// 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: Option<NonNull<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 crate::ptr::Unique;
use core::{
    cmp::Ordering,
    marker::PhantomData,
    mem::{self, MaybeUninit},
    ptr::{self, NonNull},
    slice,
};

use crate::{
    alloc::{AllocRef, Layout},
    boxed::Box,
};

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

/// The underlying representation of leaf nodes.
#[repr(C)]
struct LeafNode<K, V> {
    /// We want to be covariant in `K` and `V`.
    parent: Option<NonNull<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_array(),
            vals: MaybeUninit::uninit_array(),
            parent: None,
            parent_idx: MaybeUninit::uninit(),
            len: 0,
        }
    }
}

/// 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. Although during the process of `into_iter` or `drop`,
    /// some pointers are dangling while others still need to be traversed.
    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: unsafe { LeafNode::new() },
            edges: MaybeUninit::uninit_array(),
        }
    }
}

/// A managed, non-null pointer to a node. This is either an owned pointer to
/// `LeafNode<K, V>` or an owned pointer to `InternalNode<K, V>`.
///
/// However, `BoxedNode` contains no information as to which of the two types
/// of nodes it actually contains, 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<A: AllocRef>(node: Box<LeafNode<K, V>, A>) -> Self {
        BoxedNode {
            ptr: Box::into_unique(node),
        }
    }

    fn from_internal<A: AllocRef>(node: Box<InternalNode<K, V>, A>) -> Self {
        BoxedNode {
            ptr: Box::into_unique(node).cast(),
        }
    }

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

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

/// An owned tree.
///
/// Note that this does not have a destructor, and must be cleaned up manually.
pub struct Root<K, V> {
    node: BoxedNode<K, V>,
    /// The number of levels below the root node.
    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> {
    /// Returns the number of levels below the root.
    pub fn height(&self) -> usize {
        self.height
    }

    /// Returns a new owned tree, with its own root node that is initially empty.
    pub fn new_leaf<A: AllocRef>(alloc: &mut A) -> Self {
        Root {
            node: BoxedNode::from_leaf(Box::new_in(unsafe { LeafNode::new() }, alloc)),
            height: 0,
        }
    }

    /// Borrows and returns an immutable reference to the node owned by the root.
    pub fn node_as_ref(&self) -> NodeRef<marker::Immut<'_>, K, V, marker::LeafOrInternal> {
        NodeRef {
            height: self.height,
            node: self.node.as_ptr(),
            _marker: PhantomData,
        }
    }

    /// Borrows and returns a mutable reference to the node owned by the root.
    pub fn node_as_mut(&mut self) -> NodeRef<marker::Mut<'_>, K, V, marker::LeafOrInternal> {
        NodeRef {
            height: self.height,
            node: self.node.as_ptr(),
            _marker: PhantomData,
        }
    }

    pub fn node_as_valmut(&mut self) -> NodeRef<marker::ValMut<'_>, K, V, marker::LeafOrInternal> {
        NodeRef {
            height: self.height,
            node: self.node.as_ptr(),
            _marker: PhantomData,
        }
    }

    pub fn into_ref(self) -> NodeRef<marker::Owned, K, V, marker::LeafOrInternal> {
        NodeRef {
            height: self.height,
            node: self.node.as_ptr(),
            _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_internal_level`.
    pub fn push_internal_level<A: AllocRef>(
        &mut self,
        alloc: &mut A,
    ) -> NodeRef<marker::Mut<'_>, K, V, marker::Internal> {
        let mut new_node = Box::new_in(unsafe { InternalNode::new() }, alloc);
        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(),
            _marker: PhantomData,
        };

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

        ret
    }

    /// Removes the internal root node, using its first child as the new root node.
    /// As it is intended only to be called when the root node has only one child,
    /// no cleanup is done on any of the other children.
    /// This decreases the height by 1 and is the opposite of `push_internal_level`.
    ///
    /// Requires exclusive access to the `Root` object but not to the root node;
    /// it will not invalidate existing handles or references to the root node.
    ///
    /// Panics if there is no internal level, i.e., if the root node is a leaf.
    pub fn pop_internal_level<A: AllocRef>(&mut self, alloc: &mut A) {
        assert!(self.height > 0);

        let top = self.node.ptr;

        self.node = unsafe {
            BoxedNode::from_ptr(
                self.node_as_mut()
                    .cast_unchecked::<marker::Internal>()
                    .first_edge()
                    .descend()
                    .node,
            )
        };
        self.height -= 1;
        self.node_as_mut().as_leaf_mut().parent = None;

        unsafe {
            alloc.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>`, `Mut<'a>` or `ValMut<'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`,
///    when this is `ValMut<'a>`, the `NodeRef` acts as immutable with respect
///    to keys and tree structure, but allows mutable references to values,
///    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.
pub struct NodeRef<BorrowType, K, V, Type> {
    /// The number of levels below the node.
    height: usize,
    node: NonNull<LeafNode<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<'a, K: Send + 'a, V: Send + 'a, Type> Send for NodeRef<marker::ValMut<'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> {
    /// Exposes the data of an internal node for reading.
    ///
    /// Returns a raw ptr to avoid invalidating other references to this node,
    /// which is possible when BorrowType is marker::ValMut.
    fn as_internal_ptr(&self) -> *const InternalNode<K, V> {
        self.node.as_ptr() as *const InternalNode<K, V>
    }
}

impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Internal> {
    /// Exposes the data of an internal node for reading,
    /// when we know we have exclusive access.
    fn as_internal(&mut self) -> &InternalNode<K, V> {
        unsafe { &*self.as_internal_ptr() }
    }
}

impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Internal> {
    /// Exposes the data of an internal node for writing.
    ///
    /// We don't need to return a raw ptr because we have unique access to the entire node.
    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`.
    /// For any node, the number of possible edge handles is also `len() + 1`.
    /// Note that, despite being safe, calling this function can have the side effect
    /// of invalidating mutable references that unsafe code has created.
    pub fn len(&self) -> usize {
        // Crucially, we only access the `len` field here. If BorrowType is marker::ValMut,
        // there might be outstanding mutable references to values that we must not invalidate.
        unsafe { usize::from((*self.as_leaf_ptr()).len) }
    }

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

    /// 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,
            _marker: PhantomData,
        }
    }

    /// Exposes the leaf "portion" of any leaf or internal node.
    /// If the node is a leaf, this function simply opens up its data.
    /// If the node is an internal node, so not a leaf, it does have all the data a leaf has
    /// (header, keys and values), and this function exposes that.
    ///
    /// Returns a raw ptr to avoid invalidating other references to this node,
    /// which is possible when BorrowType is marker::ValMut.
    fn as_leaf_ptr(&self) -> *const LeafNode<K, V> {
        // The node must be valid for at least the LeafNode portion.
        // This is not a reference in the NodeRef type because we don't know if
        // it should be unique or shared.
        self.node.as_ptr()
    }

    /// Borrows a reference to one of the keys stored in the node.
    ///
    /// # Safety
    /// The node has more than `idx` initialized elements.
    pub unsafe fn key_at(&self, idx: usize) -> &K {
        unsafe { self.reborrow().into_key_at(idx) }
    }

    /// Borrows a reference to one of the values stored in the node.
    ///
    /// # Safety
    /// The node has more than `idx` initialized elements.
    unsafe fn val_at(&self, idx: usize) -> &V {
        unsafe { self.reborrow().into_val_at(idx) }
    }

    /// 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> {
        // We need to use raw pointers to nodes because, if BorrowType is marker::ValMut,
        // there might be outstanding mutable references to values that we must not invalidate.
        let leaf_ptr = self.as_leaf_ptr();
        unsafe { (*leaf_ptr).parent }
            .as_ref()
            .map(|parent| Handle {
                node: NodeRef {
                    height: self.height + 1,
                    node: parent.cast(),
                    _marker: PhantomData,
                },
                idx: unsafe { usize::from((*leaf_ptr).parent_idx.assume_init()) },
                _marker: PhantomData,
            })
            .ok_or(self)
    }

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

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

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

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

impl<'a, K: 'a, V: 'a, Type> NodeRef<marker::Immut<'a>, K, V, Type> {
    /// Exposes the data of a leaf node for reading in an immutable tree.
    fn into_leaf(self) -> &'a LeafNode<K, V> {
        // SAFETY: we can access the entire node freely and do no need raw pointers,
        // because there can be no mutable references to this Immut tree.
        unsafe { &(*self.as_leaf_ptr()) }
    }
}

impl<K, V> NodeRef<marker::Owned, K, V, marker::LeafOrInternal> {
    /// 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<A: AllocRef>(
        self,
        alloc: &mut A,
    ) -> Option<Handle<NodeRef<marker::Owned, K, V, marker::Internal>, marker::Edge>> {
        let height = self.height;
        let node = self.node;
        let ret = self.ascend().ok();
        unsafe {
            alloc.dealloc(
                node.cast(),
                if height > 0 {
                    Layout::new::<InternalNode<K, V>>()
                } else {
                    Layout::new::<LeafNode<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` or an `Internal`.
    unsafe fn cast_unchecked<NewType>(self) -> NodeRef<marker::Mut<'a>, K, V, NewType> {
        NodeRef {
            height: self.height,
            node: self.node,
            _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, the returned
    /// pointer can easily be used to make the original pointer dangling, out of
    /// bounds, or invalid under stacked borrow rules.
    // FIXME(@gereeter) consider adding yet another type parameter to `NodeRef`
    // that restricts the use of navigation methods 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,
            _marker: PhantomData,
        }
    }

    /// Exposes the leaf "portion" of any leaf or internal node for writing.
    /// If the node is a leaf, this function simply opens up its data.
    /// If the node is an internal node, so not a leaf, it does have all the data a leaf has
    /// (header, keys and values), and this function exposes that.
    ///
    /// We don't need to return a raw ptr because we have unique access to the entire node.
    fn as_leaf_mut(&mut self) -> &'a mut LeafNode<K, V> {
        unsafe { &mut (*self.node.as_ptr()) }
    }

    /// Borrows a mutable reference to one of the keys stored in the node.
    ///
    /// # Safety
    /// The node has more than `idx` initialized elements.
    pub unsafe fn key_mut_at(&mut self, idx: usize) -> &mut K {
        unsafe { self.reborrow_mut().into_key_mut_at(idx) }
    }

    /// Borrows a mutable reference to one of the values stored in the node.
    ///
    /// # Safety
    /// The node has more than `idx` initialized elements.
    pub unsafe fn val_mut_at(&mut self, idx: usize) -> &mut V {
        unsafe { self.reborrow_mut().into_val_mut_at(idx) }
    }

    fn keys_mut(&mut self) -> &mut [K] {
        // SAFETY: the caller will not be able to call further methods on self
        // until the key slice reference is dropped, as we have unique access
        // for the lifetime of the borrow.
        unsafe { self.reborrow_mut().into_key_slice_mut() }
    }

    fn vals_mut(&mut self) -> &mut [V] {
        // SAFETY: the caller will not be able to call further methods on self
        // until the value slice reference is dropped, as we have unique access
        // for the lifetime of the borrow.
        unsafe { self.reborrow_mut().into_val_slice_mut() }
    }
}

impl<'a, K: 'a, V: 'a, Type> NodeRef<marker::Immut<'a>, K, V, Type> {
    /// # Safety
    /// The node has more than `idx` initialized elements.
    unsafe fn into_key_at(self, idx: usize) -> &'a K {
        unsafe { self.into_leaf().keys.get_unchecked(idx).assume_init_ref() }
    }

    /// # Safety
    /// The node has more than `idx` initialized elements.
    unsafe fn into_val_at(self, idx: usize) -> &'a V {
        unsafe { self.into_leaf().vals.get_unchecked(idx).assume_init_ref() }
    }
}

impl<'a, K: 'a, V: 'a, Type> NodeRef<marker::Mut<'a>, K, V, Type> {
    fn into_key_slice_mut(mut self) -> &'a mut [K] {
        // SAFETY: The keys of a node must always be initialized up to length.
        unsafe {
            slice::from_raw_parts_mut(
                MaybeUninit::slice_as_mut_ptr(&mut self.as_leaf_mut().keys),
                self.len(),
            )
        }
    }

    fn into_val_slice_mut(mut self) -> &'a mut [V] {
        // SAFETY: The values of a node must always be initialized up to length.
        unsafe {
            slice::from_raw_parts_mut(
                MaybeUninit::slice_as_mut_ptr(&mut self.as_leaf_mut().vals),
                self.len(),
            )
        }
    }

    /// # Safety
    /// The node has more than `idx` initialized elements.
    unsafe fn into_key_mut_at(mut self, idx: usize) -> &'a mut K {
        debug_assert!(idx < self.len());

        let leaf = self.as_leaf_mut();
        unsafe { leaf.keys.get_unchecked_mut(idx).assume_init_mut() }
    }

    /// # Safety
    /// The node has more than `idx` initialized elements.
    unsafe fn into_val_mut_at(mut self, idx: usize) -> &'a mut V {
        debug_assert!(idx < self.len());

        let leaf = self.as_leaf_mut();
        unsafe { leaf.vals.get_unchecked_mut(idx).assume_init_mut() }
    }
}

impl<'a, K, V, Type> NodeRef<marker::ValMut<'a>, K, V, Type> {
    /// # Safety
    /// The node has more than `idx` initialized elements.
    unsafe fn into_key_val_mut_at(self, idx: usize) -> (&'a K, &'a mut V) {
        // We only create a reference to the one element we are interested in,
        // to avoid aliasing with outstanding references to other elements,
        // in particular, those returned to the caller in earlier iterations.
        let leaf = self.node.as_ptr();
        // We must coerce to unsized array pointers because of Rust issue #74679.
        let keys: *const [_] = unsafe { &raw const (*leaf).keys };
        let vals: *mut [_] = unsafe { &raw mut (*leaf).vals };
        // SAFETY: The keys and values of a node must always be initialized up to length.
        let key = unsafe { (&*keys.get_unchecked(idx)).assume_init_ref() };
        let val = unsafe { (&mut *vals.get_unchecked_mut(idx)).assume_init_mut() };
        (key, val)
    }
}

impl<'a, K: 'a, V: 'a> NodeRef<marker::Mut<'a>, K, V, marker::Leaf> {
    /// Adds a key/value pair to the end of the node.
    pub fn push(&mut self, key: K, val: V) {
        let len = &mut self.as_leaf_mut().len;
        let idx = usize::from(*len);
        assert!(idx < CAPACITY);
        *len += 1;
        unsafe {
            ptr::write(self.key_mut_at(idx), key);
            ptr::write(self.val_mut_at(idx), val);
        }
    }

    /// Adds a key/value pair to the beginning of the node.
    pub fn push_front(&mut self, key: K, val: V) {
        assert!(self.len() < CAPACITY);

        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> {
    /// # Safety
    /// 'first' and 'after_last' must be in range.
    unsafe fn correct_childrens_parent_links(&mut self, first: usize, after_last: usize) {
        debug_assert!(first <= self.len());
        debug_assert!(after_last <= self.len() + 1);
        for i in first..after_last {
            unsafe { Handle::new_edge(self.reborrow_mut(), i) }.correct_parent_link();
        }
    }

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

impl<'a, K: 'a, V: 'a> 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>) {
        assert!(edge.height == self.height - 1);

        let len = &mut self.as_leaf_mut().len;
        let idx = usize::from(*len);
        assert!(idx < CAPACITY);
        *len += 1;
        unsafe {
            ptr::write(self.key_mut_at(idx), key);
            ptr::write(self.val_mut_at(idx), val);
            self.as_internal_mut()
                .edges
                .get_unchecked_mut(idx + 1)
                .write(edge.node);
            Handle::new_edge(self.reborrow_mut(), idx + 1).correct_parent_link();
        }
    }

    /// 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>) {
        assert!(edge.height == self.height - 1);
        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::slice_as_mut_ptr(&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: 'a, V: 'a> NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal> {
    /// Removes a key/value pair from the end of this node and returns the pair.
    /// If this is an internal node, also removes the edge that was to the right
    /// of that pair and returns the orphaned node that this edge owned with its
    /// parent erased.
    pub fn pop(&mut self) -> (K, V, Option<Root<K, V>>) {
        assert!(self.len() > 0);

        let idx = self.len() - 1;

        unsafe {
            let key = ptr::read(self.key_at(idx));
            let val = ptr::read(self.val_at(idx));
            let edge = match self.reborrow_mut().force() {
                ForceResult::Leaf(_) => None,
                ForceResult::Internal(mut 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.node_as_mut().as_leaf_mut().parent = None;
                    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>>) {
        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::slice_as_mut_ptr(&mut internal.as_internal_mut().edges),
                            old_len + 1,
                        ),
                        0,
                    );

                    let mut new_root = Root {
                        node: edge,
                        height: internal.height - 1,
                    };
                    new_root.node_as_mut().as_leaf_mut().parent = None;

                    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,
                _marker: PhantomData,
            })
        } else {
            ForceResult::Internal(NodeRef {
                height: self.height,
                node: self.node,
                _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 or key/value pair this handle points to.
    pub fn into_node(self) -> Node {
        self.node
    }

    /// Returns the position of this handle in the node.
    pub fn idx(&self) -> usize {
        self.idx
    }
}

impl<BorrowType, K, V, NodeType> Handle<NodeRef<BorrowType, K, V, NodeType>, marker::KV> {
    /// Creates a new handle to a key/value pair in `node`.
    /// Unsafe because the caller must ensure that `idx < node.len()`.
    pub unsafe fn new_kv(node: NodeRef<BorrowType, K, V, NodeType>, idx: usize) -> Self {
        debug_assert!(idx < node.len());

        Handle {
            node,
            idx,
            _marker: PhantomData,
        }
    }

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

    pub fn right_edge(self) -> Handle<NodeRef<BorrowType, K, V, NodeType>, marker::Edge> {
        unsafe { 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> PartialOrd
    for Handle<NodeRef<BorrowType, K, V, NodeType>, HandleType>
{
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        if self.node.node == other.node.node {
            Some(self.idx.cmp(&other.idx))
        } else {
            None
        }
    }
}

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.
    ///
    /// For details, see `NodeRef::reborrow_mut`.
    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: unsafe { 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`.
    /// Unsafe because the caller must ensure that `idx <= node.len()`.
    pub unsafe fn new_edge(node: NodeRef<BorrowType, K, V, NodeType>, idx: usize) -> Self {
        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(unsafe { 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(unsafe { Handle::new_kv(self.node, self.idx) })
        } else {
            Err(self)
        }
    }
}

enum InsertionPlace {
    Left(usize),
    Right(usize),
}

/// Given an edge index where we want to insert into a node filled to capacity,
/// computes a sensible KV index of a split point and where to perform the insertion.
/// The goal of the split point is for its key and value to end up in a parent node;
/// the keys, values and edges to the left of the split point become the left child;
/// the keys, values and edges to the right of the split point become the right child.
fn splitpoint(edge_idx: usize) -> (usize, InsertionPlace) {
    debug_assert!(edge_idx <= CAPACITY);
    // Rust issue #74834 tries to explain these symmetric rules.
    match edge_idx {
        0..EDGE_IDX_LEFT_OF_CENTER => (KV_IDX_CENTER - 1, InsertionPlace::Left(edge_idx)),
        EDGE_IDX_LEFT_OF_CENTER => (KV_IDX_CENTER, InsertionPlace::Left(edge_idx)),
        EDGE_IDX_RIGHT_OF_CENTER => (KV_IDX_CENTER, InsertionPlace::Right(0)),
        _ => (
            KV_IDX_CENTER + 1,
            InsertionPlace::Right(edge_idx - (KV_IDX_CENTER + 1 + 1)),
        ),
    }
}

impl<'a, K: 'a, V: 'a, NodeType> Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, marker::Edge> {
    /// Helps implementations of `insert_fit` for a particular `NodeType`,
    /// by taking care of leaf data.
    /// 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.
    fn leafy_insert_fit(&mut self, key: K, val: V) {
        // Necessary for correctness, but in a private module
        debug_assert!(self.node.len() < CAPACITY);

        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;
        }
    }
}

impl<'a, K: 'a, V: 'a> 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 {
        self.leafy_insert_fit(key, val);
        unsafe { self.node.val_mut_at(self.idx) }
    }
}

impl<'a, K: 'a, V: 'a> 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 splits the node if there isn't enough room.
    ///
    /// The returned pointer points to the inserted value.
    fn insert<A: AllocRef>(
        mut self,
        key: K,
        val: V,
        alloc: &mut A,
    ) -> (InsertResult<'a, K, V, marker::Leaf>, *mut V) {
        if self.node.len() < CAPACITY {
            let val_ptr = self.insert_fit(key, val);
            let kv = unsafe { Handle::new_kv(self.node, self.idx) };
            (InsertResult::Fit(kv), val_ptr)
        } else {
            let (middle_kv_idx, insertion) = splitpoint(self.idx);
            let middle = unsafe { Handle::new_kv(self.node, middle_kv_idx) };
            let (mut left, k, v, mut right) = middle.split(alloc);
            let val_ptr = match insertion {
                InsertionPlace::Left(insert_idx) => unsafe {
                    Handle::new_edge(left.reborrow_mut(), insert_idx).insert_fit(key, val)
                },
                InsertionPlace::Right(insert_idx) => unsafe {
                    Handle::new_edge(
                        right.node_as_mut().cast_unchecked::<marker::Leaf>(),
                        insert_idx,
                    )
                    .insert_fit(key, val)
                },
            };
            (
                InsertResult::Split(SplitResult {
                    left: left.forget_type(),
                    k,
                    v,
                    right,
                }),
                val_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 = NonNull::new(self.node.as_internal_mut());
        let mut child = self.descend();
        child.as_leaf_mut().parent = ptr;
        child.as_leaf_mut().parent_idx.write(idx);
    }
}

impl<'a, K: 'a, V: 'a> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::Edge> {
    /// 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 {
            self.leafy_insert_fit(key, val);

            slice_insert(
                slice::from_raw_parts_mut(
                    MaybeUninit::slice_as_mut_ptr(&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.
    fn insert<A: AllocRef>(
        mut self,
        key: K,
        val: V,
        edge: Root<K, V>,
        alloc: &mut A,
    ) -> InsertResult<'a, K, V, marker::Internal> {
        assert!(edge.height == self.node.height - 1);

        if self.node.len() < CAPACITY {
            self.insert_fit(key, val, edge);
            let kv = unsafe { Handle::new_kv(self.node, self.idx) };
            InsertResult::Fit(kv)
        } else {
            let (middle_kv_idx, insertion) = splitpoint(self.idx);
            let middle = unsafe { Handle::new_kv(self.node, middle_kv_idx) };
            let (mut left, k, v, mut right) = middle.split(alloc);
            match insertion {
                InsertionPlace::Left(insert_idx) => unsafe {
                    Handle::new_edge(left.reborrow_mut(), insert_idx).insert_fit(key, val, edge);
                },
                InsertionPlace::Right(insert_idx) => unsafe {
                    Handle::new_edge(
                        right.node_as_mut().cast_unchecked::<marker::Internal>(),
                        insert_idx,
                    )
                    .insert_fit(key, val, edge);
                },
            }
            InsertResult::Split(SplitResult {
                left: left.forget_type(),
                k,
                v,
                right,
            })
        }
    }
}

impl<'a, K: 'a, V: 'a> 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 splits the node if there isn't enough room, and tries to
    /// insert the split off portion into the parent node recursively, until the root is reached.
    ///
    /// If the returned result is a `Fit`, its handle's node can be this edge's node or an ancestor.
    /// If the returned result is a `Split`, the `left` field will be the root node.
    /// The returned pointer points to the inserted value.
    pub fn insert_recursing<A: AllocRef>(
        self,
        key: K,
        value: V,
        alloc: &mut A,
    ) -> (InsertResult<'a, K, V, marker::LeafOrInternal>, *mut V) {
        let (mut split, val_ptr) = match self.insert(key, value, &mut *alloc) {
            (InsertResult::Fit(handle), ptr) => {
                return (InsertResult::Fit(handle.forget_node_type()), ptr);
            }
            (InsertResult::Split(split), val_ptr) => (split, val_ptr),
        };

        loop {
            split = match split.left.ascend() {
                Ok(parent) => match parent.insert(split.k, split.v, split.right, &mut *alloc) {
                    InsertResult::Fit(handle) => {
                        return (InsertResult::Fit(handle.forget_node_type()), val_ptr);
                    }
                    InsertResult::Split(split) => split,
                },
                Err(root) => {
                    return (
                        InsertResult::Split(SplitResult {
                            left: root,
                            ..split
                        }),
                        val_ptr,
                    );
                }
            };
        }
    }
}

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> {
        // We need to use raw pointers to nodes because, if BorrowType is
        // marker::ValMut, there might be outstanding mutable references to
        // values that we must not invalidate. There's no worry accessing the
        // height field because that value is copied. Beware that, once the
        // node pointer is dereferenced, we access the edges array with a
        // reference (Rust issue #73987) and invalidate any other references
        // to or inside the array, should any be around.
        let internal_node = self.node.as_internal_ptr();
        NodeRef {
            height: self.node.height - 1,
            node: unsafe { (&*(*internal_node).edges.get_unchecked(self.idx).as_ptr()).as_ptr() },
            _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) {
        (unsafe { self.node.into_key_at(self.idx) }, unsafe {
            self.node.into_val_at(self.idx)
        })
    }
}

impl<'a, K: 'a, V: 'a, NodeType> Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, marker::KV> {
    pub fn into_key_mut(self) -> &'a mut K {
        unsafe { self.node.into_key_mut_at(self.idx) }
    }

    pub fn into_val_mut(self) -> &'a mut V {
        unsafe { self.node.into_val_mut_at(self.idx) }
    }
}

impl<'a, K, V, NodeType> Handle<NodeRef<marker::ValMut<'a>, K, V, NodeType>, marker::KV> {
    pub fn into_kv_valmut(self) -> (&'a K, &'a mut V) {
        unsafe { self.node.into_key_val_mut_at(self.idx) }
    }
}

impl<'a, K: 'a, V: 'a, NodeType> Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, marker::KV> {
    pub fn kv_mut(&mut self) -> (&mut K, &mut V) {
        // We cannot call into_key_mut_at and into_val_mut_at, because calling the second one
        // invalidates the reference returned by the first.
        let leaf = self.node.as_leaf_mut();
        let key = unsafe { leaf.keys.get_unchecked_mut(self.idx).assume_init_mut() };
        let val = unsafe { leaf.vals.get_unchecked_mut(self.idx).assume_init_mut() };
        (key, val)
    }
}

impl<'a, K: 'a, V: 'a, NodeType> Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, marker::KV> {
    /// Helps implementations of `split` for a particular `NodeType`,
    /// by taking care of leaf data.
    fn leafy_split(&mut self, new_node: &mut LeafNode<K, V>) -> (K, V, usize) {
        unsafe {
            let k = ptr::read(self.node.key_at(self.idx));
            let v = ptr::read(self.node.val_at(self.idx));

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

            ptr::copy_nonoverlapping(
                self.node.key_at(self.idx + 1),
                new_node.keys.as_mut_ptr() as *mut K,
                new_len,
            );
            ptr::copy_nonoverlapping(
                self.node.val_at(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;
            (k, v, new_len)
        }
    }
}

impl<'a, K: 'a, V: 'a> 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 are extracted.
    /// - All the key/value pairs to the right of this handle are put into a newly
    ///   allocated node.
    pub fn split<A: AllocRef>(
        mut self,
        alloc: &mut A,
    ) -> (
        NodeRef<marker::Mut<'a>, K, V, marker::Leaf>,
        K,
        V,
        Root<K, V>,
    ) {
        unsafe {
            let mut new_node = Box::new_in(LeafNode::new(), alloc);

            let (k, v, _) = self.leafy_split(&mut new_node);

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

    /// Removes the key/value pair pointed to by this handle and returns it, along with the edge
    /// that the key/value pair collapsed into.
    pub fn remove(
        mut self,
    ) -> (
        (K, V),
        Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, marker::Edge>,
    ) {
        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;
            ((k, v), self.left_edge())
        }
    }
}

impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::KV> {
    /// 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
    }
}

impl<'a, K: 'a, V: 'a> 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 are extracted.
    /// - All the edges and key/value pairs to the right of this handle are put into
    ///   a newly allocated node.
    pub fn split<A: AllocRef>(
        mut self,
        alloc: &mut A,
    ) -> (
        NodeRef<marker::Mut<'a>, K, V, marker::Internal>,
        K,
        V,
        Root<K, V>,
    ) {
        unsafe {
            let mut new_node = Box::new_in(InternalNode::new(), alloc);

            let (k, v, new_len) = self.leafy_split(&mut new_node.data);
            let height = self.node.height;
            let old_node = &*self.node.as_internal_ptr();

            ptr::copy_nonoverlapping(
                old_node.edges.as_ptr().add(self.idx + 1),
                new_node.edges.as_mut_ptr(),
                new_len + 1,
            );

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

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

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

    /// 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.
    ///
    /// Panics unless this edge `.can_merge()`.
    pub fn merge<A: AllocRef>(
        mut self,
        alloc: &mut A,
    ) -> 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 right_node = self2.right_edge().descend();
        let right_len = right_node.len();

        assert!(left_len + right_len < 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.key_at(0),
                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.val_at(0),
                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 {
                // SAFETY: the height of the nodes being merged is one below the height
                // of the node of this edge, thus above zero, so they are internal.
                let mut left_node = left_node.cast_unchecked();
                let mut right_node = right_node.cast_unchecked();
                ptr::copy_nonoverlapping(
                    right_node.as_internal().edges.as_ptr(),
                    left_node
                        .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.reborrow_mut(), i).correct_parent_link();
                }

                alloc.dealloc(right_node.node.cast(), Layout::new::<InternalNode<K, V>>());
            } else {
                alloc.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 places it in the key/value storage
    /// 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.kv_mut().0, k);
            let v = mem::replace(self.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 places it in the key/value storage
    /// 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.kv_mut().0, k);
            let v = mem::replace(self.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.
            assert!(right_len + count <= CAPACITY);
            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.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.as_leaf_mut().len -= count as u16;
            right_node.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.
            assert!(left_len + count <= CAPACITY);
            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.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.as_leaf_mut().len += count as u16;
            right_node.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,
) {
    unsafe {
        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().edges.as_ptr();
    let dest_ptr = dest.as_internal_mut().edges.as_mut_ptr();
    unsafe {
        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> NodeRef<BorrowType, K, V, marker::Leaf> {
    /// Removes any static information asserting that this node is a `Leaf` node.
    pub fn forget_type(self) -> NodeRef<BorrowType, K, V, marker::LeafOrInternal> {
        NodeRef {
            height: self.height,
            node: self.node,
            _marker: PhantomData,
        }
    }
}

impl<BorrowType, K, V> NodeRef<BorrowType, K, V, marker::Internal> {
    /// Removes any static information asserting that this node is an `Internal` node.
    pub fn forget_type(self) -> NodeRef<BorrowType, K, V, marker::LeafOrInternal> {
        NodeRef {
            height: self.height,
            node: self.node,
            _marker: PhantomData,
        }
    }
}

impl<BorrowType, K, V> Handle<NodeRef<BorrowType, K, V, marker::Leaf>, marker::Edge> {
    pub fn forget_node_type(
        self,
    ) -> Handle<NodeRef<BorrowType, K, V, marker::LeafOrInternal>, marker::Edge> {
        unsafe { Handle::new_edge(self.node.forget_type(), self.idx) }
    }
}

impl<BorrowType, K, V> Handle<NodeRef<BorrowType, K, V, marker::Internal>, marker::Edge> {
    pub fn forget_node_type(
        self,
    ) -> Handle<NodeRef<BorrowType, K, V, marker::LeafOrInternal>, marker::Edge> {
        unsafe { Handle::new_edge(self.node.forget_type(), self.idx) }
    }
}

impl<BorrowType, K, V> Handle<NodeRef<BorrowType, K, V, marker::Leaf>, marker::KV> {
    pub fn forget_node_type(
        self,
    ) -> Handle<NodeRef<BorrowType, K, V, marker::LeafOrInternal>, marker::KV> {
        unsafe { Handle::new_kv(self.node.forget_type(), self.idx) }
    }
}

impl<BorrowType, K, V> Handle<NodeRef<BorrowType, K, V, marker::Internal>, marker::KV> {
    pub fn forget_node_type(
        self,
    ) -> Handle<NodeRef<BorrowType, K, V, marker::LeafOrInternal>, marker::KV> {
        unsafe { Handle::new_kv(self.node.forget_type(), self.idx) }
    }
}

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();

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

            if right_new_len > 0 {
                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.as_leaf_mut().len = left_new_len as u16;
                right_node.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),
}

/// Result of insertion, when a node needed to expand beyond its capacity.
/// Does not distinguish between `Leaf` and `Internal` because `Root` doesn't.
pub struct SplitResult<'a, K, V> {
    // Altered node in existing tree with elements and edges that belong to the left of `k`.
    pub left: NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>,
    // Some key and value split off, to be inserted elsewhere.
    pub k: K,
    pub v: V,
    // Owned, unattached, new node with elements and edges that belong to the right of `k`.
    pub right: Root<K, V>,
}

pub enum InsertResult<'a, K, V, Type> {
    Fit(Handle<NodeRef<marker::Mut<'a>, K, V, Type>, marker::KV>),
    Split(SplitResult<'a, 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 struct ValMut<'a>(PhantomData<&'a mut ()>);

    pub enum KV {}
    pub enum Edge {}
}

unsafe fn slice_insert<T>(slice: &mut [T], idx: usize, val: T) {
    unsafe {
        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 {
    unsafe {
        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
    }
}