),
                      multiple_results=True,
                      extra_name_stack="checkpoint")
  
  def _top_k(operand: TfVal, k: int) -> Tuple[TfVal, TfVal]:
    # Some types originally incompatible with tf.math.top_k can be promoted
    # to a compatible type without loss of precision.
    def promote_tf_dtype(tf_dtype):
      if tf_dtype in [tf.bool, tf.uint8, tf.uint16]:
        return tf.uint32
      if tf_dtype in [tf.int8, tf.int16]:
        return tf.int32
      if tf_dtype is tf.float16:
        return tf.float32
      return None
  
    conversion_dtype = promote_tf_dtype(operand.dtype)
    if conversion_dtype:
      values, indices = tf.math.top_k(
          tf.dtypes.cast(operand, conversion_dtype), k=k, sorted=True)
      return tf.dtypes.cast(values, operand.dtype), indices
    else:
      return tf.math.top_k(operand, k=k, sorted=True)
  
  
  tf_impl[lax.top_k_p] = _top_k
  
  
  def _sort(*operands: TfVal, dimension: int, is_stable: bool,
            num_keys: int) -> Tuple[TfVal, ...]:
    assert 1 <= num_keys <= len(operands)
    assert 0 <= dimension < len(
        operands[0].shape
    ), f"Invalid {dimension} for ndim {len(operands[0].shape)}"
  
    comparator_spec: List[tf.TensorSpec] = []
    comparator_jax_in_avals: List[core.ShapedArray] = []
    for op in operands:
      o_spec = tf.TensorSpec((), dtype=op.dtype)
      comparator_spec.extend([o_spec, o_spec])
      o_aval = core.ShapedArray((), _to_jax_dtype(op.dtype))
      comparator_jax_in_avals.extend([o_aval, o_aval])
  
    # Use the same comparator that JAX uses when compiling to XLA, to get the
    # proper NaN/Inf total order, and the lexicographic ordering.
    # The comparator is a 2N-argument TF function, with arguments [2k] and [2k +1]
    # corresponding to two scalars from operand[k].
    def lexicographic_comparator(*tf_args: TfVal) -> TfVal:
      return _convert_jax_impl(
          lax_internal._sort_lt_comparator, multiple_results=False)(
              *tf_args,
              _in_avals=comparator_jax_in_avals,
              _out_aval=core.ShapedArray((), np.bool_),
              num_keys=num_keys)
  
    xla_comparator_computation = (
        tf.function(lexicographic_comparator,
                    autograph=False).get_concrete_function(*comparator_spec))
    results = tfxla.variadic_sort(
        operands,
        dimension=dimension,
        is_stable=is_stable,
        comparator=xla_comparator_computation)
    if _WRAP_JAX_JIT_WITH_TF_FUNCTION:
      results = tuple(tf.stop_gradient(out) for out in results)  # See #7839
    return results
  
  
  tf_impl[lax.sort_p] = _sort
  
  
  def _fft(x, fft_type, fft_lengths):
    FFT, IFFT, RFFT, IRFFT = list(map(xla_client.FftType, [0, 1, 2, 3]))
    if fft_type == IRFFT:
      expected_lengths = x.shape[-len(fft_lengths):-1] + ((x.shape[-1] - 1) * 2,)
    else:
      expected_lengths = x.shape[-len(fft_lengths):]
    if expected_lengths != fft_lengths:
      raise NotImplementedError(
          f"Unsupported fft_lengths={fft_lengths} for fft_type={fft_type} of "
          f"array with shape={x.shape}.")
    tf_funcs = {
        FFT: [tf.signal.fft, tf.signal.fft2d, tf.signal.fft3d],
        IFFT: [tf.signal.ifft, tf.signal.ifft2d, tf.signal.ifft3d],
        RFFT: [tf.signal.rfft, tf.signal.rfft2d, tf.signal.rfft3d],
        IRFFT: [tf.signal.irfft, tf.signal.irfft2d, tf.signal.irfft3d]
    }
    return tf_funcs[fft_type][len(fft_lengths) - 1](x)
  
  
  tf_impl[lax.fft_p] = _fft
  
  
  def _qr(operand, full_matrices):
    return tf.linalg.qr(operand, full_matrices=full_matrices)
  
  
  tf_impl[lax.linalg.qr_p] = _qr
  
  
  def _svd(operand, full_matrices, compute_uv):
    result = tf.linalg.svd(operand, full_matrices, compute_uv)
    if not compute_uv:
      return result,
    s, u, v = result
    return s, u, tf.linalg.adjoint(v)
  
  
  tf_impl[lax.linalg.svd_p] = _svd
  
  
  def _eig(operand: TfVal, compute_left_eigenvectors: bool,
           compute_right_eigenvectors: bool):
    if compute_left_eigenvectors and compute_right_eigenvectors:
      # TODO(bchetioui): didn't find a 100% reliable, easy and satisfying way to
      # sort the left eigenvectors in the right order. The jax.numpy.linalg API
      # suggests to me that left eigenvectors are anyway seldom used, so I
      # think it is acceptable to leave as unimplemented for now.
      msg = ("Conversion of eig is not implemented when both "
             "compute_left_eigenvectors and compute_right_eigenvectors are set "
             "to True.")
      raise NotImplementedError(msg)
    elif not (compute_left_eigenvectors or compute_right_eigenvectors):
      return tuple([tf.linalg.eigvals(operand)])
    elif compute_right_eigenvectors:
      return tuple(tf.linalg.eig(operand))
    else:  # compute_left_eigenvectors == True
      wH, vl = tf.linalg.eig(tf.linalg.adjoint(operand))
      wHH = tf.math.conj(wH)
      return tuple([wHH, vl])
  
  
  tf_impl[lax.linalg.eig_p] = _eig
  
  
  def _eigh(operand: TfVal, lower: bool, _in_avals, _out_aval):
    if operand.shape[-1] == 0:
      v, w = operand, tf.reshape(operand, _eval_shape(_in_avals[0].shape[:-1]))
    else:
      if not lower:
        operand = tf.linalg.adjoint(operand)
      w, v = tf.linalg.eigh(operand)
    cast_type = {
        tf.complex64: tf.float32,
        tf.complex128: tf.float64
    }.get(operand.dtype)
    if cast_type is not None:
      w = tf.cast(w, cast_type)
    return v, w
  
  
  tf_impl_with_avals[lax.linalg.eigh_p] = _eigh
  
  
  def _lu(operand: TfVal, _in_avals, _out_aval):
    return _convert_jax_impl(lax_linalg._lu_python, extra_name_stack="lu")(
        operand, _in_avals=_in_avals, _out_aval=_out_aval)
  
  
  tf_impl_with_avals[lax.linalg.lu_p] = _lu
  
  
  def _triangular_solve(a: TfVal, b: TfVal, *, left_side: bool, lower: bool,
                        transpose_a: bool, conjugate_a: bool, unit_diagonal: bool,
                        _in_avals: Sequence[core.ShapedArray],
                        _out_aval: core.ShapedArray):
    if unit_diagonal:
      a_aval, _ = _in_avals
      a_shape = _eval_shape(a_aval.shape)
      a = tf.linalg.set_diag(a, tf.ones(a_shape[:-1], dtype=a.dtype))
    if not left_side:
      rank = len(a.shape)
      transpose_dimensions = list(range(rank - 2)) + [rank - 1, rank - 2]
      a = tf.transpose(a, transpose_dimensions)
      b = tf.transpose(b, transpose_dimensions)
      lower = not lower
    # adjoint == transpose for real dtypes, so special care need only be taken
    # for complex types.
    if a.dtype in [tf.complex64, tf.complex128]:
      if (transpose_a and not conjugate_a) or (not transpose_a and conjugate_a):
        a = tf.math.conj(a)
    result = tf.linalg.triangular_solve(a, b, lower=lower, adjoint=transpose_a)
    if not left_side:
      result = tf.transpose(result, transpose_dimensions)
    return result
  
  
  tf_impl_with_avals[lax.linalg.triangular_solve_p] = _triangular_solve
  
  
  def _linear_solve(*args: TfVal, const_lengths, jaxprs, _in_avals, _out_aval):
    return _convert_jax_impl(lax_control_flow._custom_linear_solve_impl,
                             extra_name_stack="linear_solve")(
        *args,
        const_lengths=const_lengths,
        jaxprs=jaxprs,
        _in_avals=_in_avals,
        _out_aval=_out_aval)
  
  
  tf_impl_with_avals[lax.linear_solve_p] = _linear_solve
  
  def _tridiagonal_solve(*args: TfVal, _in_avals, _out_aval, **params):
    return _convert_jax_impl(lax_linalg._tridiagonal_solve_jax,
                             multiple_results=False,
                             extra_name_stack="tridiagonal_solve")(
        *args,
        _in_avals=_in_avals,
        _out_aval=_out_aval)
  
  
  tf_impl_with_avals[lax.linalg.tridiagonal_solve_p] = _tridiagonal_solve
  
  def _custom_jvp_call_jaxpr(*args: TfVal, fun_jaxpr: core.ClosedJaxpr,
                             jvp_jaxpr_thunk: Callable,
                             num_consts: int) -> Sequence[TfVal]:
    # TODO(necula): ensure that there is no AD transformation in scope
    return _interpret_jaxpr(fun_jaxpr, *args, extra_name_stack="custom_jvp")
  
  
  tf_impl[custom_derivatives.custom_jvp_call_jaxpr_p] = _custom_jvp_call_jaxpr
  
  
  def _custom_vjp_call_jaxpr(*args: TfVal, fun_jaxpr: core.ClosedJaxpr,
                             **_) -> Sequence[TfVal]:
    # TODO(necula): ensure that there is no AD transformation in scope
    return _interpret_jaxpr(fun_jaxpr, *args, extra_name_stack="custom_vjp")
  
  
  tf_impl[custom_derivatives.custom_vjp_call_jaxpr_p] = _custom_vjp_call_jaxpr
  
  
  def _custom_lin(*args: TfVal, **_) -> Sequence[TfVal]:
    raise TypeError("can't apply forward-mode autodiff (jvp) to a custom_vjp "
                    "function.")
  
  
  tf_impl[ad.custom_lin_p] = _custom_lin
  
  
  def split_to_logical_devices(tensor: TfVal,
                               partition_dimensions: pxla.PartitionsOrReplicated):
    """Like TPUMPStrategy.experimental_split_to_logical_devices.
  
    For jax2tf purposes we want to avoid needing to thread the `strategy` object
    through the generated computation. It seems that the original function needs
    the strategy object only for error checking, which we assume is done upstream
    by JAX.
  
    Args:
      tensor: Input tensor to annotate.
      partition_dimensions: A list of integers, with one integer per tensor
        dimension, specifying in how many parts the dimension should be split. The
        product of integers must equal the number of devices per replica.
      use_sharding_op: whether to use a sharding op, or not.
  
    Returns:
      an annotated tensor.
    """
    # TODO: this is only for sharded_jit. Either remove, or implement in terms
    # of _shard_values.
    if partition_dimensions is None:
      return xla_sharding.replicate(tensor, use_sharding_op=True)
    num_partition_splits = np.prod(partition_dimensions)
    tile_assignment = np.arange(num_partition_splits).reshape(
        partition_dimensions)
    return xla_sharding.tile(tensor, tile_assignment, use_sharding_op=True)
  
  
  def _shard_value(mesh: maps.Mesh,
                   val: TfVal,
                   aval: core.ShapedArray,
                   axis_resources: pjit.ParsedPartitionSpec) -> TfVal:
    """Apply sharding to a TfVal."""
    sharding_proto: xla_client.OpSharding = pjit.get_aval_sharding_proto(
        aval, axis_resources, mesh)
    # To use xla_sharding.py, we must have a xla_data_pb2.OpSharding.
    xla_sharding_proto: xla_data_pb2.OpSharding = (
        xla_data_pb2.OpSharding(
            type=int(sharding_proto.type),
            tile_assignment_dimensions=sharding_proto.tile_assignment_dimensions,
            tile_assignment_devices=sharding_proto.tile_assignment_devices,
            replicate_on_last_tile_dim=sharding_proto.replicate_on_last_tile_dim,
            last_tile_dims=sharding_proto.last_tile_dims))
    return xla_sharding.Sharding(proto=xla_sharding_proto).apply_to_tensor(
        val, use_sharding_op=True)
  
  
  def _pjit(*args: TfVal,
            jaxpr: core.ClosedJaxpr,
            in_axis_resources: Sequence[pjit.ParsedPartitionSpec],
            out_axis_resources: Sequence[pjit.ParsedPartitionSpec],
            resource_env: maps.ResourceEnv,
            donated_invars,
            name: str,
            in_positional_semantics,
            out_positional_semantics,
            _in_avals: Sequence[core.ShapedArray],
            _out_aval: core.ShapedArray) -> TfVal:
    del donated_invars
    if resource_env.physical_mesh.is_multi_process:
      raise NotImplementedError("jax2tf translation for pjit over multi-process "
                                "meshes is not supported yet")
    # TODO: add `name` to the name stack
    shard_value_for_mesh = partial(_shard_value, resource_env.physical_mesh)
    # Apply sharding annotation to the arguments
    sharded_args: Sequence[TfVal] = tuple(
        map(shard_value_for_mesh, args, _in_avals, in_axis_resources))
    results = _interpret_jaxpr(jaxpr, *sharded_args,
                               extra_name_stack=util.wrap_name(name, "pjit"))
    sharded_results: Sequence[TfVal] = tuple(
        map(shard_value_for_mesh, results, _out_aval, out_axis_resources))
    return tuple(sharded_results)
  
  
  tf_impl_with_avals[pjit.pjit_p] = _pjit
  
  
  def _pjit_sharding_constraint(arg: TfVal, *,
                                axis_resources: pjit.ParsedPartitionSpec,
                                resource_env: maps.ResourceEnv,
                                _in_avals: Sequence[core.ShapedArray],
                                _out_aval: core.ShapedArray,
                                **kwargs) -> TfVal:
    return _shard_value(resource_env.physical_mesh, arg, _in_avals[0], axis_resources)
  
  
  tf_impl_with_avals[pjit.sharding_constraint_p] = _pjit_sharding_constraint
  
  def _dimension_size_jax2tf(op: TfVal, *, dimension):
    return tf.shape(op)[dimension]
  
  tf_impl[shape_poly.dimension_size_p] = _dimension_size_jax2tf
  
  def _dim_as_value_jax2tf(dim: shape_poly.DimSize):
    dim_tf, = _eval_shape((dim,))
    return dim_tf
  
  tf_impl[shape_poly.dim_as_value_p] = _dim_as_value_jax2tf
  
  def _register_checkpoint_pytrees():
    """Registers TF custom container types as pytrees."""
    m = tf.Module()
    # The types here are automagically changed by TensorFlow's checkpointing
    # infrastructure.
    m.a = (tf.Module(), tf.Module())
    m.b = [tf.Module(), tf.Module()]
    m.c = {"a": tf.Module()}
    tuple_wrapper = type(m.a)
    list_wrapper = type(m.b)
    dict_wrapper = type(m.c)
  
    # TF AutoTrackable swaps container types out for wrappers.
    assert tuple_wrapper is not tuple
    assert list_wrapper is not list
    assert dict_wrapper is not dict
  
    jax.tree_util.register_pytree_node(tuple_wrapper, lambda xs:
                                       (tuple(xs), None), lambda _, xs: tuple(xs))
  
    jax.tree_util.register_pytree_node(list_wrapper, lambda xs: (tuple(xs), None),
                                       lambda _, xs: list(xs))
  
    jax.tree_util.register_pytree_node(
        dict_wrapper,
        lambda s: (tuple(s.values()), tuple(s.keys())),
        lambda k, xs: dict(zip(k, xs)))
  
  
  _register_checkpoint_pytrees()
  
apis: tensorflow.math.equal tensorflow.logical_and tensorflow.identity tensorflow.__version__.split tensorflow.linalg.eigh tensorflow.function tensorflow.compiler.tf2xla.python.xla.conv tensorflow.bitwise.right_shift tensorflow.math.greater_equal tensorflow.compiler.tf2xla.python.xla.gather tensorflow.linalg.eigvals tensorflow.math.floor tensorflow.compiler.xla.xla_data_pb2.DotDimensionNumbers tensorflow.Module tensorflow.math.real tensorflow.while_loop tensorflow.cast tensorflow.math.floormod tensorflow.compiler.xla.xla_data_pb2.ScatterDimensionNumbers tensorflow.linalg.eig tensorflow.math.round numpy.array tensorflow.compiler.xla.xla_data_pb2.PrecisionConfig tensorflow.complex numpy.issubdtype tensorflow.compiler.tf2xla.python.xla.scatter tensorflow.ones tensorflow.convert_to_tensor tensorflow.math.conj tensorflow.raw_ops.AddV2 tensorflow.math.atan2 tensorflow.math.floordiv tensorflow.compiler.tf2xla.python.xla.variadic_reduce tensorflow.constant tensorflow.shape tensorflow.math.truediv tensorflow.compiler.tf2xla.python.xla.dot_general tensorflow.rank tensorflow.math.sqrt tensorflow.bitwise.bitwise_or tensorflow.math.abs tensorflow.math.imag tensorflow.stop_gradient tensorflow.bitwise.left_shift tensorflow.compiler.tf2xla.python.xla.reduce_window tensorflow.raw_ops.PopulationCount tensorflow.compiler.xla.experimental.xla_sharding.xla_sharding.Sharding tensorflow.dtypes.cast tensorflow.compiler.tf2xla.python.xla.dynamic_slice tensorflow.nest.flatten tensorflow.less tensorflow.linalg.svd tensorflow.compiler.xla.xla_data_pb2.ConvolutionDimensionNumbers tensorflow.transpose tensorflow.compiler.xla.experimental.xla_sharding.xla_sharding.tile tensorflow.compiler.xla.xla_data_pb2.GatherDimensionNumbers tensorflow.math.sign tensorflow.reverse tensorflow.linalg.adjoint tensorflow.zeros_like numpy.arange numpy.prod tensorflow.math.negative tensorflow.python.framework.ops.get_default_graph tensorflow.logical_not tensorflow.bitwise.invert tensorflow.random.uniform tensorflow.linalg.triangular_solve tensorflow.math.subtract tensorflow.broadcast_to tensorflow.reshape tensorflow.switch_case tensorflow.name_scope tensorflow.concat tensorflow.dtypes.as_dtype tensorflow.compiler.xla.experimental.xla_sharding.xla_sharding.replicate tensorflow.math.less tensorflow.raw_ops.PreventGradient tensorflow.device tensorflow.clip_by_value tensorflow.compiler.xla.xla_data_pb2.OpMetadata tensorflow.math.reciprocal tensorflow.stack tensorflow.nest.map_structure tensorflow.math.multiply tensorflow.compiler.tf2xla.python.xla.variadic_sort tensorflow.zeros tensorflow.compiler.tf2xla.python.xla.pad numpy.shape tensorflow.compiler.tf2xla.python.xla.select_and_scatter tensorflow.TensorSpec tensorflow.where tensorflow.linalg.qr tensorflow.math.top_k