node.rs.html -- source
Description: Source to the Rust file `src/liballoc/collections/btree/node.rs`.
Keywords: rust, rustlang, rust-lang

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    // This is an attempt at an implementation following the ideal
    //
    // ```
    // struct BTreeMap<K, V> {
    //     height: usize,
    //     root: Option<Box<Node<K, V, height>>>
    // }
    //
    // struct Node<K, V, height: usize> {
    //     keys: [K; 2 * B - 1],
    //     vals: [V; 2 * B - 1],
    //     edges: if height > 0 {
    //         [Box<Node<K, V, height - 1>>; 2 * B]
    //     } else { () },
    //     parent: *const Node<K, V, height + 1>,
    //     parent_idx: u16,
    //     len: u16,
    // }
    // ```
    //
    // Since Rust doesn't actually have dependent types and polymorphic recursion,
    // we make do with lots of unsafety.

    // A major goal of this module is to avoid complexity by treating the tree as a generic (if
    // weirdly shaped) container and avoiding dealing with most of the B-Tree invariants. As such,
    // this module doesn't care whether the entries are sorted, which nodes can be underfull, or
    // even what underfull means. However, we do rely on a few invariants:
    //
    // - Trees must have uniform depth/height. This means that every path down to a leaf from a
    //   given node has exactly the same length.
    // - A node of length `n` has `n` keys, `n` values, and (in an internal node) `n + 1` edges.
    //   This implies that even an empty internal node has at least one edge.

    use core::marker::PhantomData;
    use core::mem::{self, MaybeUninit};
    use core::ptr::{self, Unique, NonNull};
    use core::slice;

    use crate::alloc::{Global, Alloc, Layout};
    use crate::boxed::Box;

    const B: usize = 6;
    pub const MIN_LEN: usize = B - 1;
    pub const CAPACITY: usize = 2 * B - 1;

    /// The underlying representation of leaf nodes. Note that it is often unsafe to actually store
    /// these, since only the first `len` keys and values are assumed to be initialized. As such,
    /// these should always be put behind pointers, and specifically behind `BoxedNode` in the owned
    /// case.
    ///
    /// We have a separate type for the header and rely on it matching the prefix of `LeafNode`, in
    /// order to statically allocate a single dummy node to avoid allocations. This struct is
    /// `repr(C)` to prevent them from being reordered. `LeafNode` does not just contain a
    /// `NodeHeader` because we do not want unnecessary padding between `len` and the keys.
    /// Crucially, `NodeHeader` can be safely transmuted to different K and V. (This is exploited
    /// by `as_header`.)
    /// See `into_key_slice` for an explanation of K2. K2 cannot be safely transmuted around
    /// because the size of `NodeHeader` depends on its alignment!
    #[repr(C)]
    struct NodeHeader<K, V, K2 = ()> {
        /// We use `*const` as opposed to `*mut` so as to be covariant in `K` and `V`.
        /// This either points to an actual node or is null.
        parent: *const InternalNode<K, V>,

        /// This node's index into the parent node's `edges` array.
        /// `*node.parent.edges[node.parent_idx]` should be the same thing as `node`.
        /// This is only guaranteed to be initialized when `parent` is non-null.
        parent_idx: MaybeUninit<u16>,

        /// The number of keys and values this node stores.
        ///
        /// This next to `parent_idx` to encourage the compiler to join `len` and
        /// `parent_idx` into the same 32-bit word, reducing space overhead.
        len: u16,

        /// See `into_key_slice`.
        keys_start: [K2; 0],
    }
    #[repr(C)]
    struct LeafNode<K, V> {
        /// We use `*const` as opposed to `*mut` so as to be covariant in `K` and `V`.
        /// This either points to an actual node or is null.
        parent: *const InternalNode<K, V>,

        /// This node's index into the parent node's `edges` array.
        /// `*node.parent.edges[node.parent_idx]` should be the same thing as `node`.
        /// This is only guaranteed to be initialized when `parent` is non-null.
        parent_idx: MaybeUninit<u16>,

        /// The number of keys and values this node stores.
        ///
        /// This next to `parent_idx` to encourage the compiler to join `len` and
        /// `parent_idx` into the same 32-bit word, reducing space overhead.
        len: u16,

        /// The arrays storing the actual data of the node. Only the first `len` elements of each
        /// array are initialized and valid.
        keys: [MaybeUninit<K>; CAPACITY],
        vals: [MaybeUninit<V>; CAPACITY],
    }

    impl<K, V> LeafNode<K, V> {
        /// Creates a new `LeafNode`. Unsafe because all nodes should really be hidden behind
        /// `BoxedNode`, preventing accidental dropping of uninitialized keys and values.
        unsafe fn new() -> Self {
            LeafNode {
                // As a general policy, we leave fields uninitialized if they can be, as this should
                // be both slightly faster and easier to track in Valgrind.
                keys: [MaybeUninit::UNINIT; CAPACITY],
                vals: [MaybeUninit::UNINIT; CAPACITY],
                parent: ptr::null(),
                parent_idx: MaybeUninit::uninit(),
                len: 0
            }
        }
    }

    impl<K, V> NodeHeader<K, V> {
        fn is_shared_root(&self) -> bool {
            ptr::eq(self, &EMPTY_ROOT_NODE as *const _ as *const _)
        }
    }

    // We need to implement Sync here in order to make a static instance.
    unsafe impl Sync for NodeHeader<(), ()> {}

    // An empty node used as a placeholder for the root node, to avoid allocations.
    // We use just a header in order to save space, since no operation on an empty tree will
    // ever take a pointer past the first key.
    static EMPTY_ROOT_NODE: NodeHeader<(), ()> = NodeHeader {
        parent: ptr::null(),
        parent_idx: MaybeUninit::uninit(),
        len: 0,
        keys_start: [],
    };

    /// The underlying representation of internal nodes. As with `LeafNode`s, these should be hidden
    /// behind `BoxedNode`s to prevent dropping uninitialized keys and values. Any pointer to an
    /// `InternalNode` can be directly casted to a pointer to the underlying `LeafNode` portion of the
    /// node, allowing code to act on leaf and internal nodes generically without having to even check
    /// which of the two a pointer is pointing at. This property is enabled by the use of `repr(C)`.
    #[repr(C)]
    struct InternalNode<K, V> {
        data: LeafNode<K, V>,

        /// The pointers to the children of this node. `len + 1` of these are considered
        /// initialized and valid.
        edges: [MaybeUninit<BoxedNode<K, V>>; 2 * B],
    }

    impl<K, V> InternalNode<K, V> {
        /// Creates a new `InternalNode`.
        ///
        /// This is unsafe for two reasons. First, it returns an `InternalNode` by value, risking
        /// dropping of uninitialized fields. Second, an invariant of internal nodes is that `len + 1`
        /// edges are initialized and valid, meaning that even when the node is empty (having a
        /// `len` of 0), there must be one initialized and valid edge. This function does not set up
        /// such an edge.
        unsafe fn new() -> Self {
            InternalNode {
                data: LeafNode::new(),
                edges: [MaybeUninit::UNINIT; 2*B]
            }
        }
    }

    /// An owned pointer to a node. This basically is either `Box<LeafNode<K, V>>` or
    /// `Box<InternalNode<K, V>>`. However, it contains no information as to which of the two types
    /// of nodes is actually behind the box, and, partially due to this lack of information, has no
    /// destructor.
    struct BoxedNode<K, V> {
        ptr: Unique<LeafNode<K, V>>
    }

    impl<K, V> BoxedNode<K, V> {
        fn from_leaf(node: Box<LeafNode<K, V>>) -> Self {
            BoxedNode { ptr: Box::into_unique(node) }
        }

        fn from_internal(node: Box<InternalNode<K, V>>) -> Self {
            unsafe {
                BoxedNode { ptr: Unique::new_unchecked(Box::into_raw(node) as *mut LeafNode<K, V>) }
            }
        }

        unsafe fn from_ptr(ptr: NonNull<LeafNode<K, V>>) -> Self {
            BoxedNode { ptr: Unique::from(ptr) }
        }

        fn as_ptr(&self) -> NonNull<LeafNode<K, V>> {
            NonNull::from(self.ptr)
        }
    }

    /// An owned tree. Note that despite being owned, this does not have a destructor,
    /// and must be cleaned up manually.
    pub struct Root<K, V> {
        node: BoxedNode<K, V>,
        height: usize
    }

    unsafe impl<K: Sync, V: Sync> Sync for Root<K, V> { }
    unsafe impl<K: Send, V: Send> Send for Root<K, V> { }

    impl<K, V> Root<K, V> {
        pub fn is_shared_root(&self) -> bool {
            self.as_ref().is_shared_root()
        }

        pub fn shared_empty_root() -> Self {
            Root {
                node: unsafe {
                    BoxedNode::from_ptr(NonNull::new_unchecked(
                        &EMPTY_ROOT_NODE as *const _ as *const LeafNode<K, V> as *mut _
                    ))
                },
                height: 0,
            }
        }

        pub fn new_leaf() -> Self {
            Root {
                node: BoxedNode::from_leaf(Box::new(unsafe { LeafNode::new() })),
                height: 0
            }
        }

        pub fn as_ref(&self)
                -> NodeRef<marker::Immut<'_>, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.height,
                node: self.node.as_ptr(),
                root: self as *const _ as *mut _,
                _marker: PhantomData,
            }
        }

        pub fn as_mut(&mut self)
                -> NodeRef<marker::Mut<'_>, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.height,
                node: self.node.as_ptr(),
                root: self as *mut _,
                _marker: PhantomData,
            }
        }

        pub fn into_ref(self)
                -> NodeRef<marker::Owned, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.height,
                node: self.node.as_ptr(),
                root: ptr::null_mut(), // FIXME: Is there anything better to do here?
                _marker: PhantomData,
            }
        }

        /// Adds a new internal node with a single edge, pointing to the previous root, and make that
        /// new node the root. This increases the height by 1 and is the opposite of `pop_level`.
        pub fn push_level(&mut self)
                -> NodeRef<marker::Mut<'_>, K, V, marker::Internal> {
            debug_assert!(!self.is_shared_root());
            let mut new_node = Box::new(unsafe { InternalNode::new() });
            new_node.edges[0].write(unsafe { BoxedNode::from_ptr(self.node.as_ptr()) });

            self.node = BoxedNode::from_internal(new_node);
            self.height += 1;

            let mut ret = NodeRef {
                height: self.height,
                node: self.node.as_ptr(),
                root: self as *mut _,
                _marker: PhantomData
            };

            unsafe {
                ret.reborrow_mut().first_edge().correct_parent_link();
            }

            ret
        }

        /// Removes the root node, using its first child as the new root. This cannot be called when
        /// the tree consists only of a leaf node. As it is intended only to be called when the root
        /// has only one edge, no cleanup is done on any of the other children are elements of the root.
        /// This decreases the height by 1 and is the opposite of `push_level`.
        pub fn pop_level(&mut self) {
            debug_assert!(self.height > 0);

            let top = self.node.ptr;

            self.node = unsafe {
                BoxedNode::from_ptr(self.as_mut()
                                        .cast_unchecked::<marker::Internal>()
                                        .first_edge()
                                        .descend()
                                        .node)
            };
            self.height -= 1;
            unsafe { (*self.as_mut().as_leaf_mut()).parent = ptr::null(); }

            unsafe {
                Global.dealloc(NonNull::from(top).cast(), Layout::new::<InternalNode<K, V>>());
            }
        }
    }

    // N.B. `NodeRef` is always covariant in `K` and `V`, even when the `BorrowType`
    // is `Mut`. This is technically wrong, but cannot result in any unsafety due to
    // internal use of `NodeRef` because we stay completely generic over `K` and `V`.
    // However, whenever a public type wraps `NodeRef`, make sure that it has the
    // correct variance.
    /// A reference to a node.
    ///
    /// This type has a number of parameters that controls how it acts:
    /// - `BorrowType`: This can be `Immut<'a>` or `Mut<'a>` for some `'a` or `Owned`.
    ///    When this is `Immut<'a>`, the `NodeRef` acts roughly like `&'a Node`,
    ///    when this is `Mut<'a>`, the `NodeRef` acts roughly like `&'a mut Node`,
    ///    and when this is `Owned`, the `NodeRef` acts roughly like `Box<Node>`.
    /// - `K` and `V`: These control what types of things are stored in the nodes.
    /// - `Type`: This can be `Leaf`, `Internal`, or `LeafOrInternal`. When this is
    ///   `Leaf`, the `NodeRef` points to a leaf node, when this is `Internal` the
    ///   `NodeRef` points to an internal node, and when this is `LeafOrInternal` the
    ///   `NodeRef` could be pointing to either type of node.
    ///   Note that in case of a leaf node, this might still be the shared root!  Only turn
    ///   this into a `LeafNode` reference if you know it is not a root!  Shared references
    ///   must be dereferencable *for the entire size of their pointee*, so `&InternalNode`
    ///   pointing to the shared root is UB.
    ///   Turning this into a `NodeHeader` is always safe.
    pub struct NodeRef<BorrowType, K, V, Type> {
        height: usize,
        node: NonNull<LeafNode<K, V>>,
        // This is null unless the borrow type is `Mut`
        root: *const Root<K, V>,
        _marker: PhantomData<(BorrowType, Type)>
    }

    impl<'a, K: 'a, V: 'a, Type> Copy for NodeRef<marker::Immut<'a>, K, V, Type> { }
    impl<'a, K: 'a, V: 'a, Type> Clone for NodeRef<marker::Immut<'a>, K, V, Type> {
        fn clone(&self) -> Self {
            *self
        }
    }

    unsafe impl<BorrowType, K: Sync, V: Sync, Type> Sync
        for NodeRef<BorrowType, K, V, Type> { }

    unsafe impl<'a, K: Sync + 'a, V: Sync + 'a, Type> Send
       for NodeRef<marker::Immut<'a>, K, V, Type> { }
    unsafe impl<'a, K: Send + 'a, V: Send + 'a, Type> Send
       for NodeRef<marker::Mut<'a>, K, V, Type> { }
    unsafe impl<K: Send, V: Send, Type> Send
       for NodeRef<marker::Owned, K, V, Type> { }

    impl<BorrowType, K, V> NodeRef<BorrowType, K, V, marker::Internal> {
        fn as_internal(&self) -> &InternalNode<K, V> {
            unsafe {
                &*(self.node.as_ptr() as *mut InternalNode<K, V>)
            }
        }
    }

    impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Internal> {
        fn as_internal_mut(&mut self) -> &mut InternalNode<K, V> {
            unsafe {
                &mut *(self.node.as_ptr() as *mut InternalNode<K, V>)
            }
        }
    }

    impl<BorrowType, K, V, Type> NodeRef<BorrowType, K, V, Type> {
        /// Finds the length of the node. This is the number of keys or values. In an
        /// internal node, the number of edges is `len() + 1`.
        pub fn len(&self) -> usize {
            self.as_header().len as usize
        }

        /// Returns the height of this node in the whole tree. Zero height denotes the
        /// leaf level.
        pub fn height(&self) -> usize {
            self.height
        }

        /// Removes any static information about whether this node is a `Leaf` or an
        /// `Internal` node.
        pub fn forget_type(self) -> NodeRef<BorrowType, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.height,
                node: self.node,
                root: self.root,
                _marker: PhantomData
            }
        }

        /// Temporarily takes out another, immutable reference to the same node.
        fn reborrow(&self) -> NodeRef<marker::Immut<'_>, K, V, Type> {
            NodeRef {
                height: self.height,
                node: self.node,
                root: self.root,
                _marker: PhantomData
            }
        }

        /// Assert that this is indeed a proper leaf node, and not the shared root.
        unsafe fn as_leaf(&self) -> &LeafNode<K, V> {
            self.node.as_ref()
        }

        fn as_header(&self) -> &NodeHeader<K, V> {
            unsafe {
                &*(self.node.as_ptr() as *const NodeHeader<K, V>)
            }
        }

        pub fn is_shared_root(&self) -> bool {
            self.as_header().is_shared_root()
        }

        pub fn keys(&self) -> &[K] {
            self.reborrow().into_key_slice()
        }

        fn vals(&self) -> &[V] {
            self.reborrow().into_val_slice()
        }

        /// Finds the parent of the current node. Returns `Ok(handle)` if the current
        /// node actually has a parent, where `handle` points to the edge of the parent
        /// that points to the current node. Returns `Err(self)` if the current node has
        /// no parent, giving back the original `NodeRef`.
        ///
        /// `edge.descend().ascend().unwrap()` and `node.ascend().unwrap().descend()` should
        /// both, upon success, do nothing.
        pub fn ascend(self) -> Result<
            Handle<
                NodeRef<
                    BorrowType,
                    K, V,
                    marker::Internal
                >,
                marker::Edge
            >,
            Self
        > {
            let parent_as_leaf = self.as_header().parent as *const LeafNode<K, V>;
            if let Some(non_zero) = NonNull::new(parent_as_leaf as *mut _) {
                Ok(Handle {
                    node: NodeRef {
                        height: self.height + 1,
                        node: non_zero,
                        root: self.root,
                        _marker: PhantomData
                    },
                    idx: unsafe { usize::from(*self.as_header().parent_idx.as_ptr()) },
                    _marker: PhantomData
                })
            } else {
                Err(self)
            }
        }

        pub fn first_edge(self) -> Handle<Self, marker::Edge> {
            Handle::new_edge(self, 0)
        }

        pub fn last_edge(self) -> Handle<Self, marker::Edge> {
            let len = self.len();
            Handle::new_edge(self, len)
        }

        /// Note that `self` must be nonempty.
        pub fn first_kv(self) -> Handle<Self, marker::KV> {
            debug_assert!(self.len() > 0);
            Handle::new_kv(self, 0)
        }

        /// Note that `self` must be nonempty.
        pub fn last_kv(self) -> Handle<Self, marker::KV> {
            let len = self.len();
            debug_assert!(len > 0);
            Handle::new_kv(self, len - 1)
        }
    }

    impl<K, V> NodeRef<marker::Owned, K, V, marker::Leaf> {
        /// Similar to `ascend`, gets a reference to a node's parent node, but also
        /// deallocate the current node in the process. This is unsafe because the
        /// current node will still be accessible despite being deallocated.
        pub unsafe fn deallocate_and_ascend(self) -> Option<
            Handle<
                NodeRef<
                    marker::Owned,
                    K, V,
                    marker::Internal
                >,
                marker::Edge
            >
        > {
            debug_assert!(!self.is_shared_root());
            let node = self.node;
            let ret = self.ascend().ok();
            Global.dealloc(node.cast(), Layout::new::<LeafNode<K, V>>());
            ret
        }
    }

    impl<K, V> NodeRef<marker::Owned, K, V, marker::Internal> {
        /// Similar to `ascend`, gets a reference to a node's parent node, but also
        /// deallocate the current node in the process. This is unsafe because the
        /// current node will still be accessible despite being deallocated.
        pub unsafe fn deallocate_and_ascend(self) -> Option<
            Handle<
                NodeRef<
                    marker::Owned,
                    K, V,
                    marker::Internal
                >,
                marker::Edge
            >
        > {
            let node = self.node;
            let ret = self.ascend().ok();
            Global.dealloc(node.cast(), Layout::new::<InternalNode<K, V>>());
            ret
        }
    }

    impl<'a, K, V, Type> NodeRef<marker::Mut<'a>, K, V, Type> {
        /// Unsafely asserts to the compiler some static information about whether this
        /// node is a `Leaf`.
        unsafe fn cast_unchecked<NewType>(&mut self)
                -> NodeRef<marker::Mut<'_>, K, V, NewType> {

            NodeRef {
                height: self.height,
                node: self.node,
                root: self.root,
                _marker: PhantomData
            }
        }

        /// Temporarily takes out another, mutable reference to the same node. Beware, as
        /// this method is very dangerous, doubly so since it may not immediately appear
        /// dangerous.
        ///
        /// Because mutable pointers can roam anywhere around the tree and can even (through
        /// `into_root_mut`) mess with the root of the tree, the result of `reborrow_mut`
        /// can easily be used to make the original mutable pointer dangling, or, in the case
        /// of a reborrowed handle, out of bounds.
        // FIXME(@gereeter) consider adding yet another type parameter to `NodeRef` that restricts
        // the use of `ascend` and `into_root_mut` on reborrowed pointers, preventing this unsafety.
        unsafe fn reborrow_mut(&mut self) -> NodeRef<marker::Mut<'_>, K, V, Type> {
            NodeRef {
                height: self.height,
                node: self.node,
                root: self.root,
                _marker: PhantomData
            }
        }

        /// Returns a raw ptr to avoid asserting exclusive access to the entire node.
        fn as_leaf_mut(&mut self) -> *mut LeafNode<K, V> {
            // We are mutable, so we cannot be the root, so accessing this as a leaf is okay.
            self.node.as_ptr()
        }

        fn keys_mut(&mut self) -> &mut [K] {
            unsafe { self.reborrow_mut().into_key_slice_mut() }
        }

        fn vals_mut(&mut self) -> &mut [V] {
            unsafe { self.reborrow_mut().into_val_slice_mut() }
        }
    }

    impl<'a, K: 'a, V: 'a, Type> NodeRef<marker::Immut<'a>, K, V, Type> {
        fn into_key_slice(self) -> &'a [K] {
            // We have to be careful here because we might be pointing to the shared root.
            // In that case, we must not create an `&LeafNode`.  We could just return
            // an empty slice whenever the length is 0 (this includes the shared root),
            // but we want to avoid that run-time check.
            // Instead, we create a slice pointing into the node whenever possible.
            // We can sometimes do this even for the shared root, as the slice will be
            // empty.  We cannot *always* do this because if the type is too highly
            // aligned, the offset of `keys` in a "full node" might be outside the bounds
            // of the header!  So we do an alignment check first, that will be
            // evaluated at compile-time, and only do any run-time check in the rare case
            // that the alignment is very big.
            if mem::align_of::<K>() > mem::align_of::<LeafNode<(), ()>>() && self.is_shared_root() {
                &[]
            } else {
                // Thanks to the alignment check above, we know that `keys` will be
                // in-bounds of some allocation even if this is the shared root!
                // (We might be one-past-the-end, but that is allowed by LLVM.)
                // Getting the pointer is tricky though.  `NodeHeader` does not have a `keys`
                // field because we want its size to not depend on the alignment of `K`
                // (needed becuase `as_header` should be safe).  We cannot call `as_leaf`
                // because we might be the shared root.
                // For this reason, `NodeHeader` has this `K2` parameter (that's usually `()`
                // and hence just adds a size-0-align-1 field, not affecting layout).
                // We know that we can transmute `NodeHeader<K, V, ()>` to `NodeHeader<K, V, K>`
                // because we did the alignment check above, and hence `NodeHeader<K, V, K>`
                // is not bigger than `NodeHeader<K, V, ()>`!  Then we can use `NodeHeader<K, V, K>`
                // to compute the pointer where the keys start.
                // This entire hack will become unnecessary once
                // <https://github.com/rust-lang/rfcs/pull/2582> lands, then we can just take a raw
                // pointer to the `keys` field of `*const InternalNode<K, V>`.

                // This is a non-debug-assert because it can be completely compile-time evaluated.
                assert!(mem::size_of::<NodeHeader<K, V>>() == mem::size_of::<NodeHeader<K, V, K>>());
                let header = self.as_header() as *const _ as *const NodeHeader<K, V, K>;
                let keys = unsafe { &(*header).keys_start as *const _ as *const K };
                unsafe {
                    slice::from_raw_parts(keys, self.len())
                }
            }
        }

        fn into_val_slice(self) -> &'a [V] {
            debug_assert!(!self.is_shared_root());
            // We cannot be the root, so `as_leaf` is okay
            unsafe {
                slice::from_raw_parts(
                    MaybeUninit::first_ptr(&self.as_leaf().vals),
                    self.len()
                )
            }
        }

        fn into_slices(self) -> (&'a [K], &'a [V]) {
            let k = unsafe { ptr::read(&self) };
            (k.into_key_slice(), self.into_val_slice())
        }
    }

    impl<'a, K: 'a, V: 'a, Type> NodeRef<marker::Mut<'a>, K, V, Type> {
        /// Gets a mutable reference to the root itself. This is useful primarily when the
        /// height of the tree needs to be adjusted. Never call this on a reborrowed pointer.
        pub fn into_root_mut(self) -> &'a mut Root<K, V> {
            unsafe {
                &mut *(self.root as *mut Root<K, V>)
            }
        }

        fn into_key_slice_mut(mut self) -> &'a mut [K] {
            // Same as for `into_key_slice` above, we try to avoid a run-time check
            // (the alignment comparison will usually be performed at compile-time).
            if mem::align_of::<K>() > mem::align_of::<LeafNode<(), ()>>() && self.is_shared_root() {
                &mut []
            } else {
                unsafe {
                    slice::from_raw_parts_mut(
                        MaybeUninit::first_ptr_mut(&mut (*self.as_leaf_mut()).keys),
                        self.len()
                    )
                }
            }
        }

        fn into_val_slice_mut(mut self) -> &'a mut [V] {
            debug_assert!(!self.is_shared_root());
            unsafe {
                slice::from_raw_parts_mut(
                    MaybeUninit::first_ptr_mut(&mut (*self.as_leaf_mut()).vals),
                    self.len()
                )
            }
        }

        fn into_slices_mut(mut self) -> (&'a mut [K], &'a mut [V]) {
            debug_assert!(!self.is_shared_root());
            // We cannot use the getters here, because calling the second one
            // invalidates the reference returned by the first.
            // More precisely, it is the call to `len` that is the culprit,
            // because that creates a shared reference to the header, which *can*
            // overlap with the keys (and even the values, for ZST keys).
            unsafe {
                let len = self.len();
                let leaf = self.as_leaf_mut();
                let keys = slice::from_raw_parts_mut(
                    MaybeUninit::first_ptr_mut(&mut (*leaf).keys),
                    len
                );
                let vals = slice::from_raw_parts_mut(
                    MaybeUninit::first_ptr_mut(&mut (*leaf).vals),
                    len
                );
                (keys, vals)
            }
        }
    }

    impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Leaf> {
        /// Adds a key/value pair the end of the node.
        pub fn push(&mut self, key: K, val: V) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(self.len() < CAPACITY);
            debug_assert!(!self.is_shared_root());

            let idx = self.len();

            unsafe {
                ptr::write(self.keys_mut().get_unchecked_mut(idx), key);
                ptr::write(self.vals_mut().get_unchecked_mut(idx), val);

                (*self.as_leaf_mut()).len += 1;
            }
        }

        /// Adds a key/value pair to the beginning of the node.
        pub fn push_front(&mut self, key: K, val: V) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(self.len() < CAPACITY);
            debug_assert!(!self.is_shared_root());

            unsafe {
                slice_insert(self.keys_mut(), 0, key);
                slice_insert(self.vals_mut(), 0, val);

                (*self.as_leaf_mut()).len += 1;
            }
        }
    }

    impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Internal> {
        /// Adds a key/value pair and an edge to go to the right of that pair to
        /// the end of the node.
        pub fn push(&mut self, key: K, val: V, edge: Root<K, V>) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(edge.height == self.height - 1);
            debug_assert!(self.len() < CAPACITY);

            let idx = self.len();

            unsafe {
                ptr::write(self.keys_mut().get_unchecked_mut(idx), key);
                ptr::write(self.vals_mut().get_unchecked_mut(idx), val);
                self.as_internal_mut().edges.get_unchecked_mut(idx + 1).write(edge.node);

                (*self.as_leaf_mut()).len += 1;

                Handle::new_edge(self.reborrow_mut(), idx + 1).correct_parent_link();
            }
        }

        fn correct_childrens_parent_links(&mut self, first: usize, after_last: usize) {
            for i in first..after_last {
                Handle::new_edge(unsafe { self.reborrow_mut() }, i).correct_parent_link();
            }
        }

        fn correct_all_childrens_parent_links(&mut self) {
            let len = self.len();
            self.correct_childrens_parent_links(0, len + 1);
        }

        /// Adds a key/value pair and an edge to go to the left of that pair to
        /// the beginning of the node.
        pub fn push_front(&mut self, key: K, val: V, edge: Root<K, V>) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(edge.height == self.height - 1);
            debug_assert!(self.len() < CAPACITY);

            unsafe {
                slice_insert(self.keys_mut(), 0, key);
                slice_insert(self.vals_mut(), 0, val);
                slice_insert(
                    slice::from_raw_parts_mut(
                        MaybeUninit::first_ptr_mut(&mut self.as_internal_mut().edges),
                        self.len()+1
                    ),
                    0,
                    edge.node
                );

                (*self.as_leaf_mut()).len += 1;

                self.correct_all_childrens_parent_links();
            }
        }
    }

    impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal> {
        /// Removes a key/value pair from the end of this node. If this is an internal node,
        /// also removes the edge that was to the right of that pair.
        pub fn pop(&mut self) -> (K, V, Option<Root<K, V>>) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(self.len() > 0);

            let idx = self.len() - 1;

            unsafe {
                let key = ptr::read(self.keys().get_unchecked(idx));
                let val = ptr::read(self.vals().get_unchecked(idx));
                let edge = match self.reborrow_mut().force() {
                    ForceResult::Leaf(_) => None,
                    ForceResult::Internal(internal) => {
                        let edge = ptr::read(
                            internal.as_internal().edges.get_unchecked(idx + 1).as_ptr()
                        );
                        let mut new_root = Root { node: edge, height: internal.height - 1 };
                        (*new_root.as_mut().as_leaf_mut()).parent = ptr::null();
                        Some(new_root)
                    }
                };

                (*self.as_leaf_mut()).len -= 1;
                (key, val, edge)
            }
        }

        /// Removes a key/value pair from the beginning of this node. If this is an internal node,
        /// also removes the edge that was to the left of that pair.
        pub fn pop_front(&mut self) -> (K, V, Option<Root<K, V>>) {
            // Necessary for correctness, but this is an internal module
            debug_assert!(self.len() > 0);

            let old_len = self.len();

            unsafe {
                let key = slice_remove(self.keys_mut(), 0);
                let val = slice_remove(self.vals_mut(), 0);
                let edge = match self.reborrow_mut().force() {
                    ForceResult::Leaf(_) => None,
                    ForceResult::Internal(mut internal) => {
                        let edge = slice_remove(
                            slice::from_raw_parts_mut(
                                MaybeUninit::first_ptr_mut(&mut internal.as_internal_mut().edges),
                                old_len+1
                            ),
                            0
                        );

                        let mut new_root = Root { node: edge, height: internal.height - 1 };
                        (*new_root.as_mut().as_leaf_mut()).parent = ptr::null();

                        for i in 0..old_len {
                            Handle::new_edge(internal.reborrow_mut(), i).correct_parent_link();
                        }

                        Some(new_root)
                    }
                };

                (*self.as_leaf_mut()).len -= 1;

                (key, val, edge)
            }
        }

        fn into_kv_pointers_mut(mut self) -> (*mut K, *mut V) {
            (
                self.keys_mut().as_mut_ptr(),
                self.vals_mut().as_mut_ptr()
            )
        }
    }

    impl<BorrowType, K, V> NodeRef<BorrowType, K, V, marker::LeafOrInternal> {
        /// Checks whether a node is an `Internal` node or a `Leaf` node.
        pub fn force(self) -> ForceResult<
            NodeRef<BorrowType, K, V, marker::Leaf>,
            NodeRef<BorrowType, K, V, marker::Internal>
        > {
            if self.height == 0 {
                ForceResult::Leaf(NodeRef {
                    height: self.height,
                    node: self.node,
                    root: self.root,
                    _marker: PhantomData
                })
            } else {
                ForceResult::Internal(NodeRef {
                    height: self.height,
                    node: self.node,
                    root: self.root,
                    _marker: PhantomData
                })
            }
        }
    }

    /// A reference to a specific key/value pair or edge within a node. The `Node` parameter
    /// must be a `NodeRef`, while the `Type` can either be `KV` (signifying a handle on a key/value
    /// pair) or `Edge` (signifying a handle on an edge).
    ///
    /// Note that even `Leaf` nodes can have `Edge` handles. Instead of representing a pointer to
    /// a child node, these represent the spaces where child pointers would go between the key/value
    /// pairs. For example, in a node with length 2, there would be 3 possible edge locations - one
    /// to the left of the node, one between the two pairs, and one at the right of the node.
    pub struct Handle<Node, Type> {
        node: Node,
        idx: usize,
        _marker: PhantomData<Type>
    }

    impl<Node: Copy, Type> Copy for Handle<Node, Type> { }
    // We don't need the full generality of `#[derive(Clone)]`, as the only time `Node` will be
    // `Clone`able is when it is an immutable reference and therefore `Copy`.
    impl<Node: Copy, Type> Clone for Handle<Node, Type> {
        fn clone(&self) -> Self {
            *self
        }
    }

    impl<Node, Type> Handle<Node, Type> {
        /// Retrieves the node that contains the edge of key/value pair this handle points to.
        pub fn into_node(self) -> Node {
            self.node
        }
    }

    impl<BorrowType, K, V, NodeType> Handle<NodeRef<BorrowType, K, V, NodeType>, marker::KV> {
        /// Creates a new handle to a key/value pair in `node`. `idx` must be less than `node.len()`.
        pub fn new_kv(node: NodeRef<BorrowType, K, V, NodeType>, idx: usize) -> Self {
            // Necessary for correctness, but in a private module
            debug_assert!(idx < node.len());

            Handle {
                node,
                idx,
                _marker: PhantomData
            }
        }

        pub fn left_edge(self) -> Handle<NodeRef<BorrowType, K, V, NodeType>, marker::Edge> {
            Handle::new_edge(self.node, self.idx)
        }

        pub fn right_edge(self) -> Handle<NodeRef<BorrowType, K, V, NodeType>, marker::Edge> {
            Handle::new_edge(self.node, self.idx + 1)
        }
    }

    impl<BorrowType, K, V, NodeType, HandleType> PartialEq
            for Handle<NodeRef<BorrowType, K, V, NodeType>, HandleType> {

        fn eq(&self, other: &Self) -> bool {
            self.node.node == other.node.node && self.idx == other.idx
        }
    }

    impl<BorrowType, K, V, NodeType, HandleType>
            Handle<NodeRef<BorrowType, K, V, NodeType>, HandleType> {

        /// Temporarily takes out another, immutable handle on the same location.
        pub fn reborrow(&self)
                -> Handle<NodeRef<marker::Immut<'_>, K, V, NodeType>, HandleType> {

            // We can't use Handle::new_kv or Handle::new_edge because we don't know our type
            Handle {
                node: self.node.reborrow(),
                idx: self.idx,
                _marker: PhantomData
            }
        }
    }

    impl<'a, K, V, NodeType, HandleType>
            Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, HandleType> {

        /// Temporarily takes out another, mutable handle on the same location. Beware, as
        /// this method is very dangerous, doubly so since it may not immediately appear
        /// dangerous.
        ///
        /// Because mutable pointers can roam anywhere around the tree and can even (through
        /// `into_root_mut`) mess with the root of the tree, the result of `reborrow_mut`
        /// can easily be used to make the original mutable pointer dangling, or, in the case
        /// of a reborrowed handle, out of bounds.
        // FIXME(@gereeter) consider adding yet another type parameter to `NodeRef` that restricts
        // the use of `ascend` and `into_root_mut` on reborrowed pointers, preventing this unsafety.
        pub unsafe fn reborrow_mut(&mut self)
                -> Handle<NodeRef<marker::Mut<'_>, K, V, NodeType>, HandleType> {

            // We can't use Handle::new_kv or Handle::new_edge because we don't know our type
            Handle {
                node: self.node.reborrow_mut(),
                idx: self.idx,
                _marker: PhantomData
            }
        }
    }

    impl<BorrowType, K, V, NodeType>
            Handle<NodeRef<BorrowType, K, V, NodeType>, marker::Edge> {

        /// Creates a new handle to an edge in `node`. `idx` must be less than or equal to
        /// `node.len()`.
        pub fn new_edge(node: NodeRef<BorrowType, K, V, NodeType>, idx: usize) -> Self {
            // Necessary for correctness, but in a private module
            debug_assert!(idx <= node.len());

            Handle {
                node,
                idx,
                _marker: PhantomData
            }
        }

        pub fn left_kv(self)
                -> Result<Handle<NodeRef<BorrowType, K, V, NodeType>, marker::KV>, Self> {

            if self.idx > 0 {
                Ok(Handle::new_kv(self.node, self.idx - 1))
            } else {
                Err(self)
            }
        }

        pub fn right_kv(self)
                -> Result<Handle<NodeRef<BorrowType, K, V, NodeType>, marker::KV>, Self> {

            if self.idx < self.node.len() {
                Ok(Handle::new_kv(self.node, self.idx))
            } else {
                Err(self)
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge> {
        /// Inserts a new key/value pair between the key/value pairs to the right and left of
        /// this edge. This method assumes that there is enough space in the node for the new
        /// pair to fit.
        ///
        /// The returned pointer points to the inserted value.
        fn insert_fit(&mut self, key: K, val: V) -> *mut V {
            // Necessary for correctness, but in a private module
            debug_assert!(self.node.len() < CAPACITY);
            debug_assert!(!self.node.is_shared_root());

            unsafe {
                slice_insert(self.node.keys_mut(), self.idx, key);
                slice_insert(self.node.vals_mut(), self.idx, val);

                (*self.node.as_leaf_mut()).len += 1;

                self.node.vals_mut().get_unchecked_mut(self.idx)
            }
        }

        /// Inserts a new key/value pair between the key/value pairs to the right and left of
        /// this edge. This method splits the node if there isn't enough room.
        ///
        /// The returned pointer points to the inserted value.
        pub fn insert(mut self, key: K, val: V)
                -> (InsertResult<'a, K, V, marker::Leaf>, *mut V) {

            if self.node.len() < CAPACITY {
                let ptr = self.insert_fit(key, val);
                (InsertResult::Fit(Handle::new_kv(self.node, self.idx)), ptr)
            } else {
                let middle = Handle::new_kv(self.node, B);
                let (mut left, k, v, mut right) = middle.split();
                let ptr = if self.idx <= B {
                    unsafe {
                        Handle::new_edge(left.reborrow_mut(), self.idx).insert_fit(key, val)
                    }
                } else {
                    unsafe {
                        Handle::new_edge(
                            right.as_mut().cast_unchecked::<marker::Leaf>(),
                            self.idx - (B + 1)
                        ).insert_fit(key, val)
                    }
                };
                (InsertResult::Split(left, k, v, right), ptr)
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::Edge> {
        /// Fixes the parent pointer and index in the child node below this edge. This is useful
        /// when the ordering of edges has been changed, such as in the various `insert` methods.
        fn correct_parent_link(mut self) {
            let idx = self.idx as u16;
            let ptr = self.node.as_internal_mut() as *mut _;
            let mut child = self.descend();
            unsafe {
                (*child.as_leaf_mut()).parent = ptr;
                (*child.as_leaf_mut()).parent_idx.write(idx);
            }
        }

        /// Unsafely asserts to the compiler some static information about whether the underlying
        /// node of this handle is a `Leaf`.
        unsafe fn cast_unchecked<NewType>(&mut self)
                -> Handle<NodeRef<marker::Mut<'_>, K, V, NewType>, marker::Edge> {

            Handle::new_edge(self.node.cast_unchecked(), self.idx)
        }

        /// Inserts a new key/value pair and an edge that will go to the right of that new pair
        /// between this edge and the key/value pair to the right of this edge. This method assumes
        /// that there is enough space in the node for the new pair to fit.
        fn insert_fit(&mut self, key: K, val: V, edge: Root<K, V>) {
            // Necessary for correctness, but in an internal module
            debug_assert!(self.node.len() < CAPACITY);
            debug_assert!(edge.height == self.node.height - 1);

            unsafe {
                // This cast is a lie, but it allows us to reuse the key/value insertion logic.
                self.cast_unchecked::<marker::Leaf>().insert_fit(key, val);

                slice_insert(
                    slice::from_raw_parts_mut(
                        MaybeUninit::first_ptr_mut(&mut self.node.as_internal_mut().edges),
                        self.node.len()
                    ),
                    self.idx + 1,
                    edge.node
                );

                for i in (self.idx+1)..(self.node.len()+1) {
                    Handle::new_edge(self.node.reborrow_mut(), i).correct_parent_link();
                }
            }
        }

        /// Inserts a new key/value pair and an edge that will go to the right of that new pair
        /// between this edge and the key/value pair to the right of this edge. This method splits
        /// the node if there isn't enough room.
        pub fn insert(mut self, key: K, val: V, edge: Root<K, V>)
                -> InsertResult<'a, K, V, marker::Internal> {

            // Necessary for correctness, but this is an internal module
            debug_assert!(edge.height == self.node.height - 1);

            if self.node.len() < CAPACITY {
                self.insert_fit(key, val, edge);
                InsertResult::Fit(Handle::new_kv(self.node, self.idx))
            } else {
                let middle = Handle::new_kv(self.node, B);
                let (mut left, k, v, mut right) = middle.split();
                if self.idx <= B {
                    unsafe {
                        Handle::new_edge(left.reborrow_mut(), self.idx).insert_fit(key, val, edge);
                    }
                } else {
                    unsafe {
                        Handle::new_edge(
                            right.as_mut().cast_unchecked::<marker::Internal>(),
                            self.idx - (B + 1)
                        ).insert_fit(key, val, edge);
                    }
                }
                InsertResult::Split(left, k, v, right)
            }
        }
    }

    impl<BorrowType, K, V>
            Handle<NodeRef<BorrowType, K, V, marker::Internal>, marker::Edge> {

        /// Finds the node pointed to by this edge.
        ///
        /// `edge.descend().ascend().unwrap()` and `node.ascend().unwrap().descend()` should
        /// both, upon success, do nothing.
        pub fn descend(self) -> NodeRef<BorrowType, K, V, marker::LeafOrInternal> {
            NodeRef {
                height: self.node.height - 1,
                node: unsafe {
                    (&*self.node.as_internal().edges.get_unchecked(self.idx).as_ptr()).as_ptr()
                },
                root: self.node.root,
                _marker: PhantomData
            }
        }
    }

    impl<'a, K: 'a, V: 'a, NodeType>
            Handle<NodeRef<marker::Immut<'a>, K, V, NodeType>, marker::KV> {

        pub fn into_kv(self) -> (&'a K, &'a V) {
            let (keys, vals) = self.node.into_slices();
            unsafe {
                (keys.get_unchecked(self.idx), vals.get_unchecked(self.idx))
            }
        }
    }

    impl<'a, K: 'a, V: 'a, NodeType>
            Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, marker::KV> {

        pub fn into_kv_mut(self) -> (&'a mut K, &'a mut V) {
            let (keys, vals) = self.node.into_slices_mut();
            unsafe {
                (keys.get_unchecked_mut(self.idx), vals.get_unchecked_mut(self.idx))
            }
        }
    }

    impl<'a, K, V, NodeType> Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, marker::KV> {
        pub fn kv_mut(&mut self) -> (&mut K, &mut V) {
            unsafe {
                let (keys, vals) = self.node.reborrow_mut().into_slices_mut();
                (keys.get_unchecked_mut(self.idx), vals.get_unchecked_mut(self.idx))
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::KV> {
        /// Splits the underlying node into three parts:
        ///
        /// - The node is truncated to only contain the key/value pairs to the right of
        ///   this handle.
        /// - The key and value pointed to by this handle and extracted.
        /// - All the key/value pairs to the right of this handle are put into a newly
        ///   allocated node.
        pub fn split(mut self)
                -> (NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, K, V, Root<K, V>) {
            debug_assert!(!self.node.is_shared_root());
            unsafe {
                let mut new_node = Box::new(LeafNode::new());

                let k = ptr::read(self.node.keys().get_unchecked(self.idx));
                let v = ptr::read(self.node.vals().get_unchecked(self.idx));

                let new_len = self.node.len() - self.idx - 1;

                ptr::copy_nonoverlapping(
                    self.node.keys().as_ptr().add(self.idx + 1),
                    new_node.keys.as_mut_ptr() as *mut K,
                    new_len
                );
                ptr::copy_nonoverlapping(
                    self.node.vals().as_ptr().add(self.idx + 1),
                    new_node.vals.as_mut_ptr() as *mut V,
                    new_len
                );

                (*self.node.as_leaf_mut()).len = self.idx as u16;
                new_node.len = new_len as u16;

                (
                    self.node,
                    k, v,
                    Root {
                        node: BoxedNode::from_leaf(new_node),
                        height: 0
                    }
                )
            }
        }

        /// Removes the key/value pair pointed to by this handle, returning the edge between the
        /// now adjacent key/value pairs to the left and right of this handle.
        pub fn remove(mut self)
                -> (Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge>, K, V) {
            debug_assert!(!self.node.is_shared_root());
            unsafe {
                let k = slice_remove(self.node.keys_mut(), self.idx);
                let v = slice_remove(self.node.vals_mut(), self.idx);
                (*self.node.as_leaf_mut()).len -= 1;
                (self.left_edge(), k, v)
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::KV> {
        /// Splits the underlying node into three parts:
        ///
        /// - The node is truncated to only contain the edges and key/value pairs to the
        ///   right of this handle.
        /// - The key and value pointed to by this handle and extracted.
        /// - All the edges and key/value pairs to the right of this handle are put into
        ///   a newly allocated node.
        pub fn split(mut self)
                -> (NodeRef<marker::Mut<'a>, K, V, marker::Internal>, K, V, Root<K, V>) {
            unsafe {
                let mut new_node = Box::new(InternalNode::new());

                let k = ptr::read(self.node.keys().get_unchecked(self.idx));
                let v = ptr::read(self.node.vals().get_unchecked(self.idx));

                let height = self.node.height;
                let new_len = self.node.len() - self.idx - 1;

                ptr::copy_nonoverlapping(
                    self.node.keys().as_ptr().add(self.idx + 1),
                    new_node.data.keys.as_mut_ptr() as *mut K,
                    new_len
                );
                ptr::copy_nonoverlapping(
                    self.node.vals().as_ptr().add(self.idx + 1),
                    new_node.data.vals.as_mut_ptr() as *mut V,
                    new_len
                );
                ptr::copy_nonoverlapping(
                    self.node.as_internal().edges.as_ptr().add(self.idx + 1),
                    new_node.edges.as_mut_ptr(),
                    new_len + 1
                );

                (*self.node.as_leaf_mut()).len = self.idx as u16;
                new_node.data.len = new_len as u16;

                let mut new_root = Root {
                    node: BoxedNode::from_internal(new_node),
                    height,
                };

                for i in 0..(new_len+1) {
                    Handle::new_edge(new_root.as_mut().cast_unchecked(), i).correct_parent_link();
                }

                (
                    self.node,
                    k, v,
                    new_root
                )
            }
        }

        /// Returns `true` if it is valid to call `.merge()`, i.e., whether there is enough room in
        /// a node to hold the combination of the nodes to the left and right of this handle along
        /// with the key/value pair at this handle.
        pub fn can_merge(&self) -> bool {
            (
                self.reborrow()
                    .left_edge()
                    .descend()
                    .len()
              + self.reborrow()
                    .right_edge()
                    .descend()
                    .len()
              + 1
            ) <= CAPACITY
        }

        /// Combines the node immediately to the left of this handle, the key/value pair pointed
        /// to by this handle, and the node immediately to the right of this handle into one new
        /// child of the underlying node, returning an edge referencing that new child.
        ///
        /// Assumes that this edge `.can_merge()`.
        pub fn merge(mut self)
                -> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::Edge> {
            let self1 = unsafe { ptr::read(&self) };
            let self2 = unsafe { ptr::read(&self) };
            let mut left_node = self1.left_edge().descend();
            let left_len = left_node.len();
            let mut right_node = self2.right_edge().descend();
            let right_len = right_node.len();

            // necessary for correctness, but in a private module
            debug_assert!(left_len + right_len + 1 <= CAPACITY);

            unsafe {
                ptr::write(left_node.keys_mut().get_unchecked_mut(left_len),
                           slice_remove(self.node.keys_mut(), self.idx));
                ptr::copy_nonoverlapping(
                    right_node.keys().as_ptr(),
                    left_node.keys_mut().as_mut_ptr().add(left_len + 1),
                    right_len
                );
                ptr::write(left_node.vals_mut().get_unchecked_mut(left_len),
                           slice_remove(self.node.vals_mut(), self.idx));
                ptr::copy_nonoverlapping(
                    right_node.vals().as_ptr(),
                    left_node.vals_mut().as_mut_ptr().add(left_len + 1),
                    right_len
                );

                slice_remove(&mut self.node.as_internal_mut().edges, self.idx + 1);
                for i in self.idx+1..self.node.len() {
                    Handle::new_edge(self.node.reborrow_mut(), i).correct_parent_link();
                }
                (*self.node.as_leaf_mut()).len -= 1;

                (*left_node.as_leaf_mut()).len += right_len as u16 + 1;

                if self.node.height > 1 {
                    ptr::copy_nonoverlapping(
                        right_node.cast_unchecked().as_internal().edges.as_ptr(),
                        left_node.cast_unchecked()
                                 .as_internal_mut()
                                 .edges
                                 .as_mut_ptr()
                                 .add(left_len + 1),
                        right_len + 1
                    );

                    for i in left_len+1..left_len+right_len+2 {
                        Handle::new_edge(
                            left_node.cast_unchecked().reborrow_mut(),
                            i
                        ).correct_parent_link();
                    }

                    Global.dealloc(
                        right_node.node.cast(),
                        Layout::new::<InternalNode<K, V>>(),
                    );
                } else {
                    Global.dealloc(
                        right_node.node.cast(),
                        Layout::new::<LeafNode<K, V>>(),
                    );
                }

                Handle::new_edge(self.node, self.idx)
            }
        }

        /// This removes a key/value pair from the left child and replaces it with the key/value pair
        /// pointed to by this handle while pushing the old key/value pair of this handle into the right
        /// child.
        pub fn steal_left(&mut self) {
            unsafe {
                let (k, v, edge) = self.reborrow_mut().left_edge().descend().pop();

                let k = mem::replace(self.reborrow_mut().into_kv_mut().0, k);
                let v = mem::replace(self.reborrow_mut().into_kv_mut().1, v);

                match self.reborrow_mut().right_edge().descend().force() {
                    ForceResult::Leaf(mut leaf) => leaf.push_front(k, v),
                    ForceResult::Internal(mut internal) => internal.push_front(k, v, edge.unwrap())
                }
            }
        }

        /// This removes a key/value pair from the right child and replaces it with the key/value pair
        /// pointed to by this handle while pushing the old key/value pair of this handle into the left
        /// child.
        pub fn steal_right(&mut self) {
            unsafe {
                let (k, v, edge) = self.reborrow_mut().right_edge().descend().pop_front();

                let k = mem::replace(self.reborrow_mut().into_kv_mut().0, k);
                let v = mem::replace(self.reborrow_mut().into_kv_mut().1, v);

                match self.reborrow_mut().left_edge().descend().force() {
                    ForceResult::Leaf(mut leaf) => leaf.push(k, v),
                    ForceResult::Internal(mut internal) => internal.push(k, v, edge.unwrap())
                }
            }
        }

        /// This does stealing similar to `steal_left` but steals multiple elements at once.
        pub fn bulk_steal_left(&mut self, count: usize) {
            unsafe {
                let mut left_node = ptr::read(self).left_edge().descend();
                let left_len = left_node.len();
                let mut right_node = ptr::read(self).right_edge().descend();
                let right_len = right_node.len();

                // Make sure that we may steal safely.
                debug_assert!(right_len + count <= CAPACITY);
                debug_assert!(left_len >= count);

                let new_left_len = left_len - count;

                // Move data.
                {
                    let left_kv = left_node.reborrow_mut().into_kv_pointers_mut();
                    let right_kv = right_node.reborrow_mut().into_kv_pointers_mut();
                    let parent_kv = {
                        let kv = self.reborrow_mut().into_kv_mut();
                        (kv.0 as *mut K, kv.1 as *mut V)
                    };

                    // Make room for stolen elements in the right child.
                    ptr::copy(right_kv.0,
                              right_kv.0.add(count),
                              right_len);
                    ptr::copy(right_kv.1,
                              right_kv.1.add(count),
                              right_len);

                    // Move elements from the left child to the right one.
                    move_kv(left_kv, new_left_len + 1, right_kv, 0, count - 1);

                    // Move parent's key/value pair to the right child.
                    move_kv(parent_kv, 0, right_kv, count - 1, 1);

                    // Move the left-most stolen pair to the parent.
                    move_kv(left_kv, new_left_len, parent_kv, 0, 1);
                }

                (*left_node.reborrow_mut().as_leaf_mut()).len -= count as u16;
                (*right_node.reborrow_mut().as_leaf_mut()).len += count as u16;

                match (left_node.force(), right_node.force()) {
                    (ForceResult::Internal(left), ForceResult::Internal(mut right)) => {
                        // Make room for stolen edges.
                        let right_edges = right.reborrow_mut().as_internal_mut().edges.as_mut_ptr();
                        ptr::copy(right_edges,
                                  right_edges.add(count),
                                  right_len + 1);
                        right.correct_childrens_parent_links(count, count + right_len + 1);

                        move_edges(left, new_left_len + 1, right, 0, count);
                    },
                    (ForceResult::Leaf(_), ForceResult::Leaf(_)) => { }
                    _ => { unreachable!(); }
                }
            }
        }

        /// The symmetric clone of `bulk_steal_left`.
        pub fn bulk_steal_right(&mut self, count: usize) {
            unsafe {
                let mut left_node = ptr::read(self).left_edge().descend();
                let left_len = left_node.len();
                let mut right_node = ptr::read(self).right_edge().descend();
                let right_len = right_node.len();

                // Make sure that we may steal safely.
                debug_assert!(left_len + count <= CAPACITY);
                debug_assert!(right_len >= count);

                let new_right_len = right_len - count;

                // Move data.
                {
                    let left_kv = left_node.reborrow_mut().into_kv_pointers_mut();
                    let right_kv = right_node.reborrow_mut().into_kv_pointers_mut();
                    let parent_kv = {
                        let kv = self.reborrow_mut().into_kv_mut();
                        (kv.0 as *mut K, kv.1 as *mut V)
                    };

                    // Move parent's key/value pair to the left child.
                    move_kv(parent_kv, 0, left_kv, left_len, 1);

                    // Move elements from the right child to the left one.
                    move_kv(right_kv, 0, left_kv, left_len + 1, count - 1);

                    // Move the right-most stolen pair to the parent.
                    move_kv(right_kv, count - 1, parent_kv, 0, 1);

                    // Fix right indexing
                    ptr::copy(right_kv.0.add(count),
                              right_kv.0,
                              new_right_len);
                    ptr::copy(right_kv.1.add(count),
                              right_kv.1,
                              new_right_len);
                }

                (*left_node.reborrow_mut().as_leaf_mut()).len += count as u16;
                (*right_node.reborrow_mut().as_leaf_mut()).len -= count as u16;

                match (left_node.force(), right_node.force()) {
                    (ForceResult::Internal(left), ForceResult::Internal(mut right)) => {
                        move_edges(right.reborrow_mut(), 0, left, left_len + 1, count);

                        // Fix right indexing.
                        let right_edges = right.reborrow_mut().as_internal_mut().edges.as_mut_ptr();
                        ptr::copy(right_edges.add(count),
                                  right_edges,
                                  new_right_len + 1);
                        right.correct_childrens_parent_links(0, new_right_len + 1);
                    },
                    (ForceResult::Leaf(_), ForceResult::Leaf(_)) => { }
                    _ => { unreachable!(); }
                }
            }
        }
    }

    unsafe fn move_kv<K, V>(
        source: (*mut K, *mut V), source_offset: usize,
        dest: (*mut K, *mut V), dest_offset: usize,
        count: usize)
    {
        ptr::copy_nonoverlapping(source.0.add(source_offset),
                                 dest.0.add(dest_offset),
                                 count);
        ptr::copy_nonoverlapping(source.1.add(source_offset),
                                 dest.1.add(dest_offset),
                                 count);
    }

    // Source and destination must have the same height.
    unsafe fn move_edges<K, V>(
        mut source: NodeRef<marker::Mut<'_>, K, V, marker::Internal>, source_offset: usize,
        mut dest: NodeRef<marker::Mut<'_>, K, V, marker::Internal>, dest_offset: usize,
        count: usize)
    {
        let source_ptr = source.as_internal_mut().edges.as_mut_ptr();
        let dest_ptr = dest.as_internal_mut().edges.as_mut_ptr();
        ptr::copy_nonoverlapping(source_ptr.add(source_offset),
                                 dest_ptr.add(dest_offset),
                                 count);
        dest.correct_childrens_parent_links(dest_offset, dest_offset + count);
    }

    impl<BorrowType, K, V, HandleType>
            Handle<NodeRef<BorrowType, K, V, marker::LeafOrInternal>, HandleType> {

        /// Checks whether the underlying node is an `Internal` node or a `Leaf` node.
        pub fn force(self) -> ForceResult<
            Handle<NodeRef<BorrowType, K, V, marker::Leaf>, HandleType>,
            Handle<NodeRef<BorrowType, K, V, marker::Internal>, HandleType>
        > {
            match self.node.force() {
                ForceResult::Leaf(node) => ForceResult::Leaf(Handle {
                    node,
                    idx: self.idx,
                    _marker: PhantomData
                }),
                ForceResult::Internal(node) => ForceResult::Internal(Handle {
                    node,
                    idx: self.idx,
                    _marker: PhantomData
                })
            }
        }
    }

    impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, marker::Edge> {
        /// Move the suffix after `self` from one node to another one. `right` must be empty.
        /// The first edge of `right` remains unchanged.
        pub fn move_suffix(&mut self,
                right: &mut NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>) {
            unsafe {
                let left_new_len = self.idx;
                let mut left_node = self.reborrow_mut().into_node();

                let right_new_len = left_node.len() - left_new_len;
                let mut right_node = right.reborrow_mut();

                debug_assert!(right_node.len() == 0);
                debug_assert!(left_node.height == right_node.height);

                let left_kv = left_node.reborrow_mut().into_kv_pointers_mut();
                let right_kv = right_node.reborrow_mut().into_kv_pointers_mut();

                move_kv(left_kv, left_new_len, right_kv, 0, right_new_len);

                (*left_node.reborrow_mut().as_leaf_mut()).len = left_new_len as u16;
                (*right_node.reborrow_mut().as_leaf_mut()).len = right_new_len as u16;

                match (left_node.force(), right_node.force()) {
                    (ForceResult::Internal(left), ForceResult::Internal(right)) => {
                        move_edges(left, left_new_len + 1, right, 1, right_new_len);
                    },
                    (ForceResult::Leaf(_), ForceResult::Leaf(_)) => { }
                    _ => { unreachable!(); }
                }
            }
        }
    }

    pub enum ForceResult<Leaf, Internal> {
        Leaf(Leaf),
        Internal(Internal)
    }

    pub enum InsertResult<'a, K, V, Type> {
        Fit(Handle<NodeRef<marker::Mut<'a>, K, V, Type>, marker::KV>),
        Split(NodeRef<marker::Mut<'a>, K, V, Type>, K, V, Root<K, V>)
    }

    pub mod marker {
        use core::marker::PhantomData;

        pub enum Leaf { }
        pub enum Internal { }
        pub enum LeafOrInternal { }

        pub enum Owned { }
        pub struct Immut<'a>(PhantomData<&'a ()>);
        pub struct Mut<'a>(PhantomData<&'a mut ()>);

        pub enum KV { }
        pub enum Edge { }
    }

    unsafe fn slice_insert<T>(slice: &mut [T], idx: usize, val: T) {
        ptr::copy(
            slice.as_ptr().add(idx),
            slice.as_mut_ptr().add(idx + 1),
            slice.len() - idx
        );
        ptr::write(slice.get_unchecked_mut(idx), val);
    }

    unsafe fn slice_remove<T>(slice: &mut [T], idx: usize) -> T {
        let ret = ptr::read(slice.get_unchecked(idx));
        ptr::copy(
            slice.as_ptr().add(idx + 1),
            slice.as_mut_ptr().add(idx),
            slice.len() - idx - 1
        );
        ret
    }

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