ic_stable_structures/

btreemap.rs

//! This module implements a key/value store based on a B-Tree
//! in stable memory.
//!
//! # V2 layout
//!
//! ```text
//! ---------------------------------------- <- Address 0
//! Magic "BTR"                 ↕ 3 bytes
//! ----------------------------------------
//! Layout version              ↕ 1 byte
//! ----------------------------------------
//! Max key size                ↕ 4 bytes             Page size                   ↕ 4 bytes
//! ----------------------------------------   OR   ----------------------------------------
//! Max value size              ↕ 4 bytes             PAGE_SIZE_VALUE_MARKER      ↕ 4 bytes
//! ----------------------------------------
//! Root node address           ↕ 8 bytes
//! ----------------------------------------
//! Length (number of elements) ↕ 8 bytes
//! ---------------------------------------- <- Address 28 (PACKED_HEADER_SIZE)
//! Reserved space              ↕ 24 bytes
//! ---------------------------------------- <- Address 52 (ALLOCATOR_OFFSET)
//! Allocator
//! ----------------------------------------
//! ... free memory for nodes
//! ----------------------------------------
//! ```
//!
//! # V1 layout
//!
//! ```text
//! ---------------------------------------- <- Address 0
//! Magic "BTR"                 ↕ 3 bytes
//! ----------------------------------------
//! Layout version              ↕ 1 byte
//! ----------------------------------------
//! Max key size                ↕ 4 bytes
//! ----------------------------------------
//! Max value size              ↕ 4 bytes
//! ----------------------------------------
//! Root node address           ↕ 8 bytes
//! ----------------------------------------
//! Length (number of elements) ↕ 8 bytes
//! ---------------------------------------- <- Address 28 (PACKED_HEADER_SIZE)
//! Reserved space              ↕ 24 bytes
//! ---------------------------------------- <- Address 52 (ALLOCATOR_OFFSET)
//! Allocator
//! ----------------------------------------
//! ... free memory for nodes
//! ----------------------------------------
//! ```
mod allocator;
mod iter;
mod node;
use crate::btreemap::iter::{IterInternal, KeysIter, ValuesIter};
use crate::{
    storable::Bound as StorableBound,
    types::{Address, NULL},
    Memory, Storable,
};
use allocator::Allocator;
pub use iter::Iter;
use node::{DerivedPageSize, Entry, Node, NodeType, PageSize, Version};
use std::borrow::Cow;
use std::marker::PhantomData;
use std::ops::{Bound, RangeBounds};

#[cfg(test)]
mod proptests;

const MAGIC: &[u8; 3] = b"BTR";
const LAYOUT_VERSION: u8 = 1;
const LAYOUT_VERSION_2: u8 = 2;
// The sum of all the header fields, i.e. size of a packed header.
const PACKED_HEADER_SIZE: usize = 28;
// The offset where the allocator begins.
const ALLOCATOR_OFFSET: usize = 52;

// The default page size to use in BTreeMap V2 in bytes.
const DEFAULT_PAGE_SIZE: u32 = 1024;

// A marker to indicate that the `PageSize` stored in the header is a `PageSize::Value`.
const PAGE_SIZE_VALUE_MARKER: u32 = u32::MAX;

/// A B-Tree map implementation that stores its data into a designated memory.
///
/// # Memory Implementations
///
/// `BTreeMap` works with any memory implementation that satisfies the [`Memory`] trait:
///
/// - [`Ic0StableMemory`](crate::Ic0StableMemory): Stores data in the Internet Computer's stable memory
/// - [`VectorMemory`](crate::VectorMemory): In-memory implementation backed by a Rust `Vec<u8>`
/// - [`FileMemory`](crate::FileMemory): Persists data to disk using a file
/// - [`DefaultMemoryImpl`](crate::DefaultMemoryImpl): Default implementation that automatically selects the
///   appropriate memory backend based on the environment:
///   - Uses `Ic0StableMemory` when running in an Internet Computer canister (wasm32 target)
///   - Falls back to `VectorMemory` in other environments (like tests or non-IC contexts)
///
/// For almost all use cases, [`DefaultMemoryImpl`](crate::DefaultMemoryImpl) is recommended as it provides
/// the right implementation based on the runtime context.
///
/// # Examples
///
/// ## Basic Usage with a Single BTreeMap
///
/// ```rust
/// use ic_stable_structures::{BTreeMap, DefaultMemoryImpl};
/// let mut map: BTreeMap<u64, String, _> = BTreeMap::init(DefaultMemoryImpl::default());
///
/// map.insert(1, "hello".to_string());
/// # assert_eq!(map.get(&1), Some("hello".to_string()));
/// ```
///
/// ## Multiple BTreeMaps and Memory Management
///
/// **Important**: Each stable structure requires its own designated memory region. Attempting to
/// initialize multiple structures with the same memory will lead to data corruption.
///
/// ### What NOT to do:
///
/// ```rust,no_run
/// use ic_stable_structures::{BTreeMap, DefaultMemoryImpl};
///
/// // ERROR: Using the same memory for multiple BTreeMaps will corrupt data
/// let mut map_1: BTreeMap<u64, String, _> = BTreeMap::init(DefaultMemoryImpl::default());
/// let mut map_2: BTreeMap<u64, String, _> = BTreeMap::init(DefaultMemoryImpl::default());
///
/// map_1.insert(1, "two".to_string());
/// map_2.insert(1, "three".to_string());
/// // This assertion would fail: changes to map_2 corrupt map_1's data
/// assert_eq!(map_1.get(&1), Some("two".to_string()));
/// ```
///
/// ### Correct approach using MemoryManager:
///
/// ```rust
/// use ic_stable_structures::{
///    memory_manager::{MemoryId, MemoryManager},
///    BTreeMap, DefaultMemoryImpl,
/// };
///
/// // Initialize the memory manager with a single memory
/// let memory_manager = MemoryManager::init(DefaultMemoryImpl::default());
///
/// // Get separate virtual memories for each BTreeMap
/// let mut map_1: BTreeMap<u64, String, _> = BTreeMap::init(memory_manager.get(MemoryId::new(0)));
/// let mut map_2: BTreeMap<u64, String, _> = BTreeMap::init(memory_manager.get(MemoryId::new(1)));
///
/// map_1.insert(1, "two".to_string());
/// map_2.insert(1, "three".to_string());
/// // Now this works as expected
/// assert_eq!(map_1.get(&1), Some("two".to_string()));
/// ```
///
/// The [`MemoryManager`](crate::memory_manager::MemoryManager) creates up to 255 virtual memories
/// from a single contiguous memory, allowing multiple stable structures to safely coexist.
///
/// For complete examples of using multiple stable structures in a production environment, see the
/// [Quick Start example](https://github.com/dfinity/stable-structures/tree/main/examples/src/quick_start).
///
/// ## Custom Types
///
/// You can store custom structs in a `BTreeMap` by implementing the `Storable` trait:
///
/// ```rust
/// use ic_stable_structures::{BTreeMap, DefaultMemoryImpl, Storable, storable::Bound};
/// use std::borrow::Cow;
///
/// #[derive(Debug, PartialEq)]
/// struct User {
///     id: u64,
///     name: String,
/// }
///
/// impl Storable for User {
///     fn to_bytes(&self) -> Cow<'_, [u8]> {
///         let mut bytes = Vec::new();
///         // TODO: Convert your struct to bytes...
///         Cow::Owned(bytes)
///     }
///
///     fn into_bytes(self) -> Vec<u8> {
///         let mut bytes = Vec::new();
///         // TODO: Convert your struct to bytes...
///         bytes
///     }
///
///     fn from_bytes(bytes: Cow<[u8]>) -> Self {
///         // TODO: Convert bytes back to your struct
///         let (id, name) = (0, "".to_string());
///         User { id, name }
///     }
///
///     // Types can be bounded or unbounded:
///     // - Use Bound::Unbounded if the size can vary or isn't known in advance (recommended for most cases)
///     // - Use Bound::Bounded if you know the maximum size and want memory optimization
///     const BOUND: Bound = Bound::Unbounded;
/// }
///
/// // Now you can use your custom type in a BTreeMap
/// let mut map: BTreeMap<u64, User, _> = BTreeMap::init(DefaultMemoryImpl::default());
///
/// let user = User { id: 1, name: "Alice".to_string() };
/// map.insert(1, user);
///
/// // Retrieving the custom type
/// if let Some(user) = map.get(&1) {
///     println!("Found user: {}", user.name);
/// }
/// ```
///
/// ### Bounded vs Unbounded Types
///
/// When implementing `Storable`, you must specify whether your type is bounded or unbounded:
///
/// - **Unbounded (`Bound::Unbounded`)**:
///   - Use when your type's serialized size can vary or has no fixed maximum
///   - Recommended for most custom types, especially those containing Strings or Vecs
///   - Example: `const BOUND: Bound = Bound::Unbounded;`
///
/// - **Bounded (`Bound::Bounded{ max_size, is_fixed_size }`)**:
///   - Use when you know the maximum serialized size of your type
///   - Enables memory optimizations in the BTreeMap
///   - Example: `const BOUND: Bound = Bound::Bounded { max_size: 100, is_fixed_size: false };`
///   - For types with truly fixed size (like primitive types), set `is_fixed_size: true`
///
/// If unsure, use `Bound::Unbounded` as it's the safer choice.
///
/// # Warning
///
/// Once you've deployed with a bounded type, you cannot increase its `max_size` in
/// future versions without risking data corruption. You can, however, migrate from a bounded type
/// to an unbounded type if needed. For evolving data structures, prefer `Bound::Unbounded`.
pub struct BTreeMap<K, V, M>
where
    K: Storable + Ord + Clone,
    V: Storable,
    M: Memory,
{
    // The address of the root node. If a root node doesn't exist, the address
    // is set to NULL.
    root_addr: Address,

    version: Version,

    // An allocator used for managing memory and allocating nodes.
    allocator: Allocator<M>,

    // The number of elements in the map.
    length: u64,

    // A marker to communicate to the Rust compiler that we own these types.
    _phantom: PhantomData<(K, V)>,
}

#[derive(PartialEq, Debug)]
/// The packed header size must be <= ALLOCATOR_OFFSET.
struct BTreeHeader {
    version: Version,
    root_addr: Address,
    length: u64,
    // Reserved bytes for future extensions
}

impl<K, V, M> BTreeMap<K, V, M>
where
    K: Storable + Ord + Clone,
    V: Storable,
    M: Memory,
{
    /// Initializes a `BTreeMap`.
    ///
    /// If the memory provided already contains a `BTreeMap`, then that
    /// map is loaded. Otherwise, a new `BTreeMap` instance is created.
    pub fn init(memory: M) -> Self {
        if memory.size() == 0 {
            // Memory is empty. Create a new map.
            return BTreeMap::new(memory);
        }

        // Check if the magic in the memory corresponds to a BTreeMap.
        let mut dst = vec![0; 3];
        memory.read(0, &mut dst);
        if dst != MAGIC {
            // No BTreeMap found. Create a new instance.
            BTreeMap::new(memory)
        } else {
            // The memory already contains a BTreeMap. Load it.
            BTreeMap::load(memory)
        }
    }

    /// Initializes a v1 `BTreeMap`.
    ///
    /// This is exposed only in testing.
    #[cfg(test)]
    pub fn init_v1(memory: M) -> Self {
        if memory.size() == 0 {
            // Memory is empty. Create a new map.
            return BTreeMap::new_v1(memory);
        }

        // Check if the magic in the memory corresponds to a BTreeMap.
        let mut dst = vec![0; 3];
        memory.read(0, &mut dst);
        if dst != MAGIC {
            // No BTreeMap found. Create a new instance.
            BTreeMap::new_v1(memory)
        } else {
            // The memory already contains a BTreeMap. Load it, making sure
            // we don't migrate the BTreeMap to v2.
            BTreeMap::load_helper(memory, false)
        }
    }

    /// Creates a new instance a `BTreeMap`.
    ///
    /// The given `memory` is assumed to be exclusively reserved for this data
    /// structure and that it starts at address zero. Typically `memory` will
    /// be an instance of `RestrictedMemory`.
    ///
    /// When initialized, the data structure has the following memory layout:
    ///
    ///    |  BTreeHeader  |  Allocator | ... free memory for nodes |
    ///
    /// See `Allocator` for more details on its own memory layout.
    pub fn new(memory: M) -> Self {
        let page_size = match (K::BOUND, V::BOUND) {
            // The keys and values are both bounded.
            (
                StorableBound::Bounded {
                    max_size: max_key_size,
                    ..
                },
                StorableBound::Bounded {
                    max_size: max_value_size,
                    ..
                },
            ) => {
                // Get the maximum possible node size.
                let max_node_size = Node::<K>::max_size(max_key_size, max_value_size).get();

                // A node can have at most 11 entries, and an analysis has shown that ~70% of all
                // nodes have <= 8 entries. We can therefore use a page size that's 8/11 the
                // maximum size with little performance difference but with a significant storage
                // saving. We round the 8/11 to be 3/4.
                PageSize::Value((max_node_size * 3 / 4) as u32)
            }
            // Use a default page size.
            _ => PageSize::Value(DEFAULT_PAGE_SIZE),
        };

        let btree = Self {
            root_addr: NULL,
            allocator: Allocator::new(
                memory,
                Address::from(ALLOCATOR_OFFSET as u64),
                page_size.get().into(),
            ),
            version: Version::V2(page_size),
            length: 0,
            _phantom: PhantomData,
        };

        btree.save_header();
        btree
    }

    /// Create a v1 instance of the BTree.
    ///
    /// This is only exposed for testing.
    #[cfg(test)]
    pub fn new_v1(memory: M) -> Self {
        let max_key_size = K::BOUND.max_size();
        let max_value_size = V::BOUND.max_size();

        let btree = Self {
            root_addr: NULL,
            allocator: Allocator::new(
                memory,
                Address::from(ALLOCATOR_OFFSET as u64),
                Node::<K>::max_size(max_key_size, max_value_size),
            ),
            version: Version::V1(DerivedPageSize {
                max_key_size,
                max_value_size,
            }),
            length: 0,
            _phantom: PhantomData,
        };

        btree.save_header();
        btree
    }

    /// Loads the map from memory.
    pub fn load(memory: M) -> Self {
        Self::load_helper(memory, true)
    }

    /// Loads the map from memory, potentially migrating the map from V1 to V2.
    fn load_helper(memory: M, migrate_to_v2: bool) -> Self {
        // Read the header from memory.
        let header = Self::read_header(&memory);

        let version = match header.version {
            Version::V1(derived_page_size) => {
                // Migrate to V2 if flag is enabled.
                if migrate_to_v2 {
                    Version::V2(PageSize::Derived(derived_page_size))
                } else {
                    // Assert that the bounds are correct.
                    let max_key_size = derived_page_size.max_key_size;
                    let max_value_size = derived_page_size.max_value_size;

                    assert!(
                        K::BOUND.max_size() <= max_key_size,
                        "max_key_size must be <= {max_key_size}",
                    );

                    assert!(
                        V::BOUND.max_size() <= max_value_size,
                        "max_value_size must be <= {max_value_size}"
                    );

                    Version::V1(derived_page_size)
                }
            }
            other => other,
        };

        let allocator_addr = Address::from(ALLOCATOR_OFFSET as u64);
        Self {
            root_addr: header.root_addr,
            allocator: Allocator::load(memory, allocator_addr),
            version,
            length: header.length,
            _phantom: PhantomData,
        }
    }

    /// Reads the header from the specified memory.
    fn read_header(memory: &M) -> BTreeHeader {
        // Read the header
        let mut buf = [0; PACKED_HEADER_SIZE];
        memory.read(0, &mut buf);

        assert_eq!(&buf[0..3], MAGIC, "Bad magic.");

        match buf[3] {
            LAYOUT_VERSION => {
                // Deserialize the fields
                BTreeHeader {
                    version: Version::V1(DerivedPageSize {
                        max_key_size: u32::from_le_bytes(buf[4..8].try_into().unwrap()),
                        max_value_size: u32::from_le_bytes(buf[8..12].try_into().unwrap()),
                    }),
                    root_addr: Address::from(u64::from_le_bytes(buf[12..20].try_into().unwrap())),
                    length: u64::from_le_bytes(buf[20..28].try_into().unwrap()),
                }
            }
            LAYOUT_VERSION_2 => {
                // Load the page size.
                let page_size = {
                    // Page sizes can be stored either as a direct value or as max/value sizes.
                    let a = u32::from_le_bytes(buf[4..8].try_into().unwrap());
                    let b = u32::from_le_bytes(buf[8..12].try_into().unwrap());

                    if b == PAGE_SIZE_VALUE_MARKER {
                        // Page size is stored as a direct value
                        PageSize::Value(a)
                    } else {
                        // Page size is stored as a derived value.
                        PageSize::Derived(DerivedPageSize {
                            max_key_size: a,
                            max_value_size: b,
                        })
                    }
                };

                // Deserialize the fields
                BTreeHeader {
                    version: Version::V2(page_size),
                    root_addr: Address::from(u64::from_le_bytes(buf[12..20].try_into().unwrap())),
                    length: u64::from_le_bytes(buf[20..28].try_into().unwrap()),
                }
            }
            version => {
                panic!("Unsupported version: {version}.");
            }
        }
    }

    /// Inserts a key-value pair into the map.
    ///
    /// The previous value of the key, if present, is returned.
    ///
    /// PRECONDITION:
    ///   key.to_bytes().len() <= max_size(Key)
    ///   value.to_bytes().len() <= max_size(Value)
    pub fn insert(&mut self, key: K, value: V) -> Option<V> {
        let value = value.into_bytes_checked();

        let root = if self.root_addr == NULL {
            // No root present. Allocate one.
            let node = self.allocate_node(NodeType::Leaf);
            self.root_addr = node.address();
            self.save_header();
            node
        } else {
            // Load the root from memory.
            let mut root = self.load_node(self.root_addr);

            // Check if the key already exists in the root.
            if let Ok(idx) = root.search(&key, self.memory()) {
                // Key found, replace its value and return the old one.
                return Some(V::from_bytes(Cow::Owned(
                    self.update_value(&mut root, idx, value),
                )));
            }

            // If the root is full, we need to introduce a new node as the root.
            //
            // NOTE: In the case where we are overwriting an existing key, then introducing
            // a new root node isn't strictly necessary. However, that's a micro-optimization
            // that adds more complexity than it's worth.
            if root.is_full() {
                // The root is full. Allocate a new node that will be used as the new root.
                let mut new_root = self.allocate_node(NodeType::Internal);

                // The new root has the old root as its only child.
                new_root.push_child(self.root_addr);

                // Update the root address.
                self.root_addr = new_root.address();
                self.save_header();

                // Split the old (full) root.
                self.split_child(&mut new_root, 0);

                new_root
            } else {
                root
            }
        };

        self.insert_nonfull(root, key, value)
            .map(Cow::Owned)
            .map(V::from_bytes)
    }

    /// Inserts an entry into a node that is *not full*.
    fn insert_nonfull(&mut self, mut node: Node<K>, key: K, value: Vec<u8>) -> Option<Vec<u8>> {
        // We're guaranteed by the caller that the provided node is not full.
        assert!(!node.is_full());

        // Look for the key in the node.
        match node.search(&key, self.memory()) {
            Ok(idx) => {
                // Key found, replace its value and return the old one.
                Some(self.update_value(&mut node, idx, value))
            }
            Err(idx) => {
                // The key isn't in the node. `idx` is where that key should be inserted.

                match node.node_type() {
                    NodeType::Leaf => {
                        // The node is a non-full leaf.
                        // Insert the entry at the proper location.
                        node.insert_entry(idx, (key, value));
                        self.save_node(&mut node);

                        // Update the length.
                        self.length += 1;
                        self.save_header();

                        // No previous value to return.
                        None
                    }
                    NodeType::Internal => {
                        // The node is an internal node.
                        // Load the child that we should add the entry to.
                        let mut child = self.load_node(node.child(idx));

                        if child.is_full() {
                            // Check if the key already exists in the child.
                            if let Ok(idx) = child.search(&key, self.memory()) {
                                // Key found, replace its value and return the old one.
                                return Some(self.update_value(&mut child, idx, value));
                            }

                            // The child is full. Split the child.
                            self.split_child(&mut node, idx);

                            // The children have now changed. Search again for
                            // the child where we need to store the entry in.
                            let idx = node.search(&key, self.memory()).unwrap_or_else(|idx| idx);
                            child = self.load_node(node.child(idx));
                        }

                        // The child should now be not full.
                        assert!(!child.is_full());

                        self.insert_nonfull(child, key, value)
                    }
                }
            }
        }
    }

    /// Takes as input a nonfull internal `node` and index to its full child, then
    /// splits this child into two, adding an additional child to `node`.
    ///
    /// Example:
    /// ```ignore
    ///                          [ ... M   Y ... ]
    ///                                  |
    ///                 [ N  O  P  Q  R  S  T  U  V  W  X ]
    /// ```
    ///
    /// After splitting becomes:
    /// ```ignore
    ///                         [ ... M  S  Y ... ]
    ///                                 / \
    ///                [ N  O  P  Q  R ]   [ T  U  V  W  X ]
    /// ```
    ///
    fn split_child(&mut self, node: &mut Node<K>, full_child_idx: usize) {
        // The node must not be full.
        assert!(!node.is_full());

        // The node's child must be full.
        let mut full_child = self.load_node(node.child(full_child_idx));
        assert!(full_child.is_full());

        // Create a sibling to this full child (which has to be the same type).
        let mut sibling = self.allocate_node(full_child.node_type());
        assert_eq!(sibling.node_type(), full_child.node_type());

        // Add sibling as a new child in the node.
        node.insert_child(full_child_idx + 1, sibling.address());

        let (median_key, median_value) = full_child.split(&mut sibling, self.memory());

        node.insert_entry(full_child_idx, (median_key, median_value));

        self.save_node(&mut sibling);
        self.save_node(&mut full_child);
        self.save_node(node);
    }

    /// Returns the value for the given key, if it exists.
    pub fn get(&self, key: &K) -> Option<V> {
        if self.root_addr == NULL {
            return None;
        }
        self.traverse(self.root_addr, key, |node, idx| {
            node.extract_entry_at(idx, self.memory()).1 // Extract value.
        })
        .map(Cow::Owned)
        .map(V::from_bytes)
    }

    /// Returns true if the key exists.
    pub fn contains_key(&self, key: &K) -> bool {
        // An empty closure returns Some(()) if the key is found.
        self.root_addr != NULL && self.traverse(self.root_addr, key, |_, _| ()).is_some()
    }

    /// Recursively traverses from `node_addr`, invoking `f` if `key` is found. Stops at a leaf if not.
    fn traverse<F, R>(&self, node_addr: Address, key: &K, f: F) -> Option<R>
    where
        F: Fn(&mut Node<K>, usize) -> R,
    {
        let mut node = self.load_node(node_addr);
        // Look for the key in the current node.
        match node.search(key, self.memory()) {
            Ok(idx) => Some(f(&mut node, idx)), // Key found: apply `f`.
            Err(idx) => match node.node_type() {
                NodeType::Leaf => None, // At a leaf: key not present.
                NodeType::Internal => self.traverse(node.child(idx), key, f), // Continue search in child.
            },
        }
    }

    /// Returns `true` if the map contains no elements.
    pub fn is_empty(&self) -> bool {
        self.length == 0
    }

    /// Returns the number of elements in the map.
    pub fn len(&self) -> u64 {
        self.length
    }

    /// Returns the underlying memory.
    pub fn into_memory(self) -> M {
        self.allocator.into_memory()
    }

    /// Removes all elements from the map.
    #[deprecated(since = "0.6.3", note = "please use `clear_new` instead")]
    // TODO: In next major release (v1.0), remove this deprecated method and rename
    // `clear_new` to `clear` for consistency with standard Rust collections.
    pub fn clear(self) -> Self {
        let mem = self.allocator.into_memory();
        Self::new(mem)
    }

    /// Removes all elements from the map.
    // TODO: In next major release (v1.0), rename this method to `clear` to follow
    // standard Rust collection naming conventions.
    pub fn clear_new(&mut self) {
        self.root_addr = NULL;
        self.length = 0;
        self.allocator.clear();
        self.save_header();
    }

    /// Returns the first key-value pair in the map. The key in this
    /// pair is the minimum key in the map.
    pub fn first_key_value(&self) -> Option<(K, V)> {
        if self.root_addr == NULL {
            return None;
        }
        let root = self.load_node(self.root_addr);
        let (k, encoded_v) = root.get_min(self.memory());
        Some((k, V::from_bytes(Cow::Owned(encoded_v))))
    }

    /// Returns the last key-value pair in the map. The key in this
    /// pair is the maximum key in the map.
    pub fn last_key_value(&self) -> Option<(K, V)> {
        if self.root_addr == NULL {
            return None;
        }
        let root = self.load_node(self.root_addr);
        let (k, encoded_v) = root.get_max(self.memory());
        Some((k, V::from_bytes(Cow::Owned(encoded_v))))
    }

    fn memory(&self) -> &M {
        self.allocator.memory()
    }

    fn allocator_mut(&mut self) -> &mut Allocator<M> {
        &mut self.allocator
    }

    /// Removes a key from the map, returning the previous value at the key if it exists.
    pub fn remove(&mut self, key: &K) -> Option<V> {
        if self.root_addr == NULL {
            return None;
        }

        let root_node = self.load_node(self.root_addr);
        self.remove_helper(root_node, key)
            .map(Cow::Owned)
            .map(V::from_bytes)
    }

    /// Removes and returns the last element in the map. The key of this element is the maximum key that was in the map
    pub fn pop_last(&mut self) -> Option<(K, V)> {
        if self.root_addr == NULL {
            return None;
        }

        let root = self.load_node(self.root_addr);
        let (max_key, _) = root.get_max(self.memory());
        self.remove_helper(root, &max_key)
            .map(|v| (max_key, V::from_bytes(Cow::Owned(v))))
    }

    /// Removes and returns the first element in the map. The key of this element is the minimum key that was in the map
    pub fn pop_first(&mut self) -> Option<(K, V)> {
        if self.root_addr == NULL {
            return None;
        }

        let root = self.load_node(self.root_addr);
        let (min_key, _) = root.get_min(self.memory());
        self.remove_helper(root, &min_key)
            .map(|v| (min_key, V::from_bytes(Cow::Owned(v))))
    }

    /// A helper method for recursively removing a key from the B-tree.
    fn remove_helper(&mut self, mut node: Node<K>, key: &K) -> Option<Vec<u8>> {
        if node.address() != self.root_addr {
            // We're guaranteed that whenever this method is called an entry can be
            // removed from the node without it needing to be merged into a sibling.
            // This strengthened condition allows us to delete an entry in a single
            // pass most of the time without having to back up.
            assert!(node.can_remove_entry_without_merging());
        }

        match node.node_type() {
            NodeType::Leaf => {
                match node.search(key, self.memory()) {
                    Ok(idx) => {
                        // Case 1: The node is a leaf node and the key exists in it.
                        // This is the simplest case. The key is removed from the leaf.
                        let value = node.remove_entry(idx, self.memory()).1;
                        self.length -= 1;

                        if node.entries_len() == 0 {
                            assert_eq!(
                                node.address(), self.root_addr,
                                "Removal can only result in an empty leaf node if that node is the root"
                            );

                            // Deallocate the empty node.
                            self.deallocate_node(node);
                            self.root_addr = NULL;
                        } else {
                            self.save_node(&mut node);
                        }

                        self.save_header();
                        Some(value)
                    }
                    _ => None, // Key not found.
                }
            }
            NodeType::Internal => {
                match node.search(key, self.memory()) {
                    Ok(idx) => {
                        // Case 2: The node is an internal node and the key exists in it.

                        let left_child = self.load_node(node.child(idx));
                        if left_child.can_remove_entry_without_merging() {
                            // Case 2.a: A key can be removed from the left child without merging.
                            //
                            //                       parent
                            //                  [..., key, ...]
                            //                       /   \
                            //            [left child]   [...]
                            //           /            \
                            //        [...]         [..., key predecessor]
                            //
                            // In this case, we replace `key` with the key's predecessor from the
                            // left child's subtree, then we recursively delete the key's
                            // predecessor for the following end result:
                            //
                            //                       parent
                            //            [..., key predecessor, ...]
                            //                       /   \
                            //            [left child]   [...]
                            //           /            \
                            //        [...]          [...]

                            // Recursively delete the predecessor.
                            // TODO(EXC-1034): Do this in a single pass.
                            let predecessor = left_child.get_max(self.memory());
                            self.remove_helper(left_child, &predecessor.0)?;

                            // Replace the `key` with its predecessor.
                            let (_, old_value) = node.swap_entry(idx, predecessor, self.memory());

                            // Save the parent node.
                            self.save_node(&mut node);
                            return Some(old_value);
                        }

                        let right_child = self.load_node(node.child(idx + 1));
                        if right_child.can_remove_entry_without_merging() {
                            // Case 2.b: A key can be removed from the right child without merging.
                            //
                            //                       parent
                            //                  [..., key, ...]
                            //                       /   \
                            //                   [...]   [right child]
                            //                          /             \
                            //              [key successor, ...]     [...]
                            //
                            // In this case, we replace `key` with the key's successor from the
                            // right child's subtree, then we recursively delete the key's
                            // successor for the following end result:
                            //
                            //                       parent
                            //            [..., key successor, ...]
                            //                       /   \
                            //                  [...]   [right child]
                            //                           /            \
                            //                        [...]          [...]

                            // Recursively delete the successor.
                            // TODO(EXC-1034): Do this in a single pass.
                            let successor = right_child.get_min(self.memory());
                            self.remove_helper(right_child, &successor.0)?;

                            // Replace the `key` with its successor.
                            let (_, old_value) = node.swap_entry(idx, successor, self.memory());

                            // Save the parent node.
                            self.save_node(&mut node);
                            return Some(old_value);
                        }

                        // Case 2.c: Both the left and right child are at their minimum sizes.
                        //
                        //                       parent
                        //                  [..., key, ...]
                        //                       /   \
                        //            [left child]   [right child]
                        //
                        // In this case, we merge (left child, key, right child) into a single
                        // node. The result will look like this:
                        //
                        //                       parent
                        //                     [...  ...]
                        //                         |
                        //          [left child, `key`, right child] <= new child
                        //
                        // We then recurse on this new child to delete `key`.
                        //
                        // If `parent` becomes empty (which can only happen if it's the root),
                        // then `parent` is deleted and `new_child` becomes the new root.
                        assert!(left_child.at_minimum());
                        assert!(right_child.at_minimum());

                        // Merge the right child into the left child.
                        let mut new_child = self.merge(
                            right_child,
                            left_child,
                            node.remove_entry(idx, self.memory()),
                        );

                        // Remove the right child from the parent node.
                        node.remove_child(idx + 1);

                        if node.entries_len() == 0 {
                            // Can only happen if this node is root.
                            assert_eq!(node.address(), self.root_addr);
                            assert_eq!(node.child(0), new_child.address());
                            assert_eq!(node.children_len(), 1);

                            self.root_addr = new_child.address();

                            // Deallocate the root node.
                            self.deallocate_node(node);
                            self.save_header();
                        } else {
                            self.save_node(&mut node);
                        }

                        self.save_node(&mut new_child);

                        // Recursively delete the key.
                        self.remove_helper(new_child, key)
                    }
                    Err(idx) => {
                        // Case 3: The node is an internal node and the key does NOT exist in it.

                        // If the key does exist in the tree, it will exist in the subtree at index
                        // `idx`.
                        let mut child = self.load_node(node.child(idx));

                        if child.can_remove_entry_without_merging() {
                            // The child has enough nodes. Recurse to delete the `key` from the
                            // `child`.
                            return self.remove_helper(child, key);
                        }

                        // An entry can't be removed from the child without merging.
                        // See if it has a sibling where an entry can be removed without merging.
                        let mut left_sibling = if idx > 0 {
                            Some(self.load_node(node.child(idx - 1)))
                        } else {
                            None
                        };

                        let mut right_sibling = if idx + 1 < node.children_len() {
                            Some(self.load_node(node.child(idx + 1)))
                        } else {
                            None
                        };

                        if let Some(ref mut left_sibling) = left_sibling {
                            if left_sibling.can_remove_entry_without_merging() {
                                // Case 3.a (left):
                                // A key can be removed from the left child without merging.
                                //
                                //                            [d] (parent)
                                //                           /   \
                                //  (left sibling) [a, b, c]     [e, f] (child)
                                //                         \
                                //                         [c']
                                //
                                // In this case, we move a key down from the parent into the child
                                // and move a key from the left sibling up into the parent
                                // resulting in the following tree:
                                //
                                //                            [c] (parent)
                                //                           /   \
                                //       (left sibling) [a, b]   [d, e, f] (child)
                                //                              /
                                //                            [c']
                                //
                                // We then recurse to delete the key from the child.

                                // Remove the last entry from the left sibling.
                                let (left_sibling_key, left_sibling_value) =
                                    left_sibling.pop_entry(self.memory()).unwrap();

                                // Replace the parent's entry with the one from the left sibling.
                                let (parent_key, parent_value) = node.swap_entry(
                                    idx - 1,
                                    (left_sibling_key, left_sibling_value),
                                    self.memory(),
                                );

                                // Move the entry from the parent into the child.
                                child.insert_entry(0, (parent_key, parent_value));

                                // Move the last child from left sibling into child.
                                if let Some(last_child) = left_sibling.pop_child() {
                                    assert_eq!(left_sibling.node_type(), NodeType::Internal);
                                    assert_eq!(child.node_type(), NodeType::Internal);

                                    child.insert_child(0, last_child);
                                } else {
                                    assert_eq!(left_sibling.node_type(), NodeType::Leaf);
                                    assert_eq!(child.node_type(), NodeType::Leaf);
                                }

                                self.save_node(left_sibling);
                                self.save_node(&mut child);
                                self.save_node(&mut node);
                                return self.remove_helper(child, key);
                            }
                        }

                        if let Some(right_sibling) = &mut right_sibling {
                            if right_sibling.can_remove_entry_without_merging() {
                                // Case 3.a (right):
                                // A key can be removed from the right child without merging.
                                //
                                //                            [c] (parent)
                                //                           /   \
                                //             (child) [a, b]     [d, e, f] (right sibling)
                                //                               /
                                //                            [d']
                                //
                                // In this case, we move a key down from the parent into the child
                                // and move a key from the right sibling up into the parent
                                // resulting in the following tree:
                                //
                                //                            [d] (parent)
                                //                           /   \
                                //          (child) [a, b, c]     [e, f] (right sibling)
                                //                          \
                                //                           [d']
                                //
                                // We then recurse to delete the key from the child.

                                // Remove the first entry from the right sibling.
                                let (right_sibling_key, right_sibling_value) =
                                    right_sibling.remove_entry(0, self.memory());

                                // Replace the parent's entry with the one from the right sibling.
                                let parent_entry = node.swap_entry(
                                    idx,
                                    (right_sibling_key, right_sibling_value),
                                    self.memory(),
                                );

                                // Move the entry from the parent into the child.
                                child.push_entry(parent_entry);

                                // Move the first child of right_sibling into `child`.
                                match right_sibling.node_type() {
                                    NodeType::Internal => {
                                        assert_eq!(child.node_type(), NodeType::Internal);
                                        child.push_child(right_sibling.remove_child(0));
                                    }
                                    NodeType::Leaf => {
                                        assert_eq!(child.node_type(), NodeType::Leaf);
                                    }
                                }

                                self.save_node(right_sibling);
                                self.save_node(&mut child);
                                self.save_node(&mut node);
                                return self.remove_helper(child, key);
                            }
                        }

                        // Case 3.b: Both the left and right siblings are at their minimum sizes.

                        if let Some(left_sibling) = left_sibling {
                            // Merge child into left sibling if it exists.

                            assert!(left_sibling.at_minimum());
                            let left_sibling = self.merge(
                                child,
                                left_sibling,
                                node.remove_entry(idx - 1, self.memory()),
                            );
                            // Removing child from parent.
                            node.remove_child(idx);

                            if node.entries_len() == 0 {
                                let node_address = node.address();
                                self.deallocate_node(node);

                                if node_address == self.root_addr {
                                    // Update the root.
                                    self.root_addr = left_sibling.address();
                                    self.save_header();
                                }
                            } else {
                                self.save_node(&mut node);
                            }

                            return self.remove_helper(left_sibling, key);
                        }

                        if let Some(right_sibling) = right_sibling {
                            // Merge child into right sibling.

                            assert!(right_sibling.at_minimum());
                            let right_sibling = self.merge(
                                child,
                                right_sibling,
                                node.remove_entry(idx, self.memory()),
                            );

                            // Removing child from parent.
                            node.remove_child(idx);

                            if node.entries_len() == 0 {
                                let node_address = node.address();
                                self.deallocate_node(node);

                                if node_address == self.root_addr {
                                    // Update the root.
                                    self.root_addr = right_sibling.address();
                                    self.save_header();
                                }
                            } else {
                                self.save_node(&mut node);
                            }

                            return self.remove_helper(right_sibling, key);
                        }

                        unreachable!("At least one of the siblings must exist.");
                    }
                }
            }
        }
    }

    /// Returns an iterator over the entries of the map, sorted by key.
    ///
    /// # Example
    ///
    /// ```rust
    /// use ic_stable_structures::{BTreeMap, DefaultMemoryImpl};
    /// let mut map: BTreeMap<u64, String, _> = BTreeMap::init(DefaultMemoryImpl::default());
    ///
    /// map.insert(1, "one".to_string());
    /// map.insert(2, "two".to_string());
    ///
    /// for entry in map.iter() {
    ///     println!("{}: {}", entry.key(), entry.value());
    /// }
    /// ```
    pub fn iter(&self) -> Iter<'_, K, V, M> {
        self.iter_internal().into()
    }

    /// Returns an iterator over the entries in the map where keys
    /// belong to the specified range.
    ///
    /// # Example
    ///
    /// ```rust
    /// use ic_stable_structures::{BTreeMap, DefaultMemoryImpl};
    /// use std::ops::Bound;
    ///
    /// let mut map: BTreeMap<u64, String, _> = BTreeMap::init(DefaultMemoryImpl::default());
    /// map.insert(1, "one".to_string());
    /// map.insert(2, "two".to_string());
    /// map.insert(3, "three".to_string());
    ///
    /// // Get entries with keys between 1 and 3 (inclusive)
    /// for entry in map.range((Bound::Included(1), Bound::Included(3))) {
    ///     println!("{}: {}", entry.key(), entry.value());
    /// }
    /// ```
    pub fn range(&self, key_range: impl RangeBounds<K>) -> Iter<'_, K, V, M> {
        self.range_internal(key_range).into()
    }

    /// Returns an iterator starting just before the given key.
    ///
    /// Finds the largest key strictly less than `bound` and starts from it.
    /// Useful when `range(bound..)` skips the previous element.
    ///
    /// Returns an empty iterator if no smaller key exists.
    pub fn iter_from_prev_key(&self, bound: &K) -> Iter<'_, K, V, M> {
        if let Some(entry) = self.range(..bound).next_back() {
            let start_key = entry.key().clone();
            IterInternal::new_in_range(self, (Bound::Included(start_key), Bound::Unbounded)).into()
        } else {
            IterInternal::null(self).into()
        }
    }

    /// **Deprecated**: use `iter_from_prev_key` instead.
    ///
    /// The name `iter_upper_bound` was misleading — it suggested an inclusive
    /// upper bound. In reality, it starts from the largest key strictly less
    /// than the given bound.
    ///
    /// The new name, `iter_from_prev_key`, better reflects this behavior and
    /// improves code clarity.
    #[deprecated(note = "use `iter_from_prev_key` instead")]
    // TODO: In next major release (v1.0), remove this deprecated method to clean up the API.
    pub fn iter_upper_bound(&self, bound: &K) -> Iter<'_, K, V, M> {
        self.iter_from_prev_key(bound)
    }

    /// Returns an iterator over the keys of the map.
    pub fn keys(&self) -> KeysIter<'_, K, V, M> {
        self.iter_internal().into()
    }

    /// Returns an iterator over the keys of the map which belong to the specified range.
    pub fn keys_range(&self, key_range: impl RangeBounds<K>) -> KeysIter<'_, K, V, M> {
        self.range_internal(key_range).into()
    }

    /// Returns an iterator over the values of the map, sorted by key.
    pub fn values(&self) -> ValuesIter<'_, K, V, M> {
        self.iter_internal().into()
    }

    /// Returns an iterator over the values of the map where keys
    /// belong to the specified range.
    pub fn values_range(&self, key_range: impl RangeBounds<K>) -> ValuesIter<'_, K, V, M> {
        self.range_internal(key_range).into()
    }

    fn iter_internal(&self) -> IterInternal<'_, K, V, M> {
        IterInternal::new(self)
    }

    fn range_internal(&self, key_range: impl RangeBounds<K>) -> IterInternal<'_, K, V, M> {
        if self.root_addr == NULL {
            // Map is empty.
            return IterInternal::null(self);
        }

        let range = (
            key_range.start_bound().cloned(),
            key_range.end_bound().cloned(),
        );

        IterInternal::new_in_range(self, range)
    }

    /// Merges one node (`source`) into another (`into`), along with a median entry.
    ///
    /// Example (values are not included for brevity):
    ///
    /// Input:
    ///   Source: [1, 2, 3]
    ///   Into: [5, 6, 7]
    ///   Median: 4
    ///
    /// Output:
    ///   [1, 2, 3, 4, 5, 6, 7] (stored in the `into` node)
    ///   `source` is deallocated.
    fn merge(&mut self, source: Node<K>, mut into: Node<K>, median: Entry<K>) -> Node<K> {
        into.merge(source, median, &mut self.allocator);
        into
    }

    /// Allocates a new node of the given type.
    fn allocate_node(&mut self, node_type: NodeType) -> Node<K> {
        match self.version {
            Version::V1(page_size) => Node::new_v1(self.allocator.allocate(), node_type, page_size),
            Version::V2(page_size) => Node::new_v2(self.allocator.allocate(), node_type, page_size),
        }
    }

    /// Deallocates a node.
    #[inline]
    fn deallocate_node(&mut self, node: Node<K>) {
        node.deallocate(self.allocator_mut());
    }

    /// Loads a node from memory.
    #[inline]
    fn load_node(&self, address: Address) -> Node<K> {
        Node::load(address, self.version.page_size(), self.memory())
    }

    /// Saves the node to memory.
    #[inline]
    fn save_node(&mut self, node: &mut Node<K>) {
        node.save(self.allocator_mut());
    }

    /// Replaces the value at `idx` in the node, saves the node, and returns the old value.
    fn update_value(&mut self, node: &mut Node<K>, idx: usize, new_value: Vec<u8>) -> Vec<u8> {
        let old_value = node.swap_value(idx, new_value, self.memory());
        self.save_node(node);
        old_value
    }

    /// Saves the map to memory.
    fn save_header(&self) {
        let header = BTreeHeader {
            version: self.version,
            root_addr: self.root_addr,
            length: self.length,
        };

        Self::write_header(&header, self.memory());
    }

    /// Write the layout header to the memory.
    fn write_header(header: &BTreeHeader, memory: &M) {
        // Serialize the header
        let mut buf = [0; PACKED_HEADER_SIZE];
        buf[0..3].copy_from_slice(MAGIC.as_slice());
        match header.version {
            Version::V1(DerivedPageSize {
                max_key_size,
                max_value_size,
            })
            | Version::V2(PageSize::Derived(DerivedPageSize {
                max_key_size,
                max_value_size,
            })) => {
                buf[3] = LAYOUT_VERSION;
                buf[4..8].copy_from_slice(&max_key_size.to_le_bytes());
                buf[8..12].copy_from_slice(&max_value_size.to_le_bytes());
            }
            Version::V2(PageSize::Value(page_size)) => {
                buf[3] = LAYOUT_VERSION_2;
                buf[4..8].copy_from_slice(&page_size.to_le_bytes());
                buf[8..12].copy_from_slice(&PAGE_SIZE_VALUE_MARKER.to_le_bytes());
            }
        };
        buf[12..20].copy_from_slice(&header.root_addr.get().to_le_bytes());
        buf[20..28].copy_from_slice(&header.length.to_le_bytes());
        // Write the header
        crate::write(memory, 0, &buf);
    }
}

#[cfg(test)]
mod test {
    use super::*;
    use crate::{
        btreemap::iter::LazyEntry,
        storable::{Blob, Bound as StorableBound},
        VectorMemory,
    };
    use std::cell::RefCell;
    use std::convert::TryFrom;
    use std::rc::Rc;

    /// A helper function to clone and collect borrowed key/value pairs into a `Vec`.
    fn collect_kv<'a, K: Clone + 'a, V: Clone + 'a>(
        iter: impl Iterator<Item = (&'a K, &'a V)>,
    ) -> Vec<(K, V)> {
        iter.map(|(k, v)| (k.clone(), v.clone())).collect()
    }

    /// A helper function to collect owned key/value pairs into a `Vec`.
    fn collect<K: Clone, V: Clone>(it: impl Iterator<Item = (K, V)>) -> Vec<(K, V)> {
        it.collect()
    }

    /// A helper function to collect lazy entries into a `Vec`.
    fn collect_entry<'a, K, V, M>(it: impl Iterator<Item = LazyEntry<'a, K, V, M>>) -> Vec<(K, V)>
    where
        K: Storable + Ord + Clone + 'a,
        V: Storable + 'a,
        M: Memory + 'a,
    {
        it.map(|entry| entry.into_pair()).collect()
    }

    /// Returns a fixed‑size buffer for the given u32.
    fn monotonic_buffer<const N: usize>(i: u32) -> [u8; N] {
        let mut buf = [0u8; N];
        let bytes = i.to_be_bytes();
        buf[N - bytes.len()..].copy_from_slice(&bytes);
        buf
    }

    #[test]
    fn test_monotonic_buffer() {
        let cases: &[(u32, [u8; 4])] = &[
            (1, [0, 0, 0, 1]),
            (2, [0, 0, 0, 2]),
            ((1 << 8) - 1, [0, 0, 0, 255]),
            ((1 << 8), [0, 0, 1, 0]),
            ((1 << 16) - 1, [0, 0, 255, 255]),
            (1 << 16, [0, 1, 0, 0]),
            ((1 << 24) - 1, [0, 255, 255, 255]),
            (1 << 24, [1, 0, 0, 0]),
        ];

        for &(input, expected) in cases {
            let output = monotonic_buffer::<4>(input);
            assert_eq!(
                output, expected,
                "monotonic_buffer::<4>({}) returned {:?}, expected {:?}",
                input, output, expected
            );
        }
    }

    /// A trait to construct a value from a u32.
    trait Builder {
        fn build(i: u32) -> Self;
        fn empty() -> Self;
    }

    impl Builder for () {
        fn build(_i: u32) -> Self {}
        fn empty() -> Self {}
    }

    impl Builder for u32 {
        fn build(i: u32) -> Self {
            i
        }
        fn empty() -> Self {
            0
        }
    }

    impl<const N: usize> Builder for Blob<N> {
        fn build(i: u32) -> Self {
            Blob::try_from(&monotonic_buffer::<N>(i)[..]).unwrap()
        }
        fn empty() -> Self {
            Blob::try_from(&[][..]).unwrap()
        }
    }

    type MonotonicVec32 = Vec<u8>;
    impl Builder for MonotonicVec32 {
        fn build(i: u32) -> Self {
            monotonic_buffer::<32>(i).to_vec()
        }
        fn empty() -> Self {
            Vec::new()
        }
    }

    type MonotonicString32 = String;
    impl Builder for MonotonicString32 {
        fn build(i: u32) -> Self {
            format!("{i:0>32}")
        }
        fn empty() -> Self {
            String::new()
        }
    }

    /// Encodes an object into a byte vector.
    fn encode<T: Storable>(object: T) -> Vec<u8> {
        object.into_bytes_checked()
    }

    /// A helper method to succinctly create a blob.
    pub(crate) fn b(x: &[u8]) -> Blob<10> {
        Blob::<10>::try_from(x).unwrap()
    }

    /// Creates a new shared memory instance.
    pub(crate) fn make_memory() -> Rc<RefCell<Vec<u8>>> {
        Rc::new(RefCell::new(Vec::new()))
    }

    /// A test runner that runs the test using V1, migrated V2, and direct V2.
    pub fn run_btree_test<K, V, R, F>(f: F)
    where
        K: Storable + Ord + Clone,
        V: Storable,
        F: Fn(BTreeMap<K, V, VectorMemory>) -> R,
    {
        // V1 does not support unbounded types.
        if K::BOUND != StorableBound::Unbounded && V::BOUND != StorableBound::Unbounded {
            // Test with V1.
            let mem = make_memory();
            let tree_v1 = BTreeMap::new_v1(mem);
            f(tree_v1);

            // Test with V2 migrated from V1.
            let mem = make_memory();
            let tree_v1: BTreeMap<K, V, _> = BTreeMap::new_v1(mem);
            let tree_v2_migrated = BTreeMap::load_helper(tree_v1.into_memory(), true);
            f(tree_v2_migrated);
        }

        // Test with direct V2.
        let mem = make_memory();
        let tree_v2 = BTreeMap::new(mem);
        f(tree_v2);
    }

    /// Checks that objects from boundary u32 values are strictly increasing.
    /// This ensures multi-byte conversions preserve order.
    fn verify_monotonic<T: Builder + PartialOrd>() {
        for shift_bits in [8, 16, 24] {
            let i = (1 << shift_bits) - 1;
            assert!(
                T::build(i) < T::build(i + 1),
                "Monotonicity failed at i: {i}",
            );
        }
    }

    /// Asserts that the associated `BOUND` for `$ty` is _not_ `Unbounded`.
    macro_rules! assert_bounded {
        ($ty:ty) => {
            assert_ne!(<$ty>::BOUND, StorableBound::Unbounded, "Must be Bounded");
        };
    }

    /// Asserts that the associated `BOUND` for `$ty` _is_ `Unbounded`.
    macro_rules! assert_unbounded {
        ($ty:ty) => {
            assert_eq!(<$ty>::BOUND, StorableBound::Unbounded, "Must be Unbounded");
        };
    }

    macro_rules! run_with_key {
        ($runner:ident, $K:ty) => {{
            verify_monotonic::<$K>();

            // Empty value.
            $runner::<$K, ()>();

            // Bounded values.
            assert_bounded!(u32);
            $runner::<$K, u32>();

            assert_bounded!(Blob<20>);
            $runner::<$K, Blob<20>>();

            // Unbounded values.
            assert_unbounded!(MonotonicVec32);
            $runner::<$K, MonotonicVec32>();

            assert_unbounded!(MonotonicString32);
            $runner::<$K, MonotonicString32>();
        }};
    }

    /// Macro to apply a test function to a predefined grid of key/value types.
    macro_rules! btree_test {
        ($name:ident, $runner:ident) => {
            #[test]
            fn $name() {
                // Bounded keys.
                assert_bounded!(u32);
                run_with_key!($runner, u32);

                assert_bounded!(Blob<10>);
                run_with_key!($runner, Blob<10>);

                // Unbounded keys.
                assert_unbounded!(MonotonicVec32);
                run_with_key!($runner, MonotonicVec32);

                assert_unbounded!(MonotonicString32);
                run_with_key!($runner, MonotonicString32);
            }
        };
    }

    // Define a trait for keys that need the full set of bounds.
    trait TestKey: Storable + Ord + Clone + Builder + std::fmt::Debug {}
    impl<T> TestKey for T where T: Storable + Ord + Clone + Builder + std::fmt::Debug {}

    // Define a trait for values that need the full set of bounds.
    trait TestValue: Storable + Clone + Builder + std::fmt::Debug + PartialEq {}
    impl<T> TestValue for T where T: Storable + Clone + Builder + std::fmt::Debug + PartialEq {}

    fn insert_get_init_preserves_data<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            let n = 1_000;
            for i in 0..n {
                assert_eq!(btree.insert(key(i), value(i)), None);
                assert_eq!(btree.get(&key(i)), Some(value(i)));
            }

            // Reload the BTreeMap and verify the entry.
            let btree = BTreeMap::<K, V, VectorMemory>::init(btree.into_memory());
            for i in 0..n {
                assert_eq!(btree.get(&key(i)), Some(value(i)));
            }
        });
    }
    btree_test!(
        test_insert_get_init_preserves_data,
        insert_get_init_preserves_data
    );

    fn insert_overwrites_previous_value<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            let n = 1_000;
            for i in 0..n {
                assert_eq!(btree.insert(key(i), value(i)), None);
                assert_eq!(btree.insert(key(i), value(i + 1)), Some(value(i)));
                assert_eq!(btree.get(&key(i)), Some(value(i + 1)));
            }
        });
    }
    btree_test!(
        test_insert_overwrites_previous_value,
        insert_overwrites_previous_value
    );

    fn insert_same_key_many<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            let n = 1_000;
            assert_eq!(btree.insert(key(1), value(2)), None);
            for i in 2..n {
                assert_eq!(btree.insert(key(1), value(i + 1)), Some(value(i)));
            }
            assert_eq!(btree.get(&key(1)), Some(value(n)));
        });
    }
    btree_test!(test_insert_same_key_many, insert_same_key_many);

    fn insert_overwrite_median_key_in_full_child_node<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            for i in 1..=17 {
                assert_eq!(btree.insert(key(i), value(0)), None);
            }

            // The result should look like this:
            //                [6]
            //               /   \
            // [1, 2, 3, 4, 5]   [7, 8, 9, 10, 11, (12), 13, 14, 15, 16, 17]

            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(
                root.entries(btree.memory()),
                vec![(key(6), encode(value(0)))]
            );
            assert_eq!(root.children_len(), 2);

            // The right child should now be full, with the median key being "12"
            let right_child = btree.load_node(root.child(1));
            assert!(right_child.is_full());
            let median_index = right_child.entries_len() / 2;
            let median_key = key(12);
            assert_eq!(right_child.key(median_index, btree.memory()), &median_key);

            // Overwrite the value of the median key.
            assert_eq!(btree.insert(median_key.clone(), value(123)), Some(value(0)));
            assert_eq!(btree.get(&median_key), Some(value(123)));

            // The child has not been split and is still full.
            let right_child = btree.load_node(root.child(1));
            assert_eq!(right_child.node_type(), NodeType::Leaf);
            assert!(right_child.is_full());
        });
    }
    btree_test!(
        test_insert_overwrite_median_key_in_full_child_node,
        insert_overwrite_median_key_in_full_child_node
    );

    fn insert_overwrite_key_in_full_root_node<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            for i in 1..=11 {
                assert_eq!(btree.insert(key(i), value(0)), None);
            }

            // We now have a root that is full and looks like this:
            //
            // [1, 2, 3, 4, 5, (6), 7, 8, 9, 10, 11]
            let root = btree.load_node(btree.root_addr);
            assert!(root.is_full());

            // Overwrite an element in the root. It should NOT cause the node to be split.
            assert_eq!(btree.insert(key(6), value(456)), Some(value(0)));

            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Leaf);
            assert_eq!(btree.get(&key(6)), Some(value(456)));
            assert_eq!(root.entries_len(), 11);
        });
    }
    btree_test!(
        test_insert_overwrite_key_in_full_root_node,
        insert_overwrite_key_in_full_root_node
    );

    fn allocations_without_split<K: TestKey, V: TestValue>() {
        let key = K::build;
        run_btree_test(|mut btree| {
            assert_eq!(btree.allocator.num_allocated_chunks(), 0);

            assert_eq!(btree.insert(key(1), V::empty()), None);
            assert_eq!(btree.allocator.num_allocated_chunks(), 1);

            assert_eq!(btree.remove(&key(1)), Some(V::empty()));
            assert_eq!(btree.allocator.num_allocated_chunks(), 0);
        });
    }
    btree_test!(test_allocations_without_split, allocations_without_split);

    fn allocations_with_split<K: TestKey, V: TestValue>() {
        let key = K::build;
        run_btree_test(|mut btree| {
            // Insert entries until the root node is full.
            let mut i = 0;
            loop {
                assert_eq!(btree.insert(key(i), V::empty()), None);
                let root = btree.load_node(btree.root_addr);
                if root.is_full() {
                    break;
                }
                i += 1;
            }

            // Only need a single allocation to store up to `CAPACITY` elements.
            assert_eq!(btree.allocator.num_allocated_chunks(), 1);

            assert_eq!(btree.insert(key(255), V::empty()), None);

            // The node had to be split into three nodes.
            assert_eq!(btree.allocator.num_allocated_chunks(), 3);
        });
    }
    btree_test!(test_allocations_with_split, allocations_with_split);

    fn insert_split_node<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            for i in 1..=11 {
                assert_eq!(btree.insert(key(i), value(i)), None);
            }

            // Should now split a node.
            let root = btree.load_node(btree.root_addr);
            assert!(root.is_full());
            assert_eq!(btree.insert(key(12), value(12)), None);

            // The result should look like this:
            //                [6]
            //               /   \
            // [1, 2, 3, 4, 5]   [7, 8, 9, 10, 11, 12]

            for i in 1..=12 {
                assert_eq!(btree.get(&key(i)), Some(value(i)));
            }
        });
    }
    btree_test!(test_insert_split_node, insert_split_node);

    fn insert_split_multiple_nodes<K: TestKey, V: TestValue>() {
        let key = K::build;
        let e = |i: u32| (key(i), encode(V::empty()));
        run_btree_test(|mut btree| {
            for i in 1..=11 {
                assert_eq!(btree.insert(key(i), V::empty()), None);
            }
            // Should now split a node.
            assert_eq!(btree.insert(key(12), V::empty()), None);

            // The result should look like this:
            //                [6]
            //               /   \
            // [1, 2, 3, 4, 5]   [7, 8, 9, 10, 11, 12]

            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(root.entries(btree.memory()), vec![e(6)]);
            assert_eq!(root.children_len(), 2);

            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![e(1), e(2), e(3), e(4), e(5)]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![e(7), e(8), e(9), e(10), e(11), e(12)]
            );

            for i in 1..=12 {
                assert_eq!(btree.get(&key(i)), Some(V::empty()));
            }

            // Insert more to cause more splitting.
            assert_eq!(btree.insert(key(13), V::empty()), None);
            assert_eq!(btree.insert(key(14), V::empty()), None);
            assert_eq!(btree.insert(key(15), V::empty()), None);
            assert_eq!(btree.insert(key(16), V::empty()), None);
            assert_eq!(btree.insert(key(17), V::empty()), None);
            // Should cause another split
            assert_eq!(btree.insert(key(18), V::empty()), None);

            for i in 1..=18 {
                assert_eq!(btree.get(&key(i)), Some(V::empty()));
            }

            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(root.entries(btree.memory()), vec![e(6), e(12)],);
            assert_eq!(root.children_len(), 3);

            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![e(1), e(2), e(3), e(4), e(5)]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![e(7), e(8), e(9), e(10), e(11)]
            );

            let child_2 = btree.load_node(root.child(2));
            assert_eq!(child_2.node_type(), NodeType::Leaf);
            assert_eq!(
                child_2.entries(btree.memory()),
                vec![e(13), e(14), e(15), e(16), e(17), e(18)]
            );

            assert_eq!(btree.allocator.num_allocated_chunks(), 4);
        });
    }
    btree_test!(
        test_insert_split_multiple_nodes,
        insert_split_multiple_nodes
    );

    fn first_key_value<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree: BTreeMap<K, V, _>| {
            assert_eq!(btree.first_key_value(), None);

            let n = 1_000;
            for i in (0..n).rev() {
                assert_eq!(btree.insert(key(i), value(i)), None);
                assert_eq!(btree.first_key_value(), Some((key(i), value(i))));
            }

            for i in 0..n {
                assert_eq!(btree.remove(&key(i)), Some(value(i)));
                if !btree.is_empty() {
                    assert_eq!(btree.first_key_value(), Some((key(i + 1), value(i + 1))));
                }
            }
            assert_eq!(btree.first_key_value(), None);
        });
    }
    btree_test!(test_first_key_value, first_key_value);

    fn last_key_value<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree: BTreeMap<K, V, _>| {
            assert_eq!(btree.last_key_value(), None);

            let n = 1_000;
            for i in 0..n {
                assert_eq!(btree.insert(key(i), value(i)), None);
                assert_eq!(btree.last_key_value(), Some((key(i), value(i))));
            }

            for i in (0..n).rev() {
                assert_eq!(btree.remove(&key(i)), Some(value(i)));
                if !btree.is_empty() {
                    assert_eq!(btree.last_key_value(), Some((key(i - 1), value(i - 1))));
                }
            }
            assert_eq!(btree.last_key_value(), None);
        });
    }
    btree_test!(test_last_key_value, last_key_value);

    fn pop_first_single_entry<K: TestKey, V: TestValue>() {
        let key = K::build;
        run_btree_test(|mut btree| {
            assert_eq!(btree.allocator.num_allocated_chunks(), 0);

            assert_eq!(btree.insert(key(1), V::empty()), None);
            assert!(!btree.is_empty());
            assert_eq!(btree.allocator.num_allocated_chunks(), 1);

            assert_eq!(btree.pop_first(), Some((key(1), V::empty())));
            assert!(btree.is_empty());
            assert_eq!(btree.allocator.num_allocated_chunks(), 0);
        });
    }
    btree_test!(test_pop_first_single_entry, pop_first_single_entry);

    fn pop_last_single_entry<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            assert_eq!(btree.allocator.num_allocated_chunks(), 0);

            assert_eq!(btree.insert(key(1), value(1)), None);
            assert!(!btree.is_empty());
            assert_eq!(btree.allocator.num_allocated_chunks(), 1);

            assert_eq!(btree.pop_last(), Some((key(1), value(1))));
            assert!(btree.is_empty());
            assert_eq!(btree.allocator.num_allocated_chunks(), 0);
        });
    }
    btree_test!(test_pop_last_single_entry, pop_last_single_entry);

    fn remove_case_2a_and_2c<K: TestKey, V: TestValue>() {
        let key = K::build;
        let e = |i: u32| (key(i), encode(V::empty()));
        run_btree_test(|mut btree| {
            for i in 1..=11 {
                assert_eq!(btree.insert(key(i), V::empty()), None);
            }
            // Should now split a node.
            assert_eq!(btree.insert(key(0), V::empty()), None);

            // The result should look like this:
            //                    [6]
            //                   /   \
            // [0, 1, 2, 3, 4, 5]     [7, 8, 9, 10, 11]

            for i in 0..=11 {
                assert_eq!(btree.get(&key(i)), Some(V::empty()));
            }

            // Remove node 6. Triggers case 2.a
            assert_eq!(btree.remove(&key(6)), Some(V::empty()));

            // The result should look like this:
            //                [5]
            //               /   \
            // [0, 1, 2, 3, 4]   [7, 8, 9, 10, 11]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(root.entries(btree.memory()), vec![e(5)]);
            assert_eq!(root.children_len(), 2);

            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![e(0), e(1), e(2), e(3), e(4)]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![e(7), e(8), e(9), e(10), e(11)]
            );

            // There are three allocated nodes.
            assert_eq!(btree.allocator.num_allocated_chunks(), 3);

            // Remove node 5. Triggers case 2c
            assert_eq!(btree.remove(&key(5)), Some(V::empty()));

            // Reload the btree to verify that we saved it correctly.
            let btree = BTreeMap::<K, V, _>::load(btree.into_memory());

            // The result should look like this:
            // [0, 1, 2, 3, 4, 7, 8, 9, 10, 11]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(
                root.entries(btree.memory()),
                vec![e(0), e(1), e(2), e(3), e(4), e(7), e(8), e(9), e(10), e(11)]
            );

            // There is only one node allocated.
            assert_eq!(btree.allocator.num_allocated_chunks(), 1);
        });
    }
    btree_test!(test_remove_case_2a_and_2c, remove_case_2a_and_2c);

    fn remove_case_2b<K: TestKey, V: TestValue>() {
        let key = K::build;
        let e = |i: u32| (key(i), encode(V::empty()));
        run_btree_test(|mut btree| {
            for i in 1..=11 {
                assert_eq!(btree.insert(key(i), V::empty()), None);
            }
            // Should now split a node.
            assert_eq!(btree.insert(key(12), V::empty()), None);

            // The result should look like this:
            //                [6]
            //               /   \
            // [1, 2, 3, 4, 5]   [7, 8, 9, 10, 11, 12]

            for i in 1..=12 {
                assert_eq!(btree.get(&key(i)), Some(V::empty()));
            }

            // Remove node 6. Triggers case 2.b
            assert_eq!(btree.remove(&key(6)), Some(V::empty()));

            // The result should look like this:
            //                [7]
            //               /   \
            // [1, 2, 3, 4, 5]   [8, 9, 10, 11, 12]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(root.entries(btree.memory()), vec![e(7)]);
            assert_eq!(root.children_len(), 2);

            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![e(1), e(2), e(3), e(4), e(5)]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![e(8), e(9), e(10), e(11), e(12)]
            );

            // Remove node 7. Triggers case 2.c
            assert_eq!(btree.remove(&key(7)), Some(V::empty()));
            // The result should look like this:
            //
            // [1, 2, 3, 4, 5, 8, 9, 10, 11, 12]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Leaf);
            assert_eq!(
                root.entries(btree.memory()),
                collect([1, 2, 3, 4, 5, 8, 9, 10, 11, 12].into_iter().map(e))
            );

            assert_eq!(btree.allocator.num_allocated_chunks(), 1);
        });
    }
    btree_test!(test_remove_case_2b, remove_case_2b);

    fn remove_case_3a_right<K: TestKey, V: TestValue>() {
        let key = K::build;
        let e = |i: u32| (key(i), encode(V::empty()));
        run_btree_test(|mut btree| {
            for i in 1..=11 {
                assert_eq!(btree.insert(key(i), V::empty()), None);
            }

            // Should now split a node.
            assert_eq!(btree.insert(key(12), V::empty()), None);

            // The result should look like this:
            //                [6]
            //               /   \
            // [1, 2, 3, 4, 5]   [7, 8, 9, 10, 11, 12]

            // Remove node 3. Triggers case 3.a
            assert_eq!(btree.remove(&key(3)), Some(V::empty()));

            // The result should look like this:
            //                [7]
            //               /   \
            // [1, 2, 4, 5, 6]   [8, 9, 10, 11, 12]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(root.entries(btree.memory()), vec![e(7)]);
            assert_eq!(root.children_len(), 2);

            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![e(1), e(2), e(4), e(5), e(6)]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![e(8), e(9), e(10), e(11), e(12)]
            );

            // There are three allocated nodes.
            assert_eq!(btree.allocator.num_allocated_chunks(), 3);
        });
    }
    btree_test!(test_remove_case_3a_right, remove_case_3a_right);

    fn remove_case_3a_left<K: TestKey, V: TestValue>() {
        let key = K::build;
        let e = |i: u32| (key(i), encode(V::empty()));
        run_btree_test(|mut btree| {
            for i in 1..=11 {
                assert_eq!(btree.insert(key(i), V::empty()), None);
            }
            // Should now split a node.
            assert_eq!(btree.insert(key(0), V::empty()), None);

            // The result should look like this:
            //                   [6]
            //                  /   \
            // [0, 1, 2, 3, 4, 5]   [7, 8, 9, 10, 11]

            // Remove node 8. Triggers case 3.a left
            assert_eq!(btree.remove(&key(8)), Some(V::empty()));

            // The result should look like this:
            //                [5]
            //               /   \
            // [0, 1, 2, 3, 4]   [6, 7, 9, 10, 11]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(root.entries(btree.memory()), vec![e(5)]);
            assert_eq!(root.children_len(), 2);

            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![e(0), e(1), e(2), e(3), e(4)]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![e(6), e(7), e(9), e(10), e(11)]
            );

            // There are three allocated nodes.
            assert_eq!(btree.allocator.num_allocated_chunks(), 3);
        });
    }
    btree_test!(test_remove_case_3a_left, remove_case_3a_left);

    fn remove_case_3b_merge_into_right<K: TestKey, V: TestValue>() {
        let key = K::build;
        let e = |i: u32| (key(i), encode(V::empty()));
        run_btree_test(|mut btree| {
            for i in 1..=11 {
                assert_eq!(btree.insert(key(i), V::empty()), None);
            }
            // Should now split a node.
            assert_eq!(btree.insert(key(12), V::empty()), None);

            // The result should look like this:
            //                [6]
            //               /   \
            // [1, 2, 3, 4, 5]   [7, 8, 9, 10, 11, 12]

            for i in 1..=12 {
                assert_eq!(btree.get(&key(i)), Some(V::empty()));
            }

            // Remove node 6. Triggers case 2.b
            assert_eq!(btree.remove(&key(6)), Some(V::empty()));
            // The result should look like this:
            //                [7]
            //               /   \
            // [1, 2, 3, 4, 5]   [8, 9, 10, 11, 12]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(root.entries(btree.memory()), vec![e(7)]);
            assert_eq!(root.children_len(), 2);

            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![e(1), e(2), e(3), e(4), e(5)]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![e(8), e(9), e(10), e(11), e(12)]
            );

            // There are three allocated nodes.
            assert_eq!(btree.allocator.num_allocated_chunks(), 3);

            // Remove node 3. Triggers case 3.b
            assert_eq!(btree.remove(&key(3)), Some(V::empty()));

            // Reload the btree to verify that we saved it correctly.
            let btree = BTreeMap::<K, V, _>::load(btree.into_memory());

            // The result should look like this:
            //
            // [1, 2, 4, 5, 7, 8, 9, 10, 11, 12]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Leaf);
            assert_eq!(
                root.entries(btree.memory()),
                collect([1, 2, 4, 5, 7, 8, 9, 10, 11, 12].into_iter().map(e))
            );

            // There is only one allocated node remaining.
            assert_eq!(btree.allocator.num_allocated_chunks(), 1);
        });
    }
    btree_test!(
        test_remove_case_3b_merge_into_right,
        remove_case_3b_merge_into_right
    );

    fn remove_case_3b_merge_into_left<K: TestKey, V: TestValue>() {
        let key = K::build;
        let e = |i: u32| (key(i), encode(V::empty()));
        run_btree_test(|mut btree| {
            for i in 1..=11 {
                assert_eq!(btree.insert(key(i), V::empty()), None);
            }

            // Should now split a node.
            assert_eq!(btree.insert(key(12), V::empty()), None);

            // The result should look like this:
            //                [6]
            //               /   \
            // [1, 2, 3, 4, 5]   [7, 8, 9, 10, 11, 12]

            for i in 1..=12 {
                assert_eq!(btree.get(&key(i)), Some(V::empty()));
            }

            // Remove node 6. Triggers case 2.b
            assert_eq!(btree.remove(&key(6)), Some(V::empty()));

            // The result should look like this:
            //                [7]
            //               /   \
            // [1, 2, 3, 4, 5]   [8, 9, 10, 11, 12]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(root.entries(btree.memory()), vec![e(7)]);
            assert_eq!(root.children_len(), 2);

            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![e(1), e(2), e(3), e(4), e(5)]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![e(8), e(9), e(10), e(11), e(12)]
            );

            // There are three allocated nodes.
            assert_eq!(btree.allocator.num_allocated_chunks(), 3);

            // Remove node 10. Triggers case 3.b where we merge the right into the left.
            assert_eq!(btree.remove(&key(10)), Some(V::empty()));

            // Reload the btree to verify that we saved it correctly.
            let btree = BTreeMap::<K, V, _>::load(btree.into_memory());

            // The result should look like this:
            //
            // [1, 2, 3, 4, 5, 7, 8, 9, 11, 12], 10 is gone
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Leaf);
            assert_eq!(
                root.entries(btree.memory()),
                vec![e(1), e(2), e(3), e(4), e(5), e(7), e(8), e(9), e(11), e(12)]
            );

            // There is only one allocated node remaining.
            assert_eq!(btree.allocator.num_allocated_chunks(), 1);
        });
    }
    btree_test!(
        test_remove_case_3b_merge_into_left,
        remove_case_3b_merge_into_left
    );

    fn insert_remove_many<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            let n = 10_000;
            for i in 0..n {
                assert_eq!(btree.insert(key(i), value(i)), None);
                assert_eq!(btree.get(&key(i)), Some(value(i)));
            }

            let mut btree = BTreeMap::<K, V, _>::load(btree.into_memory());
            for i in 0..n {
                assert_eq!(btree.remove(&key(i)), Some(value(i)));
                assert_eq!(btree.get(&key(i)), None);
            }

            // We've deallocated everything.
            assert_eq!(btree.allocator.num_allocated_chunks(), 0);
        });
    }
    btree_test!(test_insert_remove_many, insert_remove_many);

    fn pop_first_many<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            let n = 10_000;

            assert!(btree.is_empty());
            assert_eq!(btree.pop_first(), None);

            for i in 0..n {
                assert_eq!(btree.insert(key(i), value(i)), None);
            }
            assert_eq!(btree.len(), n as u64);

            let mut btree = BTreeMap::<K, V, _>::load(btree.into_memory());
            for i in 0..n {
                assert_eq!(btree.pop_first(), Some((key(i), value(i))));
                assert_eq!(btree.get(&key(i)), None);
            }

            // We've deallocated everything.
            assert!(btree.is_empty());
            assert_eq!(btree.allocator.num_allocated_chunks(), 0);
        });
    }
    btree_test!(test_pop_first_many, pop_first_many);

    fn pop_last_many<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            let n = 10_000;

            assert!(btree.is_empty());
            assert_eq!(btree.pop_last(), None);

            for i in 0..n {
                assert_eq!(btree.insert(key(i), value(i)), None);
            }
            assert_eq!(btree.len(), n as u64);

            let mut btree = BTreeMap::<K, V, _>::load(btree.into_memory());
            for i in (0..n).rev() {
                assert_eq!(btree.pop_last(), Some((key(i), value(i))));
                assert_eq!(btree.get(&key(i)), None);
            }

            // We've deallocated everything.
            assert!(btree.is_empty());
            assert_eq!(btree.allocator.num_allocated_chunks(), 0);
        });
    }
    btree_test!(test_pop_last_many, pop_last_many);

    fn reloading<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            let n = 1_000;
            for i in 0..n {
                assert_eq!(btree.insert(key(i), value(i)), None);
                assert_eq!(btree.get(&key(i)), Some(value(i)));
            }
            assert_eq!(btree.len(), n as u64);

            // Reload the BTreeMap and verify the entry.
            let mut btree = BTreeMap::<K, V, VectorMemory>::load(btree.into_memory());
            assert_eq!(btree.len(), n as u64);
            for i in 0..n {
                assert_eq!(btree.get(&key(i)), Some(value(i)));
            }

            // Remove all entries and verify the entry.
            for i in 0..n {
                assert_eq!(btree.remove(&key(i)), Some(value(i)));
            }
            assert_eq!(btree.len(), 0);

            // Reload the BTreeMap and verify the entry.
            let btree = BTreeMap::<K, V, VectorMemory>::load(btree.into_memory());
            assert_eq!(btree.len(), 0);
        });
    }
    btree_test!(test_reloading, reloading);

    fn len<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            let n = 1_000;
            for i in 0..n {
                assert_eq!(btree.insert(key(i), value(i)), None);
            }

            assert_eq!(btree.len(), n as u64);
            assert!(!btree.is_empty());

            for i in 0..n {
                assert_eq!(btree.remove(&key(i)), Some(value(i)));
            }

            assert_eq!(btree.len(), 0);
            assert!(btree.is_empty());
        });
    }
    btree_test!(test_len, len);

    fn contains_key<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            let n = 1_000;
            for i in (0..n).step_by(2) {
                assert_eq!(btree.insert(key(i), value(i)), None);
            }

            // Only even keys should be present.
            for i in 0..n {
                assert_eq!(btree.contains_key(&key(i)), i % 2 == 0);
            }
        });
    }
    btree_test!(test_contains_key, contains_key);

    fn range_empty<K: TestKey, V: TestValue>() {
        let key = K::build;
        run_btree_test(|btree: BTreeMap<K, V, _>| {
            // Test prefixes that don't exist in the map.
            assert_eq!(collect_entry(btree.range(key(0)..)), vec![]);
            assert_eq!(collect_entry(btree.range(key(10)..)), vec![]);
            assert_eq!(collect_entry(btree.range(key(100)..)), vec![]);
        });
    }
    btree_test!(test_range_empty, range_empty);

    // Tests the case where the prefix is larger than all the entries in a leaf node.
    fn range_leaf_prefix_greater_than_all_entries<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            btree.insert(key(0), value(0));

            // Test a prefix that's larger than the value in the leaf node. Should be empty.
            assert_eq!(collect_entry(btree.range(key(1)..)), vec![]);
        });
    }
    btree_test!(
        test_range_leaf_prefix_greater_than_all_entries,
        range_leaf_prefix_greater_than_all_entries
    );

    // Tests the case where the prefix is larger than all the entries in an internal node.
    fn range_internal_prefix_greater_than_all_entries<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            for i in 1..=12 {
                assert_eq!(btree.insert(key(i), value(i)), None);
            }

            // The result should look like this:
            //                [6]
            //               /   \
            // [1, 2, 3, 4, 5]   [7, 8, 9, 10, 11, 12]

            // Test a prefix that's larger than the key in the internal node.
            assert_eq!(
                collect_entry(btree.range(key(7)..key(8))),
                vec![(key(7), value(7))]
            );
        });
    }
    btree_test!(
        test_range_internal_prefix_greater_than_all_entries,
        range_internal_prefix_greater_than_all_entries
    );

    fn range_various_prefixes<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            btree.insert(key(1), value(100));
            btree.insert(key(2), value(200));
            btree.insert(key(3), value(300));
            btree.insert(key(4), value(400));
            btree.insert(key(11), value(500));
            btree.insert(key(12), value(600));
            btree.insert(key(13), value(700));
            btree.insert(key(14), value(800));
            btree.insert(key(21), value(900));
            btree.insert(key(22), value(1_000));
            btree.insert(key(23), value(1_100));
            btree.insert(key(24), value(1_200));

            // The result should look like this:
            //                 [12]
            //                /    \
            // [1, 2, 3, 4, 11]    [13, 14, 21, 22, 23, 24]

            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(
                root.entries(btree.memory()),
                vec![(key(12), encode(value(600)))]
            );
            assert_eq!(root.children_len(), 2);

            // Tests a prefix that's smaller than the key in the internal node.
            assert_eq!(
                collect_entry(btree.range(key(0)..key(11))),
                vec![
                    (key(1), value(100)),
                    (key(2), value(200)),
                    (key(3), value(300)),
                    (key(4), value(400)),
                ]
            );

            // Tests a prefix that crosses several nodes.
            assert_eq!(
                collect_entry(btree.range(key(10)..key(20))),
                vec![
                    (key(11), value(500)),
                    (key(12), value(600)),
                    (key(13), value(700)),
                    (key(14), value(800)),
                ]
            );

            // Tests a prefix that's larger than the key in the internal node.
            assert_eq!(
                collect_entry(btree.range(key(20)..key(30))),
                vec![
                    (key(21), value(900)),
                    (key(22), value(1_000)),
                    (key(23), value(1_100)),
                    (key(24), value(1_200)),
                ]
            );
        });
    }
    btree_test!(test_range_various_prefixes, range_various_prefixes);

    fn range_various_prefixes_2<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            btree.insert(key(1), value(100));
            btree.insert(key(2), value(200));
            btree.insert(key(3), value(300));
            btree.insert(key(4), value(400));
            btree.insert(key(12), value(500));
            btree.insert(key(14), value(600));
            btree.insert(key(16), value(700));
            btree.insert(key(18), value(800));
            btree.insert(key(19), value(900));
            btree.insert(key(21), value(1000));
            btree.insert(key(22), value(1100));
            btree.insert(key(23), value(1200));
            btree.insert(key(24), value(1300));
            btree.insert(key(25), value(1400));
            btree.insert(key(26), value(1500));
            btree.insert(key(27), value(1600));
            btree.insert(key(28), value(1700));
            btree.insert(key(29), value(1800));

            // The result should look like this:
            //                 [14, 23]
            //                /    |   \
            // [1, 2, 3, 4, 12]    |   [24, 25, 26, 27, 28, 29]
            //                     |
            //           [16, 18, 19, 21, 22]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(
                root.entries(btree.memory()),
                vec![
                    (key(14), encode(value(600))),
                    (key(23), encode(value(1200)))
                ]
            );
            assert_eq!(root.children_len(), 3);
            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![
                    (key(1), encode(value(100))),
                    (key(2), encode(value(200))),
                    (key(3), encode(value(300))),
                    (key(4), encode(value(400))),
                    (key(12), encode(value(500))),
                ]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![
                    (key(16), encode(value(700))),
                    (key(18), encode(value(800))),
                    (key(19), encode(value(900))),
                    (key(21), encode(value(1000))),
                    (key(22), encode(value(1100))),
                ]
            );

            let child_2 = btree.load_node(root.child(2));
            assert_eq!(
                child_2.entries(btree.memory()),
                vec![
                    (key(24), encode(value(1300))),
                    (key(25), encode(value(1400))),
                    (key(26), encode(value(1500))),
                    (key(27), encode(value(1600))),
                    (key(28), encode(value(1700))),
                    (key(29), encode(value(1800))),
                ]
            );

            // Tests a prefix that doesn't exist, but is in the middle of the root node.
            assert_eq!(collect_entry(btree.range(key(15)..key(16))), vec![]);

            // Tests a prefix beginning in the middle of the tree and crossing several nodes.
            assert_eq!(
                collect_entry(btree.range(key(15)..=key(26))),
                vec![
                    (key(16), value(700)),
                    (key(18), value(800)),
                    (key(19), value(900)),
                    (key(21), value(1000)),
                    (key(22), value(1100)),
                    (key(23), value(1200)),
                    (key(24), value(1300)),
                    (key(25), value(1400)),
                    (key(26), value(1500)),
                ]
            );

            // Tests a prefix that crosses several nodes.
            assert_eq!(
                collect_entry(btree.range(key(10)..key(20))),
                vec![
                    (key(12), value(500)),
                    (key(14), value(600)),
                    (key(16), value(700)),
                    (key(18), value(800)),
                    (key(19), value(900)),
                ]
            );

            // Tests a prefix that starts from a leaf node, then iterates through the root and right
            // sibling.
            assert_eq!(
                collect_entry(btree.range(key(20)..key(30))),
                vec![
                    (key(21), value(1000)),
                    (key(22), value(1100)),
                    (key(23), value(1200)),
                    (key(24), value(1300)),
                    (key(25), value(1400)),
                    (key(26), value(1500)),
                    (key(27), value(1600)),
                    (key(28), value(1700)),
                    (key(29), value(1800)),
                ]
            );
        });
    }
    btree_test!(test_range_various_prefixes_2, range_various_prefixes_2);

    fn range_large<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            const TOTAL: u32 = 2_000;
            const MID: u32 = TOTAL / 2;

            for i in 0..TOTAL {
                assert_eq!(btree.insert(key(i), value(i)), None);
            }

            // Check range [0, MID): should yield exactly the first MID entries.
            let keys: Vec<_> = btree.range(key(0)..key(MID)).collect();
            assert_eq!(keys.len(), MID as usize);
            for (i, entry) in keys.into_iter().enumerate() {
                let j = i as u32;
                assert_eq!(*entry.key(), key(j));
                assert_eq!(entry.value(), value(j));
            }

            // Check range [MID, TOTAL): should yield the remaining entries.
            let keys: Vec<_> = btree.range(key(MID)..).collect();
            assert_eq!(keys.len(), (TOTAL - MID) as usize);
            for (i, entry) in keys.into_iter().enumerate() {
                let j = MID + i as u32;
                assert_eq!(*entry.key(), key(j));
                assert_eq!(entry.value(), value(j));
            }
        });
    }
    btree_test!(test_range_large, range_large);

    fn range_various_prefixes_with_offset<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            btree.insert(key(1), value(100));
            btree.insert(key(2), value(200));
            btree.insert(key(3), value(300));
            btree.insert(key(4), value(400));
            btree.insert(key(11), value(500));
            btree.insert(key(12), value(600));
            btree.insert(key(13), value(700));
            btree.insert(key(14), value(800));
            btree.insert(key(21), value(900));
            btree.insert(key(22), value(1000));
            btree.insert(key(23), value(1100));
            btree.insert(key(24), value(1200));

            // The result should look like this:
            //                 [12]
            //                /    \
            // [1, 2, 3, 4, 11]    [13, 14, 21, 22, 23, 24]

            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(
                root.entries(btree.memory()),
                vec![(key(12), encode(value(600)))]
            );
            assert_eq!(root.children_len(), 2);

            assert_eq!(
                collect_entry(btree.range(key(0)..key(10))),
                vec![
                    (key(1), value(100)),
                    (key(2), value(200)),
                    (key(3), value(300)),
                    (key(4), value(400)),
                ]
            );

            // Tests an offset that has a keys somewhere in the range of keys of an internal node.
            assert_eq!(
                collect_entry(btree.range(key(13)..key(20))),
                vec![(key(13), value(700)), (key(14), value(800))]
            );

            // Tests an offset that's larger than the key in the internal node.
            assert_eq!(collect_entry(btree.range(key(25)..)), vec![]);
        });
    }
    btree_test!(
        test_range_various_prefixes_with_offset,
        range_various_prefixes_with_offset
    );

    fn range_various_prefixes_with_offset_2<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            btree.insert(key(1), value(0));
            btree.insert(key(2), value(0));
            btree.insert(key(3), value(0));
            btree.insert(key(4), value(0));
            btree.insert(key(12), value(0));
            btree.insert(key(14), value(0));
            btree.insert(key(16), value(0));
            btree.insert(key(18), value(0));
            btree.insert(key(19), value(0));
            btree.insert(key(21), value(0));
            btree.insert(key(22), value(0));
            btree.insert(key(23), value(0));
            btree.insert(key(24), value(0));
            btree.insert(key(25), value(0));
            btree.insert(key(26), value(0));
            btree.insert(key(27), value(0));
            btree.insert(key(28), value(0));
            btree.insert(key(29), value(0));

            // The result should look like this:
            //                 [14, 23]
            //                /    |   \
            // [1, 2, 3, 4, 12]    |   [24, 25, 26, 27, 28, 29]
            //                     |
            //           [16, 18, 19, 21, 22]
            let root = btree.load_node(btree.root_addr);
            assert_eq!(root.node_type(), NodeType::Internal);
            assert_eq!(
                root.entries(btree.memory()),
                vec![(key(14), encode(value(0))), (key(23), encode(value(0)))]
            );
            assert_eq!(root.children_len(), 3);

            let child_0 = btree.load_node(root.child(0));
            assert_eq!(child_0.node_type(), NodeType::Leaf);
            assert_eq!(
                child_0.entries(btree.memory()),
                vec![
                    (key(1), encode(value(0))),
                    (key(2), encode(value(0))),
                    (key(3), encode(value(0))),
                    (key(4), encode(value(0))),
                    (key(12), encode(value(0))),
                ]
            );

            let child_1 = btree.load_node(root.child(1));
            assert_eq!(child_1.node_type(), NodeType::Leaf);
            assert_eq!(
                child_1.entries(btree.memory()),
                vec![
                    (key(16), encode(value(0))),
                    (key(18), encode(value(0))),
                    (key(19), encode(value(0))),
                    (key(21), encode(value(0))),
                    (key(22), encode(value(0))),
                ]
            );

            let child_2 = btree.load_node(root.child(2));
            assert_eq!(
                child_2.entries(btree.memory()),
                vec![
                    (key(24), encode(value(0))),
                    (key(25), encode(value(0))),
                    (key(26), encode(value(0))),
                    (key(27), encode(value(0))),
                    (key(28), encode(value(0))),
                    (key(29), encode(value(0))),
                ]
            );

            // Tests a offset that crosses several nodes.
            assert_eq!(
                collect_entry(btree.range(key(14)..key(20))),
                vec![
                    (key(14), value(0)),
                    (key(16), value(0)),
                    (key(18), value(0)),
                    (key(19), value(0)),
                ]
            );

            // Tests a offset that starts from a leaf node, then iterates through the root and right
            // sibling.
            assert_eq!(
                collect_entry(btree.range(key(22)..key(30))),
                vec![
                    (key(22), value(0)),
                    (key(23), value(0)),
                    (key(24), value(0)),
                    (key(25), value(0)),
                    (key(26), value(0)),
                    (key(27), value(0)),
                    (key(28), value(0)),
                    (key(29), value(0)),
                ]
            );
        });
    }
    btree_test!(
        test_range_various_prefixes_with_offset_2,
        range_various_prefixes_with_offset_2
    );

    #[test]
    #[should_panic(expected = "max_key_size must be <= 4")]
    fn v1_rejects_increases_in_max_key_size() {
        let mem = make_memory();
        let btree: BTreeMap<Blob<4>, Blob<3>, _> = BTreeMap::init_v1(mem);
        let _btree: BTreeMap<Blob<5>, Blob<3>, _> = BTreeMap::init_v1(btree.into_memory());
    }

    #[test]
    fn v2_handles_increases_in_max_key_size_and_max_value_size() {
        let mem = make_memory();
        let mut btree: BTreeMap<Blob<4>, Blob<4>, _> = BTreeMap::init(mem);
        btree.insert(
            [1u8; 4].as_slice().try_into().unwrap(),
            [1u8; 4].as_slice().try_into().unwrap(),
        );

        // Reinitialize the BTree with larger keys and value sizes.
        let mut btree: BTreeMap<Blob<5>, Blob<5>, _> = BTreeMap::init(btree.into_memory());
        btree.insert(
            [2u8; 5].as_slice().try_into().unwrap(),
            [2u8; 5].as_slice().try_into().unwrap(),
        );

        // Still able to retrieve all the entries inserted.
        assert_eq!(
            btree.get(&([1u8; 4].as_slice().try_into().unwrap())),
            Some([1u8; 4].as_slice().try_into().unwrap())
        );

        assert_eq!(
            btree.get(&([2u8; 5].as_slice().try_into().unwrap())),
            Some([2u8; 5].as_slice().try_into().unwrap())
        );
    }

    #[test]
    fn accepts_small_or_equal_key_sizes() {
        let mem = make_memory();
        let btree: BTreeMap<Blob<4>, Blob<3>, _> = BTreeMap::init(mem);
        // Smaller key size
        let btree: BTreeMap<Blob<3>, Blob<3>, _> = BTreeMap::init(btree.into_memory());
        // Equal key size
        let _btree: BTreeMap<Blob<4>, Blob<3>, _> = BTreeMap::init(btree.into_memory());
    }

    #[test]
    #[should_panic(expected = "max_value_size must be <= 3")]
    fn v1_rejects_larger_value_sizes() {
        let mem = make_memory();
        let btree: BTreeMap<Blob<4>, Blob<3>, _> = BTreeMap::init_v1(mem);
        let _btree: BTreeMap<Blob<4>, Blob<4>, _> = BTreeMap::init_v1(btree.into_memory());
    }

    #[test]
    fn accepts_small_or_equal_value_sizes() {
        let mem = make_memory();
        let btree: BTreeMap<Blob<4>, Blob<3>, _> = BTreeMap::init(mem);
        // Smaller key size
        let btree: BTreeMap<Blob<4>, Blob<2>, _> = BTreeMap::init(btree.into_memory());
        // Equal key size
        let _btree: BTreeMap<Blob<4>, Blob<3>, _> = BTreeMap::init(btree.into_memory());
    }

    fn bruteforce_range_search<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut stable_map| {
            use std::collections::BTreeMap;
            const NKEYS: u32 = 60;
            let mut std_map = BTreeMap::new();

            for i in 0..NKEYS {
                std_map.insert(key(i), value(i));
                stable_map.insert(key(i), value(i));
            }

            assert_eq!(
                collect_kv(std_map.range(..)),
                collect_entry(stable_map.range(..))
            );

            for l in 0..=NKEYS {
                assert_eq!(
                    collect_kv(std_map.range(key(l)..)),
                    collect_entry(stable_map.range(key(l)..))
                );

                assert_eq!(
                    collect_kv(std_map.range(..key(l))),
                    collect_entry(stable_map.range(..key(l)))
                );

                assert_eq!(
                    collect_kv(std_map.range(..=key(l))),
                    collect_entry(stable_map.range(..=key(l)))
                );

                for r in l + 1..=NKEYS {
                    for lbound in [Bound::Included(key(l)), Bound::Excluded(key(l))] {
                        for rbound in [Bound::Included(key(r)), Bound::Excluded(key(r))] {
                            let range = (lbound.clone(), rbound);
                            assert_eq!(
                                collect_kv(std_map.range(range.clone())),
                                collect_entry(stable_map.range(range.clone())),
                                "range: {range:?}"
                            );
                        }
                    }
                }
            }
        });
    }
    btree_test!(test_bruteforce_range_search, bruteforce_range_search);

    fn test_iter_from_prev_key<K: TestKey, V: TestValue>() {
        let (key, value) = (K::build, V::build);
        run_btree_test(|mut btree| {
            for j in 0..100 {
                btree.insert(key(j), value(j));
                for i in 0..=j {
                    assert_eq!(
                        btree
                            .iter_from_prev_key(&key(i + 1))
                            .next()
                            .map(|entry| entry.into_pair()),
                        Some((key(i), value(i))),
                        "failed to get an upper bound for key({})",
                        i + 1
                    );
                }
                assert_eq!(
                    btree
                        .iter_from_prev_key(&key(0))
                        .next()
                        .map(|entry| entry.into_pair()),
                    None,
                    "key(0) must not have an upper bound"
                );
            }
        });
    }
    btree_test!(test_test_iter_from_prev_key, test_iter_from_prev_key);

    // A buggy implementation of storable where the max_size is smaller than the serialized size.
    #[derive(Clone, Ord, PartialOrd, Eq, PartialEq)]
    struct BuggyStruct;
    impl crate::Storable for BuggyStruct {
        fn to_bytes(&self) -> Cow<'_, [u8]> {
            Cow::Borrowed(&[1, 2, 3, 4])
        }

        fn into_bytes(self) -> Vec<u8> {
            self.to_bytes().into_owned()
        }

        fn from_bytes(_: Cow<[u8]>) -> Self {
            unimplemented!();
        }

        const BOUND: StorableBound = StorableBound::Bounded {
            max_size: 1,
            is_fixed_size: false,
        };
    }

    #[test]
    #[should_panic(expected = "expected an element with length <= 1 bytes, but found 4")]
    fn v1_panics_if_key_is_bigger_than_max_size() {
        let mut btree = BTreeMap::init_v1(make_memory());
        btree.insert(BuggyStruct, ());
    }

    #[test]
    #[should_panic(expected = "expected an element with length <= 1 bytes, but found 4")]
    fn v2_panics_if_key_is_bigger_than_max_size() {
        let mut btree = BTreeMap::init(make_memory());
        btree.insert(BuggyStruct, ());
    }

    #[test]
    #[should_panic(expected = "expected an element with length <= 1 bytes, but found 4")]
    fn v1_panics_if_value_is_bigger_than_max_size() {
        let mut btree = BTreeMap::init(make_memory());
        btree.insert((), BuggyStruct);
    }

    #[test]
    #[should_panic(expected = "expected an element with length <= 1 bytes, but found 4")]
    fn v2_panics_if_value_is_bigger_than_max_size() {
        let mut btree = BTreeMap::init(make_memory());
        btree.insert((), BuggyStruct);
    }

    // To generate the memory dump file for the current version:
    //   cargo test create_btreemap_dump_file -- --include-ignored
    #[test]
    #[ignore]
    fn create_btreemap_dump_file() {
        let mem = make_memory();
        let mut btree = BTreeMap::init_v1(mem.clone());

        let key = b(&[1, 2, 3]);
        let value = b(&[4, 5, 6]);
        assert_eq!(btree.insert(key, value), None);
        assert_eq!(btree.get(&key), Some(value));

        use std::io::prelude::*;
        let mut file =
            std::fs::File::create(format!("dumps/btreemap_v{LAYOUT_VERSION}.dump")).unwrap();
        file.write_all(&mem.borrow()).unwrap();
    }

    #[test]
    fn produces_layout_identical_to_layout_version_1_with_packed_headers() {
        let mem = make_memory();
        let mut btree = BTreeMap::init_v1(mem.clone());

        let key = b(&[1, 2, 3]);
        let value = b(&[4, 5, 6]);
        assert_eq!(btree.insert(key, value), None);
        assert_eq!(btree.get(&key), Some(value));

        let btreemap_v1 = include_bytes!("../dumps/btreemap_v1_packed_headers.dump");
        assert_eq!(*mem.borrow(), btreemap_v1);
    }

    #[test]
    fn read_write_header_is_identical_to_read_write_struct() {
        #[repr(C, packed)]
        struct BTreePackedHeader {
            magic: [u8; 3],
            version: u8,
            max_key_size: u32,
            max_value_size: u32,
            root_addr: Address,
            length: u64,
            _buffer: [u8; 24],
        }
        let packed_header = BTreePackedHeader {
            magic: *MAGIC,
            version: LAYOUT_VERSION,
            root_addr: Address::from(0xDEADBEEF),
            max_key_size: 0x12345678,
            max_value_size: 0x87654321,
            length: 0xA1B2D3C4,
            _buffer: [0; 24],
        };

        let packed_mem = make_memory();
        crate::write_struct(&packed_header, Address::from(0), &packed_mem);

        let v1_header = BTreeHeader {
            version: Version::V1(DerivedPageSize {
                max_key_size: 0x12345678,
                max_value_size: 0x87654321,
            }),
            root_addr: Address::from(0xDEADBEEF),
            length: 0xA1B2D3C4,
        };

        let v1_mem = make_memory();
        BTreeMap::<Vec<_>, Vec<_>, RefCell<Vec<_>>>::write_header(&v1_header, &v1_mem);

        assert_eq!(packed_mem, v1_mem);

        let packed_header: BTreePackedHeader = crate::read_struct(Address::from(0), &v1_mem);
        let v1_header = BTreeMap::<Vec<_>, Vec<_>, RefCell<Vec<_>>>::read_header(&v1_mem);
        assert!(packed_header.magic == *MAGIC);
        assert!(packed_header.version == LAYOUT_VERSION);
        match v1_header.version {
            Version::V1(DerivedPageSize {
                max_key_size,
                max_value_size,
            }) => {
                assert!(packed_header.max_key_size == max_key_size);
                assert!(packed_header.max_value_size == max_value_size);
            }
            _ => unreachable!("version must be v1"),
        };

        assert!(packed_header.root_addr == v1_header.root_addr);
        assert!(packed_header.length == v1_header.length);
    }

    #[test]
    fn migrate_from_bounded_to_unbounded_and_back() {
        // A type that is bounded.
        #[derive(PartialOrd, Ord, Clone, Eq, PartialEq, Debug)]
        struct T;
        impl Storable for T {
            fn to_bytes(&self) -> Cow<'_, [u8]> {
                Cow::Borrowed(&[1, 2, 3])
            }

            fn into_bytes(self) -> Vec<u8> {
                self.to_bytes().into_owned()
            }

            fn from_bytes(bytes: Cow<[u8]>) -> Self {
                assert_eq!(bytes.to_vec(), vec![1, 2, 3]);
                T
            }

            const BOUND: StorableBound = StorableBound::Bounded {
                max_size: 3,
                is_fixed_size: true,
            };
        }

        // Same as the above type, but unbounded.
        #[derive(PartialOrd, Ord, Clone, Eq, PartialEq, Debug)]
        struct T2;
        impl Storable for T2 {
            fn to_bytes(&self) -> Cow<'_, [u8]> {
                Cow::Owned(vec![1, 2, 3])
            }

            fn into_bytes(self) -> Vec<u8> {
                self.to_bytes().into_owned()
            }

            fn from_bytes(bytes: Cow<[u8]>) -> Self {
                assert_eq!(bytes.to_vec(), vec![1, 2, 3]);
                T2
            }

            const BOUND: StorableBound = StorableBound::Unbounded;
        }

        // Create a v1 btreemap with the bounded type.
        let mem = make_memory();
        let mut btree: BTreeMap<T, T, _> = BTreeMap::new_v1(mem);
        btree.insert(T, T);

        // Migrate to v2 and the unbounded type.
        let btree: BTreeMap<T2, T2, _> = BTreeMap::init(btree.into_memory());
        btree.save_header();

        // Reload the BTree again and try to read the value.
        let btree: BTreeMap<T2, T2, _> = BTreeMap::init(btree.into_memory());
        assert_eq!(btree.get(&T2), Some(T2));

        // Reload the BTree again with bounded type.
        let btree: BTreeMap<T, T, _> = BTreeMap::init(btree.into_memory());
        assert_eq!(btree.get(&T), Some(T));
    }

    #[test]
    fn test_clear_new_bounded_type() {
        let mem = make_memory();
        let mut btree: BTreeMap<Blob<4>, Blob<4>, _> = BTreeMap::new(mem.clone());

        btree.insert(
            [1u8; 4].as_slice().try_into().unwrap(),
            [1u8; 4].as_slice().try_into().unwrap(),
        );

        assert_ne!(btree.len(), 0);
        assert_ne!(btree.allocator.num_allocated_chunks(), 0);
        assert_ne!(btree.root_addr, NULL);

        btree.clear_new();

        let header_actual = BTreeMap::<Blob<4>, Blob<4>, _>::read_header(&mem);

        BTreeMap::<Blob<4>, Blob<4>, _>::new(mem.clone());

        let header_expected = BTreeMap::<Blob<4>, Blob<4>, _>::read_header(&mem);

        assert_eq!(header_actual, header_expected);
    }

    #[test]
    fn test_clear_new_unbounded_type() {
        let mem = make_memory();
        let mut btree: BTreeMap<String, String, _> = BTreeMap::new(mem.clone());
        btree.insert("asd".into(), "bce".into());

        assert_ne!(btree.len(), 0);
        assert_ne!(btree.allocator.num_allocated_chunks(), 0);
        assert_ne!(btree.root_addr, NULL);

        btree.clear_new();

        let header_actual = BTreeMap::<String, String, _>::read_header(&mem);

        BTreeMap::<String, String, _>::new(mem.clone());

        let header_expected = BTreeMap::<String, String, _>::read_header(&mem);

        assert_eq!(header_actual, header_expected);
    }

    #[test]
    fn deallocating_node_with_overflows() {
        let mem = make_memory();
        let mut btree: BTreeMap<Vec<u8>, Vec<u8>, _> = BTreeMap::new(mem.clone());

        // No allocated chunks yet.
        assert_eq!(btree.allocator.num_allocated_chunks(), 0);

        // Insert and remove an entry that's large and requires overflow pages.
        btree.insert(vec![0; 10_000], vec![]);

        // At least two chunks should be allocated.
        // One for the node itself and at least one overflow page.
        assert!(btree.allocator.num_allocated_chunks() >= 2);
        btree.remove(&vec![0; 10_000]);

        // All chunks have been deallocated.
        assert_eq!(btree.allocator.num_allocated_chunks(), 0);
    }

    #[test]
    fn repeatedly_deallocating_nodes_with_overflows() {
        let mem = make_memory();
        let mut btree: BTreeMap<Vec<u8>, Vec<u8>, _> = BTreeMap::new(mem.clone());

        // No allocated chunks yet.
        assert_eq!(btree.allocator.num_allocated_chunks(), 0);

        for _ in 0..100 {
            for i in 0..100 {
                btree.insert(vec![i; 10_000], vec![]);
            }

            for i in 0..100 {
                btree.remove(&vec![i; 10_000]);
            }
        }

        // All chunks have been deallocated.
        assert_eq!(btree.allocator.num_allocated_chunks(), 0);
    }

    #[test]
    fn deallocating_root_does_not_leak_memory() {
        let mem = make_memory();
        let mut btree: BTreeMap<Vec<u8>, _, _> = BTreeMap::new(mem.clone());

        for i in 1..=11 {
            // Large keys are stored so that each node overflows.
            assert_eq!(btree.insert(vec![i; 10_000], ()), None);
        }

        // Should now split a node.
        assert_eq!(btree.insert(vec![0; 10_000], ()), None);

        // The btree should look like this:
        //                    [6]
        //                   /   \
        // [0, 1, 2, 3, 4, 5]     [7, 8, 9, 10, 11]
        let root = btree.load_node(btree.root_addr);
        assert_eq!(root.node_type(), NodeType::Internal);
        assert_eq!(root.keys(btree.memory()), vec![&[6; 10_000]]);
        assert_eq!(root.children_len(), 2);

        // Remove the element in the root.
        btree.remove(&vec![6; 10_000]);

        // The btree should look like this:
        //                 [5]
        //                /   \
        // [0, 1, 2, 3, 4]     [7, 8, 9, 10, 11]
        let root = btree.load_node(btree.root_addr);
        assert_eq!(root.node_type(), NodeType::Internal);
        assert_eq!(root.keys(btree.memory()), vec![&[5; 10_000]]);
        assert_eq!(root.children_len(), 2);

        // Remove the element in the root. This triggers the case where the root
        // node is deallocated and the children are merged into a single node.
        btree.remove(&vec![5; 10_000]);

        // The btree should look like this:
        //      [0, 1, 2, 3, 4, 7, 8, 9, 10, 11]
        let root = btree.load_node(btree.root_addr);
        assert_eq!(root.node_type(), NodeType::Leaf);
        assert_eq!(
            root.keys(btree.memory()),
            vec![
                &[0; 10_000],
                &[1; 10_000],
                &[2; 10_000],
                &[3; 10_000],
                &[4; 10_000],
                &[7; 10_000],
                &[8; 10_000],
                &[9; 10_000],
                &[10; 10_000],
                &[11; 10_000],
            ]
        );

        // Delete everything else.
        for i in 0..=11 {
            btree.remove(&vec![i; 10_000]);
        }

        assert_eq!(btree.allocator.num_allocated_chunks(), 0);
    }
}