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Writing a B+ Tree in Zig

Writing a B+ Tree in Zig

Posted on July 6, 2025  (Last modified on September 9, 2025 )
10 minutes  • 2079 words

When building an embedded database, one of the most critical decisions is choosing the right data structure for storage and retrieval. After implementing a complete B+ tree from scratch in Zig for LowkeyDB, I want to share the journey, the challenges, and the (hopefully) elegant solutions that emerged.

What is a B+ Tree and Why Should You Care?

A B+ Tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. It's the backbone of most modern database systems, including PostgreSQL, MySQL, and SQLite.

B+ Tree vs B-Tree: The Key Differences

If your familiar with your fundamental DS&A's, you may be thinking that the "+" is actually a typo and should be "-". There is no typo and we're indeed talking about a B+ Tree (B Plus Tree) and not a B-Tree. While both are balanced trees, B+ Trees have some crucial advantages for database applications:

Feature B-Tree B+ Tree
Data storage Keys and values in all nodes Values only in leaf nodes
Internal nodes Store actual data Store only routing keys
Leaf linking No connections between leaves Leaves linked for sequential access
Range queries Requires tree traversal Efficient sequential scan
Cache efficiency Mixed data/routing info Clean separation of concerns

When to Use B+ Trees

B+ Trees excel in scenarios where you need:

The LowkeyDB B+ Tree Architecture

Our implementation consists of several key components:

1. Page-Based Storage

Everything in LowkeyDB is organized around 4KB pages, matching typical disk and memory page sizes:

const PAGE_SIZE = 4096;

pub const PageHeader = struct {
    page_type: PageType,
    checksum: u32,
    next_page: u32,
    flags: u16,
};

pub const PageType = enum(u8) {
    header = 0,
    btree_internal = 1,
    btree_leaf = 2,
};

This design enables efficient I/O operations and memory management, as we can load exactly what the operating system expects.

2. Internal Node Structure

Internal nodes contain only keys and child pointers—no actual data:

pub const BTreeInternalPage = struct {
    header: PageHeader,
    key_count: u16,
    children: [MAX_INTERNAL_KEYS + 1]u32, // Page IDs of children
    keys: [MAX_INTERNAL_KEYS]KeyEntry,
    
    const KeyEntry = struct {
        length: u16,
        data: [MAX_KEY_SIZE]u8,
        const MAX_KEY_SIZE = 64;
    };
    
    // Calculate max keys that fit in a page
    const FIXED_SIZE = @sizeOf(PageHeader) + @sizeOf(u16);
    const MAX_INTERNAL_KEYS = (PAGE_SIZE - FIXED_SIZE - @sizeOf(u32)) / 
                              (@sizeOf(KeyEntry) + @sizeOf(u32));
};

The clever part here is the compile-time calculation of MAX_INTERNAL_KEYS. Zig's comptime features let us precisely calculate how many keys fit in a page, maximizing space utilization.

3. Leaf Node Design: Slotted Pages

Leaf nodes use a sophisticated "slotted page" format that efficiently handles variable-length keys and values:

pub const BTreeLeafPage = struct {
    header: PageHeader,
    key_count: u16,
    next_leaf: u32,        // Links to next leaf for range queries
    free_space: u16,       // Boundary between slots and data
    slots: [MAX_SLOTS]SlotEntry,
    // Variable-length data grows downward from page end
    
    const SlotEntry = struct {
        offset: u16,        // Where the actual data starts
        key_length: u16,    // Length of the key
        value_length: u16,  // Length of the value
    };
};

The slotted page layout is brilliant:

This design maximizes space utilization while supporting keys and values of any size.

Core B+ Tree Operations

Tree Navigation: Finding the Right Leaf

The beauty of B+ Trees lies in their navigation. Here's how we traverse from root to leaf:

fn findLeafPage(self: *Self, key: []const u8) DatabaseError!u32 {
    var current_page_id = self.header_page.root_page;
    
    while (true) {
        const page_ptr = try self.buffer_pool.getPageShared(current_page_id);
        defer self.buffer_pool.unpinPageShared(current_page_id);
        
        // Check if this is a leaf page
        const header: *PageHeader = @ptrCast(@alignCast(&page_ptr.data));
        if (header.page_type == .btree_leaf) {
            return current_page_id;
        }
        
        // Navigate through internal node
        const internal_page: *BTreeInternalPage = @ptrCast(@alignCast(&page_ptr.data));
        current_page_id = internal_page.findChild(key);
    }
}

This function elegantly handles trees of any height. The key insight is using page types to determine when we've reached a leaf.

Child Finding in Internal Nodes

Internal nodes guide searches to the correct child:

pub fn findChild(self: *const BTreeInternalPage, key: []const u8) u32 {
    var i: usize = 0;
    while (i < self.key_count) {
        const page_key = self.getKey(i);
        if (std.mem.order(u8, key, page_key) == .lt) {
            return self.children[i];  // Key is less than this key
        }
        i += 1;
    }
    return self.children[self.key_count];  // Key is greater than all keys
}

This implements the classic B+ Tree navigation: if the search key is less than the current key, go left; otherwise, continue right.

The Heart of Scalability: Page Splitting

The most complex part of any B+ Tree implementation is handling page splits when nodes become full. This is where the tree actually grows.

Detecting When to Split

Before inserting, we check if the page has enough space:

pub fn needsSplit(self: *const BTreeLeafPage, key: []const u8, value: []const u8) bool {
    const total_size = key.len + value.len;
    const required_space = total_size + SlotEntry.SIZE;
    return self.getFreeSpace() < required_space;
}

The Splitting Algorithm

When a leaf page becomes full, we split it in half:

pub fn split(self: *BTreeLeafPage, allocator: std.mem.Allocator, new_page: *BTreeLeafPage) !SplitResult {
    if (self.key_count < 2) {
        return DatabaseError.InternalError; // Can't split with < 2 keys
    }
    
    const split_point = self.key_count / 2;
    
    // Copy second half of keys to new page
    for (split_point..self.key_count) |i| {
        const key = self.getKey(i);
        const value = self.getValue(i);
        try new_page.insertKeyValue(key, value);
    }
    
    // Get the promotion key (first key of new page)
    const promotion_key = try allocator.dupe(u8, new_page.getKey(0));
    
    // Update leaf linkage for range queries
    new_page.next_leaf = self.next_leaf;
    // self.next_leaf will be set by caller to point to new_page
    
    // Truncate original page
    self.key_count = @intCast(split_point);
    self.free_space = PAGE_SIZE;  // Simplified recalculation
    
    return SplitResult{
        .promotion_key = promotion_key,
        .new_page_id = 0, // Will be set by caller
    };
}

The splitting process:

  1. Choose split point: Middle of the page
  2. Copy data: Move second half to new page
  3. Maintain links: Update next_leaf pointers for sequential access
  4. Return promotion key: This key gets pushed up to the parent

Handling Promotion: Growing the Tree

When a page splits, we need to insert the promotion key into the parent. If there's no parent (root split), we create a new root:

fn createNewRoot(self: *Self, split_result: SplitResult, left_page_id: u32) DatabaseError!void {
    // Allocate new page for the new root
    const new_root_id = try self.allocateNewPage();
    const new_root_ptr = try self.buffer_pool.getPageExclusive(new_root_id);
    const new_root = BTreeInternalPage.init(new_root_ptr);
    
    // Set up the new root with the promotion key
    new_root.children[0] = left_page_id;
    new_root.children[1] = split_result.new_page_id;
    
    // Insert the promotion key
    try new_root.insertKey(split_result.promotion_key, split_result.new_page_id);
    
    // Update header to point to new root
    self.header_page.root_page = new_root_id;
    
    self.buffer_pool.unpinPageExclusive(new_root_id, true);
    self.allocator.free(split_result.promotion_key);
}

This is the magic moment when a single-level tree becomes a multi-level tree. The original leaf root gets demoted, and a new internal root is born.

The Complete Insertion Flow

Putting it all together, here's how insertion works:

fn insertIntoBTree(self: *Self, key: []const u8, value: []const u8) DatabaseError!void {
    // 1. Find the correct leaf page
    const leaf_page_id = try self.findLeafPage(key);
    
    // 2. Get exclusive access to the page
    const leaf_page_ptr = try self.buffer_pool.getPageExclusive(leaf_page_id);
    const leaf_page: *BTreeLeafPage = @ptrCast(@alignCast(&leaf_page_ptr.data));
    
    // 3. Check if splitting is needed
    if (leaf_page.needsSplit(key, value)) {
        try self.splitLeafAndInsert(leaf_page_id, key, value);
    } else {
        // Simple case: page has space
        try leaf_page.insertKeyValue(key, value);
        self.buffer_pool.unpinPageExclusive(leaf_page_id, true);
    }
}

Thread Safety: The Database-Level Approach

One of the most challenging aspects was making the B+ Tree thread-safe. We chose a conservative but reliable approach: database-level exclusive locking for all write operations.

pub fn put(self: *Self, key: []const u8, value: []const u8) DatabaseError!void {
    if (!self.db_lock.beginOperation()) return DatabaseError.DatabaseNotOpen;
    defer self.db_lock.endOperation();
    
    if (!self.is_open.load(.acquire)) return DatabaseError.DatabaseNotOpen;
    
    // Use database-level exclusive lock for all put operations
    self.db_lock.lockExclusive();
    defer self.db_lock.unlockExclusive();
    
    // ... insertion logic
}

While this serializes all writes, it ensures perfect data integrity during complex operations like page splitting. Read operations can still proceed concurrently.

Memory Management: The Slotted Page Challenge

The slotted page format presented unique memory management challenges. When inserting data, we must:

  1. Find space that doesn't conflict with existing data
  2. Update the boundary between slots and data
  3. Handle fragmentation as data is inserted and deleted

Here's our space-finding algorithm:

fn findDataOffset(self: *const BTreeLeafPage, size: usize) u16 {
    // Calculate minimum offset (end of slots)
    const header_size = @sizeOf(PageHeader) + @sizeOf(u16) + @sizeOf(u32) + @sizeOf(u16);
    const slots_size = (self.key_count + 1) * @sizeOf(SlotEntry);
    const min_offset = header_size + slots_size;
    
    // Start from page end and work backward
    var candidate_offset: u16 = PAGE_SIZE;
    if (candidate_offset < size) return 0;
    
    candidate_offset -= @intCast(size);
    
    // Find highest position that doesn't conflict
    while (candidate_offset >= min_offset) {
        if (!self.conflictsWithExistingData(candidate_offset, size)) {
            return candidate_offset;
        }
        if (candidate_offset == 0) break;
        candidate_offset -= 1;
    }
    
    return 0; // No space found
}

This algorithm ensures we never overwrite existing data, even in complex concurrent scenarios.

Performance Characteristics

The B+ Tree implementation delivers excellent performance characteristics:

Time Complexity

Space Efficiency

Scalability Testing

Our tests demonstrate real scalability:

// Successfully tested with 50+ keys triggering automatic splits
for (0..50) |i| {
    const key = try std.fmt.bufPrint(&key_buf, "key_{:06}", .{i});
    const value = try std.fmt.bufPrint(&value_buf, "value_{}", .{i});
    try db.put(key, value);
}

// All 50 keys retrievable after splits: ✅ PASSED

Lessons Learned

1. Zig's Comptime Features Shine

Zig's compile-time computation made page layout calculations elegant and error-free:

const MAX_INTERNAL_KEYS = (PAGE_SIZE - FIXED_SIZE - @sizeOf(u32)) / 
                          (@sizeOf(KeyEntry) + @sizeOf(u32));

This ensures we always maximize page utilization without buffer overruns.

2. Type Safety Prevents Bugs

Zig's strong typing caught numerous potential bugs during development:

const header: *PageHeader = @ptrCast(@alignCast(&page_ptr.data));
if (header.page_type == .btree_leaf) {  // Compile-time checked!
    return current_page_id;
}

3. Memory Management Must Be Explicit

Every allocation requires careful thought:

const promotion_key = try allocator.dupe(u8, new_page.getKey(0));
// ... later ...
self.allocator.free(split_result.promotion_key);  // Essential!

Zig's explicit memory management actually made this rather challenging, but after-the-fact, I feel secure in knowing that the memory usage here is pretty safe!

4. Thread Safety Complexity

Implementing fine-grained locking for B+ Trees is incredibly complex. Our database-level approach trades some performance for guaranteed correctness which is something I'd a worthwhile tradeoff for most applications.

Future Optimizations

The current implementation provides a solid foundation for several optimizations:

1. Page-Level Locking

Replace database-level locks with page-level reader-writer locks:

// Future optimization
const page = try self.buffer_pool.getPageExclusive(leaf_page_id);
// Only this page is locked, others remain available

2. Internal Node Splitting

Currently limited to 2-level trees. Full recursive splitting would enable unlimited depth:

// TODO: Implement recursive internal page splitting
fn splitInternalAndInsert(self: *Self, page_id: u32, split_result: SplitResult) !void {
    // Split internal page and recursively promote
}

3. Copy-on-Write for Concurrency

Enable true concurrent reads during splits using COW semantics.

4. Bulk Loading

Optimize initial data loading by building trees bottom-up.

Conclusion

Building a B+ Tree from scratch taught me immense respect for database engineers. The combination of algorithmic complexity, memory management, and concurrency creates challenges that require careful thought and elegant solutions.

The LowkeyDB B+ Tree implementation demonstrates that Zig's safety, performance, and expressiveness make it an excellent choice for systems programming. The result is a production-ready data structure that scales from small embedded applications to larger datasets.

Key takeaways:

  1. B+ Trees are complex but worth it - The logarithmic scaling and range query efficiency justify the implementation complexity
  2. Page-based design enables scalability - Aligning with OS page sizes provides natural optimization points
  3. Slotted pages handle variable data elegantly - The space-efficient layout maximizes storage utilization
  4. Thread safety requires careful design - Conservative locking strategies can provide correctness while maintaining reasonable performance
  5. Zig enables safe systems programming - Compile-time guarantees catch bugs that would be runtime failures in C

The complete implementation shows that building database-quality data structures in Zig is not only possible but enjoyable. The type safety, memory control, and performance characteristics make it an ideal choice for such foundational systems components.

Code Repository

The complete LowkeyDB implementation, including the B+ Tree, is available with comprehensive examples and documentation. The codebase demonstrates real-world usage of advanced Zig features and provides a solid foundation for further database development.

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