# Copyright 2018 The JAX Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from __future__ import annotations

import collections
from collections.abc import Hashable, Iterable
from dataclasses import dataclass
import difflib
import functools
from functools import partial
import operator as op
import textwrap
from typing import Any, Callable, NamedTuple, TypeVar, Union, overload
import warnings

from jax._src import traceback_util
from jax._src.lib import pytree
from jax._src.lib import xla_extension_version
from jax._src.util import safe_zip
from jax._src.util import unzip2


traceback_util.register_exclusion(__file__)

T = TypeVar("T")
U = TypeVar("U", bound=type[Any])

Leaf = Any
PyTreeDef = pytree.PyTreeDef

# TODO(phawkins): make this unconditional when jaxlib 0.4.14 is the minimum.
default_registry: pytree.PyTreeRegistry | None
if xla_extension_version >= 169:
  default_registry = pytree.default_registry()
  # Set __module__ and __name__, which allow this registry to be pickled by
  # reference.
  default_registry.__module__ = __name__
  default_registry.__name__ = "default_registry"
else:
  default_registry = None

def tree_flatten(tree: Any,
                 is_leaf: Callable[[Any], bool] | None = None
                 ) -> tuple[list[Leaf], PyTreeDef]:
  """Flattens a pytree.

  The flattening order (i.e. the order of elements in the output list)
  is deterministic, corresponding to a left-to-right depth-first tree
  traversal.

  Args:
    tree: a pytree to flatten.
    is_leaf: an optionally specified function that will be called at each
      flattening step. It should return a boolean, with true stopping the
      traversal and the whole subtree being treated as a leaf, and false
      indicating the flattening should traverse the current object.

  Returns:
    A pair where the first element is a list of leaf values and the second
    element is a treedef representing the structure of the flattened tree.
  """
  if default_registry:
    return default_registry.flatten(tree, is_leaf)
  else:
    return pytree.flatten(tree, is_leaf)  # type: ignore


def tree_unflatten(treedef: PyTreeDef, leaves: Iterable[Leaf]) -> Any:
  """Reconstructs a pytree from the treedef and the leaves.

  The inverse of :func:`tree_flatten`.

  Args:
    treedef: the treedef to reconstruct
    leaves: the iterable of leaves to use for reconstruction. The iterable must
      match the leaves of the treedef.

  Returns:
    The reconstructed pytree, containing the ``leaves`` placed in the structure
    described by ``treedef``.
  """
  return treedef.unflatten(leaves)


def tree_leaves(tree: Any,
                is_leaf: Callable[[Any], bool] | None = None
                ) -> list[Leaf]:
  """Gets the leaves of a pytree."""
  if default_registry:
    return default_registry.flatten(tree, is_leaf)[0]
  else:
    return pytree.flatten(tree, is_leaf)[0]  # type: ignore


def tree_structure(tree: Any,
                   is_leaf: None | (Callable[[Any],
                                              bool]) = None) -> PyTreeDef:
  """Gets the treedef for a pytree."""
  if default_registry:
    return default_registry.flatten(tree, is_leaf)[1]
  else:
    return pytree.flatten(tree, is_leaf)[1]  # type: ignore


def treedef_tuple(treedefs: Iterable[PyTreeDef]) -> PyTreeDef:
  """Makes a tuple treedef from an iterable of child treedefs."""
  if default_registry:
    return pytree.tuple(default_registry, list(treedefs))  # type: ignore
  else:
    return pytree.tuple(list(treedefs))  # type: ignore



def treedef_children(treedef: PyTreeDef) -> list[PyTreeDef]:
  return treedef.children()


def treedef_is_leaf(treedef: PyTreeDef) -> bool:
  return treedef.num_nodes == 1


def treedef_is_strict_leaf(treedef: PyTreeDef) -> bool:
  return treedef.num_nodes == 1 and treedef.num_leaves == 1


def all_leaves(iterable: Iterable[Any],
               is_leaf: Callable[[Any], bool] | None = None) -> bool:
  """Tests whether all elements in the given iterable are all leaves.

  >>> tree = {"a": [1, 2, 3]}
  >>> assert all_leaves(jax.tree_util.tree_leaves(tree))
  >>> assert not all_leaves([tree])

  This function is useful in advanced cases, for example if a library allows
  arbitrary map operations on a flat iterable of leaves it may want to check
  if the result is still a flat iterable of leaves.

  Args:
    iterable: Iterable of leaves.

  Returns:
    A boolean indicating if all elements in the input are leaves.
  """
  if is_leaf is None:
    if default_registry:
      return pytree.all_leaves(default_registry, iterable)  # type: ignore
    else:
      return pytree.all_leaves(iterable)  # type: ignore
  else:
    lst = list(iterable)
    return lst == tree_leaves(lst, is_leaf)


_Children = TypeVar("_Children", bound=Iterable[Any])
_AuxData = TypeVar("_AuxData", bound=Hashable)

def register_pytree_node(nodetype: type[T],
                         flatten_func: Callable[[T], tuple[_Children, _AuxData]],
                         unflatten_func: Callable[[_AuxData, _Children], T]):
  """Extends the set of types that are considered internal nodes in pytrees.

  See :ref:`example usage <pytrees>`.

  Args:
    nodetype: a Python type to treat as an internal pytree node.
    flatten_func: a function to be used during flattening, taking a value of
      type ``nodetype`` and returning a pair, with (1) an iterable for the
      children to be flattened recursively, and (2) some hashable auxiliary data
      to be stored in the treedef and to be passed to the ``unflatten_func``.
    unflatten_func: a function taking two arguments: the auxiliary data that was
      returned by ``flatten_func`` and stored in the treedef, and the
      unflattened children. The function should return an instance of
      ``nodetype``.
  """
  if default_registry:
    default_registry.register_node(nodetype, flatten_func, unflatten_func)
  else:
    pytree.register_node(nodetype, flatten_func, unflatten_func)  # type: ignore
  _registry[nodetype] = _RegistryEntry(flatten_func, unflatten_func)


def register_pytree_node_class(cls: U) -> U:
  """Extends the set of types that are considered internal nodes in pytrees.

  This function is a thin wrapper around ``register_pytree_node``, and provides
  a class-oriented interface::

    @register_pytree_node_class
    class Special:
      def __init__(self, x, y):
        self.x = x
        self.y = y
      def tree_flatten(self):
        return ((self.x, self.y), None)
      @classmethod
      def tree_unflatten(cls, aux_data, children):
        return cls(*children)
  """
  register_pytree_node(cls, op.methodcaller("tree_flatten"), cls.tree_unflatten)
  return cls


def tree_map(f: Callable[..., Any],
             tree: Any,
             *rest: Any,
             is_leaf: Callable[[Any], bool] | None = None) -> Any:
  """Maps a multi-input function over pytree args to produce a new pytree.

  Args:
    f: function that takes ``1 + len(rest)`` arguments, to be applied at the
      corresponding leaves of the pytrees.
    tree: a pytree to be mapped over, with each leaf providing the first
      positional argument to ``f``.
    rest: a tuple of pytrees, each of which has the same structure as ``tree``
      or has ``tree`` as a prefix.
    is_leaf: an optionally specified function that will be called at each
      flattening step. It should return a boolean, which indicates whether the
      flattening should traverse the current object, or if it should be stopped
      immediately, with the whole subtree being treated as a leaf.

  Returns:
    A new pytree with the same structure as ``tree`` but with the value at each
    leaf given by ``f(x, *xs)`` where ``x`` is the value at the corresponding
    leaf in ``tree`` and ``xs`` is the tuple of values at corresponding nodes in
    ``rest``.

  Examples:

    >>> import jax.tree_util
    >>> jax.tree_util.tree_map(lambda x: x + 1, {"x": 7, "y": 42})
    {'x': 8, 'y': 43}

    If multiple inputs are passed, the structure of the tree is taken from the
    first input; subsequent inputs need only have ``tree`` as a prefix:

    >>> jax.tree_util.tree_map(lambda x, y: [x] + y, [5, 6], [[7, 9], [1, 2]])
    [[5, 7, 9], [6, 1, 2]]
  """
  leaves, treedef = tree_flatten(tree, is_leaf)
  all_leaves = [leaves] + [treedef.flatten_up_to(r) for r in rest]
  return treedef.unflatten(f(*xs) for xs in zip(*all_leaves))


def build_tree(treedef: PyTreeDef, xs: Any) -> Any:
  return treedef.from_iterable_tree(xs)


def tree_transpose(outer_treedef: PyTreeDef, inner_treedef: PyTreeDef,
                   pytree_to_transpose: Any) -> Any:
  """Transform a tree having tree structure (outer, inner) into one having structure

  (inner, outer).
  """
  flat, treedef = tree_flatten(pytree_to_transpose)
  inner_size = inner_treedef.num_leaves
  outer_size = outer_treedef.num_leaves
  if treedef.num_leaves != (inner_size * outer_size):
    expected_treedef = outer_treedef.compose(inner_treedef)
    raise TypeError(f"Mismatch\n{treedef}\n != \n{expected_treedef}")
  iter_flat = iter(flat)
  lol = [
      [next(iter_flat) for _ in range(inner_size)] for __ in range(outer_size)
  ]
  transposed_lol = zip(*lol)
  subtrees = map(partial(tree_unflatten, outer_treedef), transposed_lol)
  return tree_unflatten(inner_treedef, subtrees)


# TODO(mattjj): remove the Python-side registry when the C++-side registry is
# sufficiently queryable that we can express _replace_nones. That may mean once
# we have a flatten_one function.
_RegistryEntry = collections.namedtuple("_RegistryEntry", ["to_iter", "from_iter"])
_registry = {
    tuple: _RegistryEntry(lambda xs: (xs, None), lambda _, xs: tuple(xs)),
    list: _RegistryEntry(lambda xs: (xs, None), lambda _, xs: list(xs)),
    dict: _RegistryEntry(lambda xs: unzip2(sorted(xs.items()))[::-1],
                         lambda keys, xs: dict(zip(keys, xs))),
    type(None): _RegistryEntry(lambda z: ((), None), lambda _, xs: None),
}

def _replace_nones(sentinel, tree):
  """Replaces ``None`` in ``tree`` with ``sentinel``."""
  if tree is None:
    return sentinel
  else:
    handler = _registry.get(type(tree))
    if handler:
      children, metadata = handler.to_iter(tree)
      proc_children = [_replace_nones(sentinel, child) for child in children]
      return handler.from_iter(metadata, proc_children)
    elif isinstance(tree, tuple) and hasattr(tree, "_fields"):
      # handle namedtuple as a special case, based on heuristic
      children = iter(tree)
      proc_children = [_replace_nones(sentinel, child) for child in children]
      return type(tree)(*proc_children)
    else:
      return tree


no_initializer = object()


@overload
def tree_reduce(function: Callable[[T, Any], T],
                tree: Any,
                *,
                is_leaf: Callable[[Any], bool] | None = None) -> T:
    ...


@overload
def tree_reduce(function: Callable[[T, Any], T],
                tree: Any,
                initializer: T,
                is_leaf: Callable[[Any], bool] | None = None) -> T:
    ...


def tree_reduce(function: Callable[[T, Any], T],
                tree: Any,
                initializer: Any = no_initializer,
                is_leaf: Callable[[Any], bool] | None = None) -> T:
  if initializer is no_initializer:
    return functools.reduce(function, tree_leaves(tree, is_leaf=is_leaf))
  else:
    return functools.reduce(function, tree_leaves(tree, is_leaf=is_leaf), initializer)

def tree_all(tree: Any) -> bool:
  return all(tree_leaves(tree))


register_pytree_node(
  collections.OrderedDict,
  lambda x: (tuple(x.values()), tuple(x.keys())),
  lambda keys, values: collections.OrderedDict(safe_zip(keys, values)))

register_pytree_node(
  collections.defaultdict,
  lambda x: (tuple(x.values()), (x.default_factory, tuple(x.keys()))),
  lambda s, values: collections.defaultdict(s[0], safe_zip(s[1], values)))  # type: ignore[index,call-overload]


class _HashableCallableShim:
  """Object that delegates __call__, __hash__, and __eq__ to another object."""

  def __init__(self, fun):
    self.fun = fun

  def __call__(self, *args, **kw):
    return self.fun(*args, **kw)

  def __hash__(self):
    return hash(self.fun)

  def __eq__(self, other):
    if isinstance(other, _HashableCallableShim):
      return self.fun == other.fun
    return self.fun == other

  def __repr__(self):
    return f'_HashableCallableShim({repr(self.fun)})'


class Partial(functools.partial):
  """A version of functools.partial that works in pytrees.

  Use it for partial function evaluation in a way that is compatible with JAX's
  transformations, e.g., ``Partial(func, *args, **kwargs)``.

  (You need to explicitly opt-in to this behavior because we didn't want to give
  functools.partial different semantics than normal function closures.)

  For example, here is a basic usage of ``Partial`` in a manner similar to
  ``functools.partial``:

  >>> import jax.numpy as jnp
  >>> add_one = Partial(jnp.add, 1)
  >>> add_one(2)
  Array(3, dtype=int32, weak_type=True)

  Pytree compatibility means that the resulting partial function can be passed
  as an argument within transformed JAX functions, which is not possible with a
  standard ``functools.partial`` function:

  >>> from jax import jit
  >>> @jit
  ... def call_func(f, *args):
  ...   return f(*args)
  ...
  >>> call_func(add_one, 2)
  Array(3, dtype=int32, weak_type=True)

  Passing zero arguments to ``Partial`` effectively wraps the original function,
  making it a valid argument in JAX transformed functions:

  >>> call_func(Partial(jnp.add), 1, 2)
  Array(3, dtype=int32, weak_type=True)

  Had we passed ``jnp.add`` to ``call_func`` directly, it would have resulted in
  a
  ``TypeError``.

  Note that if the result of ``Partial`` is used in the context where the
  value is traced, it results in all bound arguments being traced when passed
  to the partially-evaluated function:

  >>> print_zero = Partial(print, 0)
  >>> print_zero()
  0
  >>> call_func(print_zero)  # doctest:+ELLIPSIS
  Traced<ShapedArray(int32[], weak_type=True)>with<DynamicJaxprTrace...>
  """

  def __new__(klass, func, *args, **kw):
    # In Python 3.10+, if func is itself a functools.partial instance,
    # functools.partial.__new__ would merge the arguments of this Partial
    # instance with the arguments of the func. We box func in a class that does
    # not (yet) have a `func` attribute to defeat this optimization, since we
    # care exactly which arguments are considered part of the pytree.
    if isinstance(func, functools.partial):
      original_func = func
      func = _HashableCallableShim(original_func)
      out = super().__new__(klass, func, *args, **kw)
      func.func = original_func.func
      func.args = original_func.args
      func.keywords = original_func.keywords
      return out
    else:
      return super().__new__(klass, func, *args, **kw)


register_pytree_node(
    Partial,
    lambda partial_: ((partial_.args, partial_.keywords), partial_.func),
    lambda func, xs: Partial(func, *xs[0], **xs[1]),  # type: ignore[index]
)


def broadcast_prefix(prefix_tree: Any, full_tree: Any,
                     is_leaf: Callable[[Any], bool] | None = None
                     ) -> list[Any]:
  # If prefix_tree is not a tree prefix of full_tree, this code can raise a
  # ValueError; use prefix_errors to find disagreements and raise more precise
  # error messages.
  result = []
  num_leaves = lambda t: tree_structure(t).num_leaves
  add_leaves = lambda x, subtree: result.extend([x] * num_leaves(subtree))
  tree_map(add_leaves, prefix_tree, full_tree, is_leaf=is_leaf)
  return result

def flatten_one_level(pytree: Any) -> tuple[list[Any], Hashable]:
  """Flatten the given pytree node by one level.

  Args:
    pytree: A valid pytree node, either built-in or registered via
      ``register_pytree_node`` or ``register_pytree_with_keys``.

  Returns:
    A pair of the pytree's flattened children and its hashable metadata.

  Raises:
    ValueError: If the given pytree is not a built-in or registered container
    via ``register_pytree_node`` or ``register_pytree_with_keys``.
  """
  handler = _registry.get(type(pytree))
  if handler:
    children, meta = handler.to_iter(pytree)
    return list(children), meta
  elif isinstance(pytree, tuple) and hasattr(pytree, '_fields'):
    # handle namedtuple as a special case, based on heuristic
    return [getattr(pytree, s) for s in pytree._fields], None
  else:
    raise ValueError(f"can't tree-flatten type: {type(pytree)}")

def prefix_errors(prefix_tree: Any, full_tree: Any,
                  is_leaf: Callable[[Any], bool] | None = None,
                  ) -> list[Callable[[str], ValueError]]:
  return list(_prefix_error((), prefix_tree, full_tree, is_leaf))

def equality_errors(
    tree1: Any, tree2: Any, is_leaf: Callable[[Any], bool] | None = None,
) -> Iterable[tuple[KeyPath, str, str, str]]:
  """Helper to describe structural differences between two pytrees.

  Args:
    tree1, tree2: pytrees to compare.

  Usage:

    raise Exception(
        "Value 1 and value 2 must have the same pytree structure, but they have "
        "the following structural differences:\n" +
        ("\n".join(
           f"   - {keystr(path)} is a {thing1} in value 1 and a {thing2} in "
           f" value 2, so {explanation}.\n"
           for path, thing1, thing2, explanation
           in equality_errors(val1, val2))))
  """
  yield from _equality_errors((), tree1, tree2, is_leaf)

# TODO(mattjj): maybe share some logic with _prefix_error?
def _equality_errors(path, t1, t2, is_leaf):
  # If both are leaves, this isn't a structure equality error.
  if (treedef_is_strict_leaf(tree_structure(t1, is_leaf=is_leaf)) and
      treedef_is_strict_leaf(tree_structure(t2, is_leaf=is_leaf))): return

  # The trees may disagree because they are different types:
  if type(t1) != type(t2):
    yield path, str(type(t1)), str(type(t2)), 'their Python types differ'
    return  # no more errors to find

  # Or they may disagree because their roots have different numbers or keys of
  # children (with special-case handling of list/tuple):
  if isinstance(t1, (list, tuple)):
    assert type(t1) == type(t2)
    if len(t1) != len(t2):
      yield (path,
             f'{type(t1).__name__} of length {len(t1)}',
             f'{type(t2).__name__} of length {len(t2)}',
             'the lengths do not match')
      return  # no more errors to find
  t1_children, t1_meta = flatten_one_level(t1)
  t2_children, t2_meta = flatten_one_level(t2)
  t1_keys, t2_keys = _child_keys(t1), _child_keys(t2)
  try:
    diff = ' '.join(repr(k.key) for k in
                    set(t1_keys).symmetric_difference(set(t2_keys)))
  except:
    diff = ''
  if len(t1_children) != len(t2_children):
    yield (path,
           f'{type(t1)} with {len(t1_children)} child'
           f'{"ren" if len(t1_children) > 1 else ""}',
           f'{type(t2)} with {len(t2_children)} child'
           f'{"ren" if len(t2_children) > 1 else ""}',
           'the numbers of children do not match' +
           (diff and f', with the symmetric difference of key sets: {{{diff}}}')
           )
    return  # no more errors to find

  # Or they may disagree if their roots have different pytree metadata:
  if t1_meta != t2_meta:
    yield (path,
           f'{type(t1)} with pytree metadata {t1_meta}',
           f'{type(t2)} with pytree metadata {t2_meta}',
           'the pytree node metadata does not match')
    return  # no more errors to find

  # If the root types and numbers of children agree, there must be a mismatch in
  # a subtree, so recurse:
  assert t1_keys == t2_keys, \
      f"equal pytree nodes gave different tree keys: {t1_keys} and {t2_keys}"
  for k, c1, c2 in zip(t1_keys, t1_children, t2_children):
    yield from _equality_errors((*path, k), c1, c2, is_leaf)


# TODO(ivyzheng): Remove old APIs when all users migrated.

class _DeprecatedKeyPathEntry(NamedTuple):
  key: Any

  def pprint(self) -> str:
    assert False  # must override

class GetitemKeyPathEntry(_DeprecatedKeyPathEntry):
  def pprint(self) -> str:
    return f'[{repr(self.key)}]'
  def __str__(self):
    return self.pprint()

class AttributeKeyPathEntry(_DeprecatedKeyPathEntry):
  def pprint(self) -> str:
    return f'.{self.key}'
  def __str__(self):
    return self.pprint()

class FlattenedKeyPathEntry(_DeprecatedKeyPathEntry):  # fallback
  def pprint(self) -> str:
    return f'[<flat index {self.key}>]'
  def __str__(self):
    return self.pprint()


@dataclass(frozen=True)
class SequenceKey():
  idx: int
  def __str__(self):
    return f'[{repr(self.idx)}]'

@dataclass(frozen=True)
class DictKey():
  key: Hashable
  def __str__(self):
    return f'[{repr(self.key)}]'

@dataclass(frozen=True)
class GetAttrKey():
  name: str
  def __str__(self):
    return f'.{self.name}'

@dataclass(frozen=True)
class FlattenedIndexKey():
  key: int
  def __str__(self):
    return f'[<flat index {self.key}>]'

BuiltInKeyEntry = Union[SequenceKey, DictKey, GetAttrKey, FlattenedIndexKey]

KeyEntry = TypeVar("KeyEntry", bound=Hashable)
KeyPath = tuple[KeyEntry, ...]

def keystr(keys: KeyPath):
  """Helper to pretty-print a tuple of keys.

  Args:
    keys: A tuple of ``KeyEntry`` or any class that can be converted to string.

  Returns:
    A string that joins all string representations of the keys.
  """
  return ''.join([str(k) for k in keys])


class _RegistryWithKeypathsEntry(NamedTuple):
  flatten_with_keys: Callable[..., Any]
  unflatten_func: Callable[..., Any]


def register_keypaths(
    ty: type[T], handler: Callable[[T], tuple[KeyEntry, ...]]
) -> None:
  """[Deprecated] Register the method to get keypaths for type.

  Please use ``register_pytree_with_keys`` instead.

  Only works if the type was already registered with ``register_pytree_node``.
  """
  warnings.warn(
      (
          "jax.tree_util.register_keypaths is deprecated, and will be removed"
          " in a future release. Please use `register_pytree_with_keys()`"
          " instead."
      ),
      category=FutureWarning,
      stacklevel=2,
  )
  _register_keypaths(ty, handler)


def _register_keypaths(
    ty: type[T], handler: Callable[[T], tuple[KeyEntry, ...]]
) -> None:
  def flatten_with_keys(xs):
    children, treedef = _registry[ty].to_iter(xs)
    return list(zip(handler(xs), children)), treedef
  if ty in _registry:
    _registry_with_keypaths[ty] = _RegistryWithKeypathsEntry(
        flatten_with_keys, _registry[ty].from_iter
    )


_registry_with_keypaths = {}

_register_keypaths(
    tuple, lambda xs: tuple(SequenceKey(i) for i in range(len(xs)))
)
_register_keypaths(
    list, lambda xs: tuple(SequenceKey(i) for i in range(len(xs)))
)
_register_keypaths(dict, lambda xs: tuple(DictKey(k) for k in sorted(xs)))

_register_keypaths(
    collections.defaultdict, lambda x: tuple(DictKey(k) for k in x.keys())
)

_register_keypaths(
    collections.OrderedDict, lambda x: tuple(DictKey(k) for k in x.keys())
)


def register_pytree_with_keys(
    nodetype: type[T],
    flatten_with_keys: Callable[
        [T], tuple[Iterable[tuple[KeyEntry, Any]], _AuxData]
    ],
    unflatten_func: Callable[[_AuxData, Iterable[Any]], T],
    flatten_func: None | (
        Callable[[T], tuple[Iterable[Any], _AuxData]]
    ) = None,
):
  """Extends the set of types that are considered internal nodes in pytrees.

  This is a more powerful alternative to ``register_pytree_node`` that allows
  you to access each pytree leaf's key path when flattening and tree-mapping.

  Args:
    nodetype: a Python type to treat as an internal pytree node.
    flatten_with_keys: a function to be used during flattening, taking a value
      of type ``nodetype`` and returning a pair, with (1) an iterable for tuples
      of each key path and its child, and (2) some hashable auxiliary data to be
      stored in the treedef and to be passed to the ``unflatten_func``.
    unflatten_func: a function taking two arguments: the auxiliary data that was
      returned by ``flatten_func`` and stored in the treedef, and the
      unflattened children. The function should return an instance of
      ``nodetype``.
    flatten_func: an optional function similar to ``flatten_with_keys``, but
      returns only children and auxiliary data. It must return the children
      in the same order as ``flatten_with_keys``, and return the same aux data.
      This argument is optional and only needed for faster traversal when
      calling functions without keys like ``tree_map`` and ``tree_flatten``.
  """
  if not flatten_func:
    def flatten_func_impl(tree):
      key_children, treedef = flatten_with_keys(tree)
      return [c for _, c in key_children], treedef
    flatten_func = flatten_func_impl

  register_pytree_node(nodetype, flatten_func, unflatten_func)
  _registry_with_keypaths[nodetype] = _RegistryWithKeypathsEntry(
      flatten_with_keys, unflatten_func
  )


def register_pytree_with_keys_class(cls: U) -> U:
  """Extends the set of types that are considered internal nodes in pytrees.

  This function is similar to ``register_pytree_node_class``, but requires a
  class that defines how it could be flattened with keys.

  It is a thin wrapper around ``register_pytree_with_keys``, and
  provides a class-oriented interface::

    @register_pytree_with_keys_class
    class Special:
      def __init__(self, x, y):
        self.x = x
        self.y = y
      def tree_flatten_with_keys(self):
        return (((GetAttrKey('x'), self.x), (GetAttrKey('y'), self.y)), None)
      @classmethod
      def tree_unflatten(cls, aux_data, children):
        return cls(*children)
  """
  flatten_func = (
      op.methodcaller("tree_flatten") if hasattr(cls, "tree_flatten") else None
  )
  register_pytree_with_keys(
      cls, op.methodcaller("tree_flatten_with_keys"), cls.tree_unflatten,
      flatten_func
  )
  return cls


def tree_flatten_with_path(
    tree: Any, is_leaf: Callable[[Any], bool] | None = None
) -> tuple[list[tuple[KeyPath, Any]], PyTreeDef]:
  """Flattens a pytree like ``tree_flatten``, but also returns each leaf's key path.

  Args:
    tree: a pytree to flatten. If it contains a custom type, it must be
      registered with ``register_pytree_with_keys``.
  Returns:
    A pair which the first element is a list of key-leaf pairs, each of
    which contains a leaf and its key path. The second element is a treedef
    representing the structure of the flattened tree.
  """
  _, tree_def = tree_flatten(tree, is_leaf)
  return _generate_key_paths(tree, is_leaf), tree_def


def tree_leaves_with_path(
    tree: Any, is_leaf: Callable[[Any], bool] | None = None
) -> list[tuple[KeyPath, Any]]:
  """Gets the leaves of a pytree like ``tree_leaves`` and returns each leaf's key path.

  Args:
    tree: a pytree. If it contains a custom type, it must be registered with
      ``register_pytree_with_keys``.
  Returns:
    A list of key-leaf pairs, each of which contains a leaf and its key path.
  """
  return _generate_key_paths(tree, is_leaf)


def generate_key_paths(
    tree: Any, is_leaf: Callable[[Any], bool] | None = None
) -> list[tuple[KeyPath, Any]]:
  return list(_generate_key_paths_((), tree, is_leaf))
_generate_key_paths = generate_key_paths  # alias for backward compat


# The overall logic should be same as PyTreeDef::FlattenIntoImpl
def _generate_key_paths_(
    key_path: KeyPath,
    tree: Any,
    is_leaf: Callable[[Any], bool] | None = None,
) -> Iterable[tuple[KeyPath, Any]]:
  if is_leaf and is_leaf(tree):
    yield key_path, tree
    return
  key_handler = _registry_with_keypaths.get(type(tree))
  handler = _registry.get(type(tree))
  if key_handler:
    key_children, _ = key_handler.flatten_with_keys(tree)
    for k, c in key_children:
      yield from _generate_key_paths_((*key_path, k), c, is_leaf)
  elif handler:
    children, _ = handler.to_iter(tree)
    for i, c in enumerate(children):
      k = FlattenedIndexKey(i)
      yield from _generate_key_paths_((*key_path, k), c, is_leaf)
  elif isinstance(tree, tuple) and hasattr(tree, '_fields'):
    # handle namedtuple as a special case, based on heuristic
    key_children = [(GetAttrKey(s), getattr(tree, s)) for s in tree._fields]
    for k, c in key_children:
      yield from _generate_key_paths_(tuple((*key_path, k)), c, is_leaf)
  else:
    yield key_path, tree  # strict leaf type


def tree_map_with_path(f: Callable[..., Any],
                       tree: Any, *rest: Any,
                       is_leaf: Callable[[Any], bool] | None = None) -> Any:
  """Maps a multi-input function over pytree key path and args to produce a new pytree.

  This is a more powerful alternative of ``tree_map`` that can take the key path
  of each leaf as input argument as well.

  Args:
    f: function that takes ``2 + len(rest)`` arguments, aka. the key path and
      each corresponding leaves of the pytrees.
    tree: a pytree to be mapped over, with each leaf's key path as the first
      positional argument and the leaf itself as the second argument to ``f``.
    *rest: a tuple of pytrees, each of which has the same structure as ``tree``
      or has ``tree`` as a prefix.

  Returns:
    A new pytree with the same structure as ``tree`` but with the value at each
    leaf given by ``f(kp, x, *xs)`` where ``kp`` is the key path of the leaf at
    the corresponding leaf in ``tree``, ``x`` is the leaf value and ``xs`` is
    the tuple of values at corresponding nodes in ``rest``.
  """

  keypath_leaves, treedef = tree_flatten_with_path(tree, is_leaf)
  keypath_leaves = list(zip(*keypath_leaves))
  all_keypath_leaves = keypath_leaves + [treedef.flatten_up_to(r) for r in rest]
  return treedef.unflatten(f(*xs) for xs in zip(*all_keypath_leaves))


def _child_keys(pytree: Any) -> KeyPath:
  assert not treedef_is_strict_leaf(tree_structure(pytree))
  handler = _registry_with_keypaths.get(type(pytree))
  if handler:
    return tuple(k for k, _ in handler.flatten_with_keys(pytree)[0])
  elif isinstance(pytree, tuple) and hasattr(pytree, '_fields'):
    # handle namedtuple as a special case, based on heuristic
    return tuple(GetAttrKey(s) for s in pytree._fields)
  else:
    num_children = len(treedef_children(tree_structure(pytree)))
    return tuple(FlattenedIndexKey(i) for i in range(num_children))



def _prefix_error(
    key_path: KeyPath,
    prefix_tree: Any,
    full_tree: Any,
    is_leaf: Callable[[Any], bool] | None = None,
) -> Iterable[Callable[[str], ValueError]]:
  # A leaf is a valid prefix of any tree:
  if treedef_is_strict_leaf(tree_structure(prefix_tree, is_leaf=is_leaf)):
    return

  # The subtrees may disagree because their roots are of different types:
  if type(prefix_tree) != type(full_tree):
    yield lambda name: ValueError(
      "pytree structure error: different types at key path\n"
      f"    {{name}}{keystr(key_path)}\n"
      f"At that key path, the prefix pytree {{name}} has a subtree of type\n"
      f"    {type(prefix_tree)}\n"
      f"but at the same key path the full pytree has a subtree of different type\n"
      f"    {type(full_tree)}.".format(name=name))
    return  # don't look for more errors in this subtree

  # Or they may disagree if their roots have different numbers or keys of
  # children. Because both prefix_tree and full_tree have the same type at this
  # point, and because prefix_tree is not a leaf, each can be flattened once:
  prefix_tree_children, prefix_tree_meta = flatten_one_level(prefix_tree)
  full_tree_children, full_tree_meta = flatten_one_level(full_tree)
  prefix_tree_keys = _child_keys(prefix_tree)
  full_tree_keys = _child_keys(full_tree)
  # First we check special case types (list and tuple, though if they were
  # pytrees we could check strings and sets here, basically Sequences) so that
  # we can report length disagreement rather than integer keys:
  if isinstance(prefix_tree, (list, tuple)):
    if len(prefix_tree) != len(full_tree):
      ty = type(prefix_tree)
      yield lambda name: ValueError(
          f"pytree structure error: different lengths of {ty.__name__} at key path\n"
          f"    {{name}}{keystr(key_path)}\n"
          f"At that key path, the prefix pytree {{name}} has a subtree of type "
          f"{ty.__name__} of length {len(prefix_tree)}, but the full pytree "
          f"has a subtree of the same type but of length {len(full_tree)}."
          .format(name=name))
      return  # don't look for more errors in this subtree
  else:
    # Next we handle the general case of checking child keys.
    try:
      diff = set(prefix_tree_keys).symmetric_difference(set(full_tree_keys))
    except:
      diff = None
    if len(prefix_tree_children) != len(full_tree_children):
      yield lambda name: ValueError(
        "pytree structure error: different numbers of pytree children at key path\n"
        f"    {{name}}{keystr(key_path)}\n"
        f"At that key path, the prefix pytree {{name}} has a subtree of type\n"
        f"    {type(prefix_tree)}\n"
        f"with {len(prefix_tree_children)} child keys\n"
        f"    {' '.join(str(k.key) for k in prefix_tree_keys)}\n"
        f"but at the same key path the full pytree has a subtree of the same "
        f"type but with {len(full_tree_children)} child keys\n"
        f"    {' '.join(str(k.key) for k in full_tree_keys)}\n"
        .format(name=name)
        + ("" if diff is None else
           f"so the symmetric difference on key sets is\n"
           f"    {' '.join(str(k.key) for k in diff)}"))
      return  # don't look for more errors in this subtree

  # Or they may disagree if their roots have different pytree metadata:
  if prefix_tree_meta != full_tree_meta:
    prefix_tree_meta_str = str(prefix_tree_meta)
    full_tree_meta_str = str(full_tree_meta)
    metadata_diff = textwrap.indent(
        "\n".join(
            difflib.ndiff(prefix_tree_meta_str.splitlines(),
                          full_tree_meta_str.splitlines())),
        prefix="    ")
    yield lambda name: ValueError(
      "pytree structure error: different pytree metadata at key path\n"
      f"    {{name}}{keystr(key_path)}\n"
      f"At that key path, the prefix pytree {{name}} has a subtree of type\n"
      f"    {type(prefix_tree)}\n"
      f"with metadata\n"
      f"    {prefix_tree_meta_str}\n"
      f"but at the same key path the full pytree has a subtree of the same "
      f"type but with metadata\n"
      f"    {full_tree_meta_str}\n"
      f"so the diff in the metadata at these pytree nodes is\n"
      f"{metadata_diff}".format(name=name))
    return  # don't look for more errors in this subtree

  # If the root types and numbers of children agree, there must be an error
  # in a subtree, so recurse:
  assert prefix_tree_keys == full_tree_keys, \
    ("equal pytree nodes gave differing prefix_tree_keys: "
     f"{prefix_tree_keys} and {full_tree_keys}")
  for k, t1, t2 in zip(prefix_tree_keys, prefix_tree_children, full_tree_children):
    yield from _prefix_error((*key_path, k), t1, t2)