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Diffstat (limited to 'library/alloc/src/collections/btree/node.rs')
| -rw-r--r-- | library/alloc/src/collections/btree/node.rs | 1753 |
1 files changed, 1753 insertions, 0 deletions
diff --git a/library/alloc/src/collections/btree/node.rs b/library/alloc/src/collections/btree/node.rs new file mode 100644 index 000000000..d831161bc --- /dev/null +++ b/library/alloc/src/collections/btree/node.rs @@ -0,0 +1,1753 @@ +// 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>> } else { () }; 2 * B], +// parent: Option<(NonNull<Node<K, V, height + 1>>, 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 `n + 1` edges. +// This implies that even an empty node has at least one edge. +// For a leaf node, "having an edge" only means we can identify a position in the node, +// since leaf edges are empty and need no data representation. In an internal node, +// an edge both identifies a position and contains a pointer to a child node. + +use core::marker::PhantomData; +use core::mem::{self, MaybeUninit}; +use core::ptr::{self, NonNull}; +use core::slice::SliceIndex; + +use crate::alloc::{Allocator, Layout}; +use crate::boxed::Box; + +const B: usize = 6; +pub const CAPACITY: usize = 2 * B - 1; +pub const MIN_LEN_AFTER_SPLIT: usize = 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 and part of the representation of internal nodes. +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. + 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> { + /// Initializes a new `LeafNode` in-place. + unsafe fn init(this: *mut Self) { + // 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. + unsafe { + // parent_idx, keys, and vals are all MaybeUninit + ptr::addr_of_mut!((*this).parent).write(None); + ptr::addr_of_mut!((*this).len).write(0); + } + } + + /// Creates a new boxed `LeafNode`. + fn new<A: Allocator + Clone>(alloc: A) -> Box<Self, A> { + unsafe { + let mut leaf = Box::new_uninit_in(alloc); + LeafNode::init(leaf.as_mut_ptr()); + leaf.assume_init() + } + } +} + +/// 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 cast 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)] +// gdb_providers.py uses this type name for introspection. +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, except that near the end, while the tree is held + /// through borrow type `Dying`, some of these pointers are dangling. + edges: [MaybeUninit<BoxedNode<K, V>>; 2 * B], +} + +impl<K, V> InternalNode<K, V> { + /// Creates a new boxed `InternalNode`. + /// + /// # Safety + /// An invariant of internal nodes is that they have at least one + /// initialized and valid edge. This function does not set up + /// such an edge. + unsafe fn new<A: Allocator + Clone>(alloc: A) -> Box<Self, A> { + unsafe { + let mut node = Box::<Self, _>::new_uninit_in(alloc); + // We only need to initialize the data; the edges are MaybeUninit. + LeafNode::init(ptr::addr_of_mut!((*node.as_mut_ptr()).data)); + node.assume_init() + } + } +} + +/// 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, +/// is not a separate type and has no destructor. +type BoxedNode<K, V> = NonNull<LeafNode<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`: A dummy type that describes the kind of borrow and carries a lifetime. +/// - When this is `Immut<'a>`, the `NodeRef` acts roughly like `&'a Node`. +/// - When this is `ValMut<'a>`, the `NodeRef` acts roughly like `&'a Node` +/// with respect to keys and tree structure, but also allows many +/// mutable references to values throughout the tree to coexist. +/// - When this is `Mut<'a>`, the `NodeRef` acts roughly like `&'a mut Node`, +/// although insert methods allow a mutable pointer to a value to coexist. +/// - When this is `Owned`, the `NodeRef` acts roughly like `Box<Node>`, +/// but does not have a destructor, and must be cleaned up manually. +/// - When this is `Dying`, the `NodeRef` still acts roughly like `Box<Node>`, +/// but has methods to destroy the tree bit by bit, and ordinary methods, +/// while not marked as unsafe to call, can invoke UB if called incorrectly. +/// Since any `NodeRef` allows navigating through the tree, `BorrowType` +/// effectively applies to the entire tree, not just to the node itself. +/// - `K` and `V`: These are the types of keys and values 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. +/// `Type` is named `NodeType` when used outside `NodeRef`. +/// +/// Both `BorrowType` and `NodeType` restrict what methods we implement, to +/// exploit static type safety. There are limitations in the way we can apply +/// such restrictions: +/// - For each type parameter, we can only define a method either generically +/// or for one particular type. For example, we cannot define a method like +/// `into_kv` generically for all `BorrowType`, or once for all types that +/// carry a lifetime, because we want it to return `&'a` references. +/// Therefore, we define it only for the least powerful type `Immut<'a>`. +/// - We cannot get implicit coercion from say `Mut<'a>` to `Immut<'a>`. +/// Therefore, we have to explicitly call `reborrow` on a more powerful +/// `NodeRef` in order to reach a method like `into_kv`. +/// +/// All methods on `NodeRef` that return some kind of reference, either: +/// - Take `self` by value, and return the lifetime carried by `BorrowType`. +/// Sometimes, to invoke such a method, we need to call `reborrow_mut`. +/// - Take `self` by reference, and (implicitly) return that reference's +/// lifetime, instead of the lifetime carried by `BorrowType`. That way, +/// the borrow checker guarantees that the `NodeRef` remains borrowed as long +/// as the returned reference is used. +/// The methods supporting insert bend this rule by returning a raw pointer, +/// i.e., a reference without any lifetime. +pub struct NodeRef<BorrowType, K, V, Type> { + /// The number of levels that the node and the level of leaves are apart, a + /// constant of the node that cannot be entirely described by `Type`, and that + /// the node itself does not store. We only need to store the height of the root + /// node, and derive every other node's height from it. + /// Must be zero if `Type` is `Leaf` and non-zero if `Type` is `Internal`. + height: usize, + /// The pointer to the leaf or internal node. The definition of `InternalNode` + /// ensures that the pointer is valid either way. + node: NonNull<LeafNode<K, V>>, + _marker: PhantomData<(BorrowType, Type)>, +} + +/// The root node of an owned tree. +/// +/// Note that this does not have a destructor, and must be cleaned up manually. +pub type Root<K, V> = NodeRef<marker::Owned, K, V, marker::LeafOrInternal>; + +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> {} +unsafe impl<K: Send, V: Send, Type> Send for NodeRef<marker::Dying, K, V, Type> {} + +impl<K, V> NodeRef<marker::Owned, K, V, marker::Leaf> { + pub fn new_leaf<A: Allocator + Clone>(alloc: A) -> Self { + Self::from_new_leaf(LeafNode::new(alloc)) + } + + fn from_new_leaf<A: Allocator + Clone>(leaf: Box<LeafNode<K, V>, A>) -> Self { + NodeRef { height: 0, node: NonNull::from(Box::leak(leaf)), _marker: PhantomData } + } +} + +impl<K, V> NodeRef<marker::Owned, K, V, marker::Internal> { + fn new_internal<A: Allocator + Clone>(child: Root<K, V>, alloc: A) -> Self { + let mut new_node = unsafe { InternalNode::new(alloc) }; + new_node.edges[0].write(child.node); + unsafe { NodeRef::from_new_internal(new_node, child.height + 1) } + } + + /// # Safety + /// `height` must not be zero. + unsafe fn from_new_internal<A: Allocator + Clone>( + internal: Box<InternalNode<K, V>, A>, + height: usize, + ) -> Self { + debug_assert!(height > 0); + let node = NonNull::from(Box::leak(internal)).cast(); + let mut this = NodeRef { height, node, _marker: PhantomData }; + this.borrow_mut().correct_all_childrens_parent_links(); + this + } +} + +impl<BorrowType, K, V> NodeRef<BorrowType, K, V, marker::Internal> { + /// Unpack a node reference that was packed as `NodeRef::parent`. + fn from_internal(node: NonNull<InternalNode<K, V>>, height: usize) -> Self { + debug_assert!(height > 0); + NodeRef { height, node: node.cast(), _marker: PhantomData } + } +} + +impl<BorrowType, K, V> NodeRef<BorrowType, K, V, marker::Internal> { + /// Exposes the data of an internal node. + /// + /// Returns a raw ptr to avoid invalidating other references to this node. + fn as_internal_ptr(this: &Self) -> *mut InternalNode<K, V> { + // SAFETY: the static node type is `Internal`. + this.node.as_ptr() as *mut InternalNode<K, V> + } +} + +impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Internal> { + /// Borrows exclusive access to the data of an internal node. + fn as_internal_mut(&mut self) -> &mut InternalNode<K, V> { + let ptr = Self::as_internal_ptr(self); + unsafe { &mut *ptr } + } +} + +impl<BorrowType, K, V, Type> NodeRef<BorrowType, K, V, Type> { + /// Finds the length of the node. This is the number of keys or values. + /// The number of edges is `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(self)).len) } + } + + /// Returns the number of levels that the node and leaves are apart. Zero + /// height means the node is a leaf itself. If you picture trees with the + /// root on top, the number says at which elevation the node appears. + /// If you picture trees with leaves on top, the number says how high + /// the tree extends above the node. + pub fn height(&self) -> usize { + self.height + } + + /// Temporarily takes out another, immutable reference to the same node. + pub 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. + /// + /// Returns a raw ptr to avoid invalidating other references to this node. + fn as_leaf_ptr(this: &Self) -> *mut 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. + this.node.as_ptr() + } +} + +impl<BorrowType: marker::BorrowType, K, V, Type> NodeRef<BorrowType, K, V, Type> { + /// 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`. + /// + /// The method name assumes you picture trees with the root node on top. + /// + /// `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> { + assert!(BorrowType::PERMITS_TRAVERSAL); + // 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: *const _ = Self::as_leaf_ptr(&self); + unsafe { (*leaf_ptr).parent } + .as_ref() + .map(|parent| Handle { + node: NodeRef::from_internal(*parent, self.height + 1), + 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<BorrowType, K, V, Type> NodeRef<BorrowType, K, V, Type> { + /// Could be a public implementation of PartialEq, but only used in this module. + fn eq(&self, other: &Self) -> bool { + let Self { node, height, _marker } = self; + if node.eq(&other.node) { + debug_assert_eq!(*height, other.height); + true + } else { + false + } + } +} + +impl<'a, K: 'a, V: 'a, Type> NodeRef<marker::Immut<'a>, K, V, Type> { + /// Exposes the leaf portion of any leaf or internal node in an immutable tree. + fn into_leaf(self) -> &'a LeafNode<K, V> { + let ptr = Self::as_leaf_ptr(&self); + // SAFETY: there can be no mutable references into this tree borrowed as `Immut`. + unsafe { &*ptr } + } + + /// Borrows a view into the keys stored in the node. + pub fn keys(&self) -> &[K] { + let leaf = self.into_leaf(); + unsafe { + MaybeUninit::slice_assume_init_ref(leaf.keys.get_unchecked(..usize::from(leaf.len))) + } + } +} + +impl<K, V> NodeRef<marker::Dying, K, V, marker::LeafOrInternal> { + /// Similar to `ascend`, gets a reference to a node's parent node, but also + /// deallocates 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: Allocator + Clone>( + self, + alloc: A, + ) -> Option<Handle<NodeRef<marker::Dying, K, V, marker::Internal>, marker::Edge>> { + let height = self.height; + let node = self.node; + let ret = self.ascend().ok(); + unsafe { + alloc.deallocate( + 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> { + /// Temporarily takes out another mutable reference to the same node. Beware, as + /// this method is very dangerous, doubly so since it might 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 } + } + + /// Borrows exclusive access to the leaf portion of a leaf or internal node. + fn as_leaf_mut(&mut self) -> &mut LeafNode<K, V> { + let ptr = Self::as_leaf_ptr(self); + // SAFETY: we have exclusive access to the entire node. + unsafe { &mut *ptr } + } + + /// Offers exclusive access to the leaf portion of a leaf or internal node. + fn into_leaf_mut(mut self) -> &'a mut LeafNode<K, V> { + let ptr = Self::as_leaf_ptr(&mut self); + // SAFETY: we have exclusive access to the entire node. + unsafe { &mut *ptr } + } +} + +impl<K, V, Type> NodeRef<marker::Dying, K, V, Type> { + /// Borrows exclusive access to the leaf portion of a dying leaf or internal node. + fn as_leaf_dying(&mut self) -> &mut LeafNode<K, V> { + let ptr = Self::as_leaf_ptr(self); + // SAFETY: we have exclusive access to the entire node. + unsafe { &mut *ptr } + } +} + +impl<'a, K: 'a, V: 'a, Type> NodeRef<marker::Mut<'a>, K, V, Type> { + /// Borrows exclusive access to an element of the key storage area. + /// + /// # Safety + /// `index` is in bounds of 0..CAPACITY + unsafe fn key_area_mut<I, Output: ?Sized>(&mut self, index: I) -> &mut Output + where + I: SliceIndex<[MaybeUninit<K>], Output = Output>, + { + // 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.as_leaf_mut().keys.as_mut_slice().get_unchecked_mut(index) } + } + + /// Borrows exclusive access to an element or slice of the node's value storage area. + /// + /// # Safety + /// `index` is in bounds of 0..CAPACITY + unsafe fn val_area_mut<I, Output: ?Sized>(&mut self, index: I) -> &mut Output + where + I: SliceIndex<[MaybeUninit<V>], Output = Output>, + { + // 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.as_leaf_mut().vals.as_mut_slice().get_unchecked_mut(index) } + } +} + +impl<'a, K: 'a, V: 'a> NodeRef<marker::Mut<'a>, K, V, marker::Internal> { + /// Borrows exclusive access to an element or slice of the node's storage area for edge contents. + /// + /// # Safety + /// `index` is in bounds of 0..CAPACITY + 1 + unsafe fn edge_area_mut<I, Output: ?Sized>(&mut self, index: I) -> &mut Output + where + I: SliceIndex<[MaybeUninit<BoxedNode<K, V>>], Output = Output>, + { + // SAFETY: the caller will not be able to call further methods on self + // until the edge slice reference is dropped, as we have unique access + // for the lifetime of the borrow. + unsafe { self.as_internal_mut().edges.as_mut_slice().get_unchecked_mut(index) } + } +} + +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(mut 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::as_leaf_ptr(&mut self); + let keys = unsafe { ptr::addr_of!((*leaf).keys) }; + let vals = unsafe { ptr::addr_of_mut!((*leaf).vals) }; + // We must coerce to unsized array pointers because of Rust issue #74679. + let keys: *const [_] = keys; + let vals: *mut [_] = vals; + 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, Type> NodeRef<marker::Mut<'a>, K, V, Type> { + /// Borrows exclusive access to the length of the node. + pub fn len_mut(&mut self) -> &mut u16 { + &mut self.as_leaf_mut().len + } +} + +impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::Internal> { + /// # Safety + /// Every item returned by `range` is a valid edge index for the node. + unsafe fn correct_childrens_parent_links<R: Iterator<Item = usize>>(&mut self, range: R) { + for i in range { + debug_assert!(i <= self.len()); + 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) }; + } +} + +impl<'a, K: 'a, V: 'a> NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal> { + /// Sets the node's link to its parent edge, + /// without invalidating other references to the node. + fn set_parent_link(&mut self, parent: NonNull<InternalNode<K, V>>, parent_idx: usize) { + let leaf = Self::as_leaf_ptr(self); + unsafe { (*leaf).parent = Some(parent) }; + unsafe { (*leaf).parent_idx.write(parent_idx as u16) }; + } +} + +impl<K, V> NodeRef<marker::Owned, K, V, marker::LeafOrInternal> { + /// Clears the root's link to its parent edge. + fn clear_parent_link(&mut self) { + let mut root_node = self.borrow_mut(); + let leaf = root_node.as_leaf_mut(); + leaf.parent = None; + } +} + +impl<K, V> NodeRef<marker::Owned, K, V, marker::LeafOrInternal> { + /// Returns a new owned tree, with its own root node that is initially empty. + pub fn new<A: Allocator + Clone>(alloc: A) -> Self { + NodeRef::new_leaf(alloc).forget_type() + } + + /// Adds a new internal node with a single edge pointing to the previous root node, + /// make that new node the root node, and return it. This increases the height by 1 + /// and is the opposite of `pop_internal_level`. + pub fn push_internal_level<A: Allocator + Clone>( + &mut self, + alloc: A, + ) -> NodeRef<marker::Mut<'_>, K, V, marker::Internal> { + super::mem::take_mut(self, |old_root| NodeRef::new_internal(old_root, alloc).forget_type()); + + // `self.borrow_mut()`, except that we just forgot we're internal now: + NodeRef { height: self.height, node: self.node, _marker: PhantomData } + } + + /// 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 keys, values and other children. + /// This decreases the height by 1 and is the opposite of `push_internal_level`. + /// + /// Requires exclusive access to the `NodeRef` object but not to the root node; + /// it will not invalidate other 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: Allocator + Clone>(&mut self, alloc: A) { + assert!(self.height > 0); + + let top = self.node; + + // SAFETY: we asserted to be internal. + let internal_self = unsafe { self.borrow_mut().cast_to_internal_unchecked() }; + // SAFETY: we borrowed `self` exclusively and its borrow type is exclusive. + let internal_node = unsafe { &mut *NodeRef::as_internal_ptr(&internal_self) }; + // SAFETY: the first edge is always initialized. + self.node = unsafe { internal_node.edges[0].assume_init_read() }; + self.height -= 1; + self.clear_parent_link(); + + unsafe { + alloc.deallocate(top.cast(), Layout::new::<InternalNode<K, V>>()); + } + } +} + +impl<K, V, Type> NodeRef<marker::Owned, K, V, Type> { + /// Mutably borrows the owned root node. Unlike `reborrow_mut`, this is safe + /// because the return value cannot be used to destroy the root, and there + /// cannot be other references to the tree. + pub fn borrow_mut(&mut self) -> NodeRef<marker::Mut<'_>, K, V, Type> { + NodeRef { height: self.height, node: self.node, _marker: PhantomData } + } + + /// Slightly mutably borrows the owned root node. + pub fn borrow_valmut(&mut self) -> NodeRef<marker::ValMut<'_>, K, V, Type> { + NodeRef { height: self.height, node: self.node, _marker: PhantomData } + } + + /// Irreversibly transitions to a reference that permits traversal and offers + /// destructive methods and little else. + pub fn into_dying(self) -> NodeRef<marker::Dying, K, V, Type> { + NodeRef { height: self.height, node: self.node, _marker: PhantomData } + } +} + +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, and returns + /// the mutable reference of the inserted value. + pub fn push(&mut self, key: K, val: V) -> &mut V { + let len = self.len_mut(); + let idx = usize::from(*len); + assert!(idx < CAPACITY); + *len += 1; + unsafe { + self.key_area_mut(idx).write(key); + self.val_area_mut(idx).write(val) + } + } +} + +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 = self.len_mut(); + let idx = usize::from(*len); + assert!(idx < CAPACITY); + *len += 1; + unsafe { + self.key_area_mut(idx).write(key); + self.val_area_mut(idx).write(val); + self.edge_area_mut(idx + 1).write(edge.node); + Handle::new_edge(self.reborrow_mut(), idx + 1).correct_parent_link(); + } + } +} + +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> 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, + }) + } + } +} + +impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal> { + /// Unsafely asserts to the compiler the static information that this node is a `Leaf`. + unsafe fn cast_to_leaf_unchecked(self) -> NodeRef<marker::Mut<'a>, K, V, marker::Leaf> { + debug_assert!(self.height == 0); + NodeRef { height: self.height, node: self.node, _marker: PhantomData } + } + + /// Unsafely asserts to the compiler the static information that this node is an `Internal`. + unsafe fn cast_to_internal_unchecked(self) -> NodeRef<marker::Mut<'a>, K, V, marker::Internal> { + debug_assert!(self.height > 0); + 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 { + let Self { node, idx, _marker } = self; + node.eq(&other.node) && *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 might 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) + } + } +} + +pub enum LeftOrRight<T> { + Left(T), + Right(T), +} + +/// 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, LeftOrRight<usize>) { + 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, LeftOrRight::Left(edge_idx)), + EDGE_IDX_LEFT_OF_CENTER => (KV_IDX_CENTER, LeftOrRight::Left(edge_idx)), + EDGE_IDX_RIGHT_OF_CENTER => (KV_IDX_CENTER, LeftOrRight::Right(0)), + _ => (KV_IDX_CENTER + 1, LeftOrRight::Right(edge_idx - (KV_IDX_CENTER + 1 + 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 { + debug_assert!(self.node.len() < CAPACITY); + let new_len = self.node.len() + 1; + + unsafe { + slice_insert(self.node.key_area_mut(..new_len), self.idx, key); + slice_insert(self.node.val_area_mut(..new_len), self.idx, val); + *self.node.len_mut() = new_len as u16; + + self.node.val_area_mut(self.idx).assume_init_mut() + } + } +} + +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: Allocator + Clone>( + mut self, + key: K, + val: V, + alloc: A, + ) -> (Option<SplitResult<'a, K, V, marker::Leaf>>, *mut V) { + if self.node.len() < CAPACITY { + let val_ptr = self.insert_fit(key, val); + (None, val_ptr) + } else { + let (middle_kv_idx, insertion) = splitpoint(self.idx); + let middle = unsafe { Handle::new_kv(self.node, middle_kv_idx) }; + let mut result = middle.split(alloc); + let mut insertion_edge = match insertion { + LeftOrRight::Left(insert_idx) => unsafe { + Handle::new_edge(result.left.reborrow_mut(), insert_idx) + }, + LeftOrRight::Right(insert_idx) => unsafe { + Handle::new_edge(result.right.borrow_mut(), insert_idx) + }, + }; + let val_ptr = insertion_edge.insert_fit(key, val); + (Some(result), 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 that this edge + /// links to. This is useful when the ordering of edges has been changed, + fn correct_parent_link(self) { + // Create backpointer without invalidating other references to the node. + let ptr = unsafe { NonNull::new_unchecked(NodeRef::as_internal_ptr(&self.node)) }; + let idx = self.idx; + let mut child = self.descend(); + child.set_parent_link(ptr, 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>) { + debug_assert!(self.node.len() < CAPACITY); + debug_assert!(edge.height == self.node.height - 1); + let new_len = self.node.len() + 1; + + unsafe { + slice_insert(self.node.key_area_mut(..new_len), self.idx, key); + slice_insert(self.node.val_area_mut(..new_len), self.idx, val); + slice_insert(self.node.edge_area_mut(..new_len + 1), self.idx + 1, edge.node); + *self.node.len_mut() = new_len as u16; + + self.node.correct_childrens_parent_links(self.idx + 1..new_len + 1); + } + } + + /// 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: Allocator + Clone>( + mut self, + key: K, + val: V, + edge: Root<K, V>, + alloc: A, + ) -> Option<SplitResult<'a, K, V, marker::Internal>> { + assert!(edge.height == self.node.height - 1); + + if self.node.len() < CAPACITY { + self.insert_fit(key, val, edge); + None + } else { + let (middle_kv_idx, insertion) = splitpoint(self.idx); + let middle = unsafe { Handle::new_kv(self.node, middle_kv_idx) }; + let mut result = middle.split(alloc); + let mut insertion_edge = match insertion { + LeftOrRight::Left(insert_idx) => unsafe { + Handle::new_edge(result.left.reborrow_mut(), insert_idx) + }, + LeftOrRight::Right(insert_idx) => unsafe { + Handle::new_edge(result.right.borrow_mut(), insert_idx) + }, + }; + insertion_edge.insert_fit(key, val, edge); + Some(result) + } + } +} + +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 some `SplitResult`, the `left` field will be the root node. + /// The returned pointer points to the inserted value, which in the case of `SplitResult` + /// is in the `left` or `right` tree. + pub fn insert_recursing<A: Allocator + Clone>( + self, + key: K, + value: V, + alloc: A, + ) -> (Option<SplitResult<'a, K, V, marker::LeafOrInternal>>, *mut V) { + let (mut split, val_ptr) = match self.insert(key, value, alloc.clone()) { + (None, val_ptr) => return (None, val_ptr), + (Some(split), val_ptr) => (split.forget_node_type(), val_ptr), + }; + + loop { + split = match split.left.ascend() { + Ok(parent) => { + match parent.insert(split.kv.0, split.kv.1, split.right, alloc.clone()) { + None => return (None, val_ptr), + Some(split) => split.forget_node_type(), + } + } + Err(root) => return (Some(SplitResult { left: root, ..split }), val_ptr), + }; + } + } +} + +impl<BorrowType: marker::BorrowType, K, V> + Handle<NodeRef<BorrowType, K, V, marker::Internal>, marker::Edge> +{ + /// Finds the node pointed to by this edge. + /// + /// The method name assumes you picture trees with the root node on top. + /// + /// `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> { + assert!(BorrowType::PERMITS_TRAVERSAL); + // 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 parent_ptr = NodeRef::as_internal_ptr(&self.node); + let node = unsafe { (*parent_ptr).edges.get_unchecked(self.idx).assume_init_read() }; + NodeRef { node, height: self.node.height - 1, _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) { + debug_assert!(self.idx < self.node.len()); + let leaf = self.node.into_leaf(); + let k = unsafe { leaf.keys.get_unchecked(self.idx).assume_init_ref() }; + let v = unsafe { leaf.vals.get_unchecked(self.idx).assume_init_ref() }; + (k, v) + } +} + +impl<'a, K: 'a, V: 'a, NodeType> Handle<NodeRef<marker::Mut<'a>, K, V, NodeType>, marker::KV> { + pub fn key_mut(&mut self) -> &mut K { + unsafe { self.node.key_area_mut(self.idx).assume_init_mut() } + } + + pub fn into_val_mut(self) -> &'a mut V { + debug_assert!(self.idx < self.node.len()); + let leaf = self.node.into_leaf_mut(); + unsafe { leaf.vals.get_unchecked_mut(self.idx).assume_init_mut() } + } +} + +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) { + debug_assert!(self.idx < self.node.len()); + // We cannot call separate key and value methods, because calling the second one + // invalidates the reference returned by the first. + unsafe { + let leaf = self.node.as_leaf_mut(); + let key = leaf.keys.get_unchecked_mut(self.idx).assume_init_mut(); + let val = leaf.vals.get_unchecked_mut(self.idx).assume_init_mut(); + (key, val) + } + } + + /// Replaces the key and value that the KV handle refers to. + pub fn replace_kv(&mut self, k: K, v: V) -> (K, V) { + let (key, val) = self.kv_mut(); + (mem::replace(key, k), mem::replace(val, v)) + } +} + +impl<K, V, NodeType> Handle<NodeRef<marker::Dying, K, V, NodeType>, marker::KV> { + /// Extracts the key and value that the KV handle refers to. + /// # Safety + /// The node that the handle refers to must not yet have been deallocated. + pub unsafe fn into_key_val(mut self) -> (K, V) { + debug_assert!(self.idx < self.node.len()); + let leaf = self.node.as_leaf_dying(); + unsafe { + let key = leaf.keys.get_unchecked_mut(self.idx).assume_init_read(); + let val = leaf.vals.get_unchecked_mut(self.idx).assume_init_read(); + (key, val) + } + } + + /// Drops the key and value that the KV handle refers to. + /// # Safety + /// The node that the handle refers to must not yet have been deallocated. + #[inline] + pub unsafe fn drop_key_val(mut self) { + debug_assert!(self.idx < self.node.len()); + let leaf = self.node.as_leaf_dying(); + unsafe { + leaf.keys.get_unchecked_mut(self.idx).assume_init_drop(); + leaf.vals.get_unchecked_mut(self.idx).assume_init_drop(); + } + } +} + +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 split_leaf_data(&mut self, new_node: &mut LeafNode<K, V>) -> (K, V) { + debug_assert!(self.idx < self.node.len()); + let old_len = self.node.len(); + let new_len = old_len - self.idx - 1; + new_node.len = new_len as u16; + unsafe { + let k = self.node.key_area_mut(self.idx).assume_init_read(); + let v = self.node.val_area_mut(self.idx).assume_init_read(); + + move_to_slice( + self.node.key_area_mut(self.idx + 1..old_len), + &mut new_node.keys[..new_len], + ); + move_to_slice( + self.node.val_area_mut(self.idx + 1..old_len), + &mut new_node.vals[..new_len], + ); + + *self.node.len_mut() = self.idx as u16; + (k, v) + } + } +} + +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 left 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: Allocator + Clone>(mut self, alloc: A) -> SplitResult<'a, K, V, marker::Leaf> { + let mut new_node = LeafNode::new(alloc); + + let kv = self.split_leaf_data(&mut new_node); + + let right = NodeRef::from_new_leaf(new_node); + SplitResult { left: self.node, kv, right } + } + + /// 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>) { + let old_len = self.node.len(); + unsafe { + let k = slice_remove(self.node.key_area_mut(..old_len), self.idx); + let v = slice_remove(self.node.val_area_mut(..old_len), self.idx); + *self.node.len_mut() = (old_len - 1) as u16; + ((k, v), self.left_edge()) + } + } +} + +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 + /// left 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: Allocator + Clone>( + mut self, + alloc: A, + ) -> SplitResult<'a, K, V, marker::Internal> { + let old_len = self.node.len(); + unsafe { + let mut new_node = InternalNode::new(alloc); + let kv = self.split_leaf_data(&mut new_node.data); + let new_len = usize::from(new_node.data.len); + move_to_slice( + self.node.edge_area_mut(self.idx + 1..old_len + 1), + &mut new_node.edges[..new_len + 1], + ); + + let height = self.node.height; + let right = NodeRef::from_new_internal(new_node, height); + + SplitResult { left: self.node, kv, right } + } + } +} + +/// Represents a session for evaluating and performing a balancing operation +/// around an internal key-value pair. +pub struct BalancingContext<'a, K, V> { + parent: Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::KV>, + left_child: NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, + right_child: NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, +} + +impl<'a, K, V> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Internal>, marker::KV> { + pub fn consider_for_balancing(self) -> BalancingContext<'a, K, V> { + let self1 = unsafe { ptr::read(&self) }; + let self2 = unsafe { ptr::read(&self) }; + BalancingContext { + parent: self, + left_child: self1.left_edge().descend(), + right_child: self2.right_edge().descend(), + } + } +} + +impl<'a, K, V> NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal> { + /// Chooses a balancing context involving the node as a child, thus between + /// the KV immediately to the left or to the right in the parent node. + /// Returns an `Err` if there is no parent. + /// Panics if the parent is empty. + /// + /// Prefers the left side, to be optimal if the given node is somehow + /// underfull, meaning here only that it has fewer elements than its left + /// sibling and than its right sibling, if they exist. In that case, + /// merging with the left sibling is faster, since we only need to move + /// the node's N elements, instead of shifting them to the right and moving + /// more than N elements in front. Stealing from the left sibling is also + /// typically faster, since we only need to shift the node's N elements to + /// the right, instead of shifting at least N of the sibling's elements to + /// the left. + pub fn choose_parent_kv(self) -> Result<LeftOrRight<BalancingContext<'a, K, V>>, Self> { + match unsafe { ptr::read(&self) }.ascend() { + Ok(parent_edge) => match parent_edge.left_kv() { + Ok(left_parent_kv) => Ok(LeftOrRight::Left(BalancingContext { + parent: unsafe { ptr::read(&left_parent_kv) }, + left_child: left_parent_kv.left_edge().descend(), + right_child: self, + })), + Err(parent_edge) => match parent_edge.right_kv() { + Ok(right_parent_kv) => Ok(LeftOrRight::Right(BalancingContext { + parent: unsafe { ptr::read(&right_parent_kv) }, + left_child: self, + right_child: right_parent_kv.right_edge().descend(), + })), + Err(_) => unreachable!("empty internal node"), + }, + }, + Err(root) => Err(root), + } + } +} + +impl<'a, K, V> BalancingContext<'a, K, V> { + pub fn left_child_len(&self) -> usize { + self.left_child.len() + } + + pub fn right_child_len(&self) -> usize { + self.right_child.len() + } + + pub fn into_left_child(self) -> NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal> { + self.left_child + } + + pub fn into_right_child(self) -> NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal> { + self.right_child + } + + /// Returns whether merging is possible, i.e., whether there is enough room + /// in a node to combine the central KV with both adjacent child nodes. + pub fn can_merge(&self) -> bool { + self.left_child.len() + 1 + self.right_child.len() <= CAPACITY + } +} + +impl<'a, K: 'a, V: 'a> BalancingContext<'a, K, V> { + /// Performs a merge and lets a closure decide what to return. + fn do_merge< + F: FnOnce( + NodeRef<marker::Mut<'a>, K, V, marker::Internal>, + NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, + ) -> R, + R, + A: Allocator, + >( + self, + result: F, + alloc: A, + ) -> R { + let Handle { node: mut parent_node, idx: parent_idx, _marker } = self.parent; + let old_parent_len = parent_node.len(); + let mut left_node = self.left_child; + let old_left_len = left_node.len(); + let mut right_node = self.right_child; + let right_len = right_node.len(); + let new_left_len = old_left_len + 1 + right_len; + + assert!(new_left_len <= CAPACITY); + + unsafe { + *left_node.len_mut() = new_left_len as u16; + + let parent_key = slice_remove(parent_node.key_area_mut(..old_parent_len), parent_idx); + left_node.key_area_mut(old_left_len).write(parent_key); + move_to_slice( + right_node.key_area_mut(..right_len), + left_node.key_area_mut(old_left_len + 1..new_left_len), + ); + + let parent_val = slice_remove(parent_node.val_area_mut(..old_parent_len), parent_idx); + left_node.val_area_mut(old_left_len).write(parent_val); + move_to_slice( + right_node.val_area_mut(..right_len), + left_node.val_area_mut(old_left_len + 1..new_left_len), + ); + + slice_remove(&mut parent_node.edge_area_mut(..old_parent_len + 1), parent_idx + 1); + parent_node.correct_childrens_parent_links(parent_idx + 1..old_parent_len); + *parent_node.len_mut() -= 1; + + if parent_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.reborrow_mut().cast_to_internal_unchecked(); + let mut right_node = right_node.cast_to_internal_unchecked(); + move_to_slice( + right_node.edge_area_mut(..right_len + 1), + left_node.edge_area_mut(old_left_len + 1..new_left_len + 1), + ); + + left_node.correct_childrens_parent_links(old_left_len + 1..new_left_len + 1); + + alloc.deallocate(right_node.node.cast(), Layout::new::<InternalNode<K, V>>()); + } else { + alloc.deallocate(right_node.node.cast(), Layout::new::<LeafNode<K, V>>()); + } + } + result(parent_node, left_node) + } + + /// Merges the parent's key-value pair and both adjacent child nodes into + /// the left child node and returns the shrunk parent node. + /// + /// Panics unless we `.can_merge()`. + pub fn merge_tracking_parent<A: Allocator + Clone>( + self, + alloc: A, + ) -> NodeRef<marker::Mut<'a>, K, V, marker::Internal> { + self.do_merge(|parent, _child| parent, alloc) + } + + /// Merges the parent's key-value pair and both adjacent child nodes into + /// the left child node and returns that child node. + /// + /// Panics unless we `.can_merge()`. + pub fn merge_tracking_child<A: Allocator + Clone>( + self, + alloc: A, + ) -> NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal> { + self.do_merge(|_parent, child| child, alloc) + } + + /// Merges the parent's key-value pair and both adjacent child nodes into + /// the left child node and returns the edge handle in that child node + /// where the tracked child edge ended up, + /// + /// Panics unless we `.can_merge()`. + pub fn merge_tracking_child_edge<A: Allocator + Clone>( + self, + track_edge_idx: LeftOrRight<usize>, + alloc: A, + ) -> Handle<NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, marker::Edge> { + let old_left_len = self.left_child.len(); + let right_len = self.right_child.len(); + assert!(match track_edge_idx { + LeftOrRight::Left(idx) => idx <= old_left_len, + LeftOrRight::Right(idx) => idx <= right_len, + }); + let child = self.merge_tracking_child(alloc); + let new_idx = match track_edge_idx { + LeftOrRight::Left(idx) => idx, + LeftOrRight::Right(idx) => old_left_len + 1 + idx, + }; + unsafe { Handle::new_edge(child, new_idx) } + } + + /// Removes a key-value pair from the left child and places it in the key-value storage + /// of the parent, while pushing the old parent key-value pair into the right child. + /// Returns a handle to the edge in the right child corresponding to where the original + /// edge specified by `track_right_edge_idx` ended up. + pub fn steal_left( + mut self, + track_right_edge_idx: usize, + ) -> Handle<NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, marker::Edge> { + self.bulk_steal_left(1); + unsafe { Handle::new_edge(self.right_child, 1 + track_right_edge_idx) } + } + + /// Removes a key-value pair from the right child and places it in the key-value storage + /// of the parent, while pushing the old parent key-value pair onto the left child. + /// Returns a handle to the edge in the left child specified by `track_left_edge_idx`, + /// which didn't move. + pub fn steal_right( + mut self, + track_left_edge_idx: usize, + ) -> Handle<NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, marker::Edge> { + self.bulk_steal_right(1); + unsafe { Handle::new_edge(self.left_child, track_left_edge_idx) } + } + + /// This does stealing similar to `steal_left` but steals multiple elements at once. + pub fn bulk_steal_left(&mut self, count: usize) { + assert!(count > 0); + unsafe { + let left_node = &mut self.left_child; + let old_left_len = left_node.len(); + let right_node = &mut self.right_child; + let old_right_len = right_node.len(); + + // Make sure that we may steal safely. + assert!(old_right_len + count <= CAPACITY); + assert!(old_left_len >= count); + + let new_left_len = old_left_len - count; + let new_right_len = old_right_len + count; + *left_node.len_mut() = new_left_len as u16; + *right_node.len_mut() = new_right_len as u16; + + // Move leaf data. + { + // Make room for stolen elements in the right child. + slice_shr(right_node.key_area_mut(..new_right_len), count); + slice_shr(right_node.val_area_mut(..new_right_len), count); + + // Move elements from the left child to the right one. + move_to_slice( + left_node.key_area_mut(new_left_len + 1..old_left_len), + right_node.key_area_mut(..count - 1), + ); + move_to_slice( + left_node.val_area_mut(new_left_len + 1..old_left_len), + right_node.val_area_mut(..count - 1), + ); + + // Move the left-most stolen pair to the parent. + let k = left_node.key_area_mut(new_left_len).assume_init_read(); + let v = left_node.val_area_mut(new_left_len).assume_init_read(); + let (k, v) = self.parent.replace_kv(k, v); + + // Move parent's key-value pair to the right child. + right_node.key_area_mut(count - 1).write(k); + right_node.val_area_mut(count - 1).write(v); + } + + match (left_node.reborrow_mut().force(), right_node.reborrow_mut().force()) { + (ForceResult::Internal(mut left), ForceResult::Internal(mut right)) => { + // Make room for stolen edges. + slice_shr(right.edge_area_mut(..new_right_len + 1), count); + + // Steal edges. + move_to_slice( + left.edge_area_mut(new_left_len + 1..old_left_len + 1), + right.edge_area_mut(..count), + ); + + right.correct_childrens_parent_links(0..new_right_len + 1); + } + (ForceResult::Leaf(_), ForceResult::Leaf(_)) => {} + _ => unreachable!(), + } + } + } + + /// The symmetric clone of `bulk_steal_left`. + pub fn bulk_steal_right(&mut self, count: usize) { + assert!(count > 0); + unsafe { + let left_node = &mut self.left_child; + let old_left_len = left_node.len(); + let right_node = &mut self.right_child; + let old_right_len = right_node.len(); + + // Make sure that we may steal safely. + assert!(old_left_len + count <= CAPACITY); + assert!(old_right_len >= count); + + let new_left_len = old_left_len + count; + let new_right_len = old_right_len - count; + *left_node.len_mut() = new_left_len as u16; + *right_node.len_mut() = new_right_len as u16; + + // Move leaf data. + { + // Move the right-most stolen pair to the parent. + let k = right_node.key_area_mut(count - 1).assume_init_read(); + let v = right_node.val_area_mut(count - 1).assume_init_read(); + let (k, v) = self.parent.replace_kv(k, v); + + // Move parent's key-value pair to the left child. + left_node.key_area_mut(old_left_len).write(k); + left_node.val_area_mut(old_left_len).write(v); + + // Move elements from the right child to the left one. + move_to_slice( + right_node.key_area_mut(..count - 1), + left_node.key_area_mut(old_left_len + 1..new_left_len), + ); + move_to_slice( + right_node.val_area_mut(..count - 1), + left_node.val_area_mut(old_left_len + 1..new_left_len), + ); + + // Fill gap where stolen elements used to be. + slice_shl(right_node.key_area_mut(..old_right_len), count); + slice_shl(right_node.val_area_mut(..old_right_len), count); + } + + match (left_node.reborrow_mut().force(), right_node.reborrow_mut().force()) { + (ForceResult::Internal(mut left), ForceResult::Internal(mut right)) => { + // Steal edges. + move_to_slice( + right.edge_area_mut(..count), + left.edge_area_mut(old_left_len + 1..new_left_len + 1), + ); + + // Fill gap where stolen edges used to be. + slice_shl(right.edge_area_mut(..old_right_len + 1), count); + + left.correct_childrens_parent_links(old_left_len + 1..new_left_len + 1); + right.correct_childrens_parent_links(0..new_right_len + 1); + } + (ForceResult::Leaf(_), ForceResult::Leaf(_)) => {} + _ => unreachable!(), + } + } + } +} + +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, Type> Handle<NodeRef<BorrowType, K, V, marker::LeafOrInternal>, Type> { + /// 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>, Type>, + Handle<NodeRef<BorrowType, K, V, marker::Internal>, Type>, + > { + 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, Type> Handle<NodeRef<marker::Mut<'a>, K, V, marker::LeafOrInternal>, Type> { + /// Unsafely asserts to the compiler the static information that the handle's node is a `Leaf`. + pub unsafe fn cast_to_leaf_unchecked( + self, + ) -> Handle<NodeRef<marker::Mut<'a>, K, V, marker::Leaf>, Type> { + let node = unsafe { self.node.cast_to_leaf_unchecked() }; + 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 new_left_len = self.idx; + let mut left_node = self.reborrow_mut().into_node(); + let old_left_len = left_node.len(); + + let new_right_len = old_left_len - new_left_len; + let mut right_node = right.reborrow_mut(); + + assert!(right_node.len() == 0); + assert!(left_node.height == right_node.height); + + if new_right_len > 0 { + *left_node.len_mut() = new_left_len as u16; + *right_node.len_mut() = new_right_len as u16; + + move_to_slice( + left_node.key_area_mut(new_left_len..old_left_len), + right_node.key_area_mut(..new_right_len), + ); + move_to_slice( + left_node.val_area_mut(new_left_len..old_left_len), + right_node.val_area_mut(..new_right_len), + ); + match (left_node.force(), right_node.force()) { + (ForceResult::Internal(mut left), ForceResult::Internal(mut right)) => { + move_to_slice( + left.edge_area_mut(new_left_len + 1..old_left_len + 1), + right.edge_area_mut(1..new_right_len + 1), + ); + right.correct_childrens_parent_links(1..new_right_len + 1); + } + (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. +pub struct SplitResult<'a, K, V, NodeType> { + // Altered node in existing tree with elements and edges that belong to the left of `kv`. + pub left: NodeRef<marker::Mut<'a>, K, V, NodeType>, + // Some key and value that existed before and were split off, to be inserted elsewhere. + pub kv: (K, V), + // Owned, unattached, new node with elements and edges that belong to the right of `kv`. + pub right: NodeRef<marker::Owned, K, V, NodeType>, +} + +impl<'a, K, V> SplitResult<'a, K, V, marker::Leaf> { + pub fn forget_node_type(self) -> SplitResult<'a, K, V, marker::LeafOrInternal> { + SplitResult { left: self.left.forget_type(), kv: self.kv, right: self.right.forget_type() } + } +} + +impl<'a, K, V> SplitResult<'a, K, V, marker::Internal> { + pub fn forget_node_type(self) -> SplitResult<'a, K, V, marker::LeafOrInternal> { + SplitResult { left: self.left.forget_type(), kv: self.kv, right: self.right.forget_type() } + } +} + +pub mod marker { + use core::marker::PhantomData; + + pub enum Leaf {} + pub enum Internal {} + pub enum LeafOrInternal {} + + pub enum Owned {} + pub enum Dying {} + pub struct Immut<'a>(PhantomData<&'a ()>); + pub struct Mut<'a>(PhantomData<&'a mut ()>); + pub struct ValMut<'a>(PhantomData<&'a mut ()>); + + pub trait BorrowType { + // Whether node references of this borrow type allow traversing + // to other nodes in the tree. + const PERMITS_TRAVERSAL: bool = true; + } + impl BorrowType for Owned { + // Traversal isn't needed, it happens using the result of `borrow_mut`. + // By disabling traversal, and only creating new references to roots, + // we know that every reference of the `Owned` type is to a root node. + const PERMITS_TRAVERSAL: bool = false; + } + impl BorrowType for Dying {} + impl<'a> BorrowType for Immut<'a> {} + impl<'a> BorrowType for Mut<'a> {} + impl<'a> BorrowType for ValMut<'a> {} + + pub enum KV {} + pub enum Edge {} +} + +/// Inserts a value into a slice of initialized elements followed by one uninitialized element. +/// +/// # Safety +/// The slice has more than `idx` elements. +unsafe fn slice_insert<T>(slice: &mut [MaybeUninit<T>], idx: usize, val: T) { + unsafe { + let len = slice.len(); + debug_assert!(len > idx); + let slice_ptr = slice.as_mut_ptr(); + if len > idx + 1 { + ptr::copy(slice_ptr.add(idx), slice_ptr.add(idx + 1), len - idx - 1); + } + (*slice_ptr.add(idx)).write(val); + } +} + +/// Removes and returns a value from a slice of all initialized elements, leaving behind one +/// trailing uninitialized element. +/// +/// # Safety +/// The slice has more than `idx` elements. +unsafe fn slice_remove<T>(slice: &mut [MaybeUninit<T>], idx: usize) -> T { + unsafe { + let len = slice.len(); + debug_assert!(idx < len); + let slice_ptr = slice.as_mut_ptr(); + let ret = (*slice_ptr.add(idx)).assume_init_read(); + ptr::copy(slice_ptr.add(idx + 1), slice_ptr.add(idx), len - idx - 1); + ret + } +} + +/// Shifts the elements in a slice `distance` positions to the left. +/// +/// # Safety +/// The slice has at least `distance` elements. +unsafe fn slice_shl<T>(slice: &mut [MaybeUninit<T>], distance: usize) { + unsafe { + let slice_ptr = slice.as_mut_ptr(); + ptr::copy(slice_ptr.add(distance), slice_ptr, slice.len() - distance); + } +} + +/// Shifts the elements in a slice `distance` positions to the right. +/// +/// # Safety +/// The slice has at least `distance` elements. +unsafe fn slice_shr<T>(slice: &mut [MaybeUninit<T>], distance: usize) { + unsafe { + let slice_ptr = slice.as_mut_ptr(); + ptr::copy(slice_ptr, slice_ptr.add(distance), slice.len() - distance); + } +} + +/// Moves all values from a slice of initialized elements to a slice +/// of uninitialized elements, leaving behind `src` as all uninitialized. +/// Works like `dst.copy_from_slice(src)` but does not require `T` to be `Copy`. +fn move_to_slice<T>(src: &mut [MaybeUninit<T>], dst: &mut [MaybeUninit<T>]) { + assert!(src.len() == dst.len()); + unsafe { + ptr::copy_nonoverlapping(src.as_ptr(), dst.as_mut_ptr(), src.len()); + } +} + +#[cfg(test)] +mod tests; |