B-Tree indexing

benchmarks/sekp256k1.ts

@@ -7,6 +7,7 @@ const alicePublicKey = await alice.getPublicKey();
 const bobPublicKey = await bob.getPublicKey();
 
 const keyStart = performance.now();
+
 const aliceSharedSecret = await alice.getSharedSecret(bobPublicKey);
 const bobSharedSecret = await bob.getSharedSecret(alicePublicKey);
 

benchmarks/storage.ts

@@ -49,7 +49,13 @@ function fmtOps(ops: number): string {
 /**
  * Run a full suite of benchmarks against a given storage instance.
  */
-async function benchmarkStorage(label: string, storage: BaseStorage<Doc>, docs: Doc[]) {
+async function benchmarkStorage(
+  label: string,
+  storage: BaseStorage<Doc>,
+  docs: Doc[],
+  options: { supportsRangeOps?: boolean; hasAgeIndex?: boolean } = {},
+) {
+  const { supportsRangeOps = true, hasAgeIndex = false } = options;
   const count = docs.length;
   console.log(`\n${'='.repeat(60)}`);
   console.log(` ${label}  (${count.toLocaleString()} documents)`);
@@ -67,32 +73,63 @@ async function benchmarkStorage(label: string, storage: BaseStorage<Doc>, docs:
   });
   console.log(`  find()              ${findAllMs.toFixed(2)}ms  (${fmtOps((count / findAllMs) * 1000)} docs/sec)`);
 
-  // --- Find by indexed field (single-key lookup, repeated) ---
+  // --- Find by indexed field (equality) ---
   const lookupCount = Math.min(count, 1_000);
   const findIndexedMs = await time(async () => {
     for (let i = 0; i < lookupCount; i++) {
-      await storage.findOne({ id: `id-${i}` } as Partial<Doc>);
+      await storage.findOne({ id: `id-${i}` });
     }
   });
   console.log(`  findOne indexed      ${findIndexedMs.toFixed(2)}ms  (${fmtOps((lookupCount / findIndexedMs) * 1000)} ops/sec)  [${lookupCount} lookups]`);
 
-  // --- Find by non-indexed field (full scan, repeated) ---
+  // --- Find by non-indexed field (full scan) ---
   const scanCount = Math.min(count, 1_000);
   const findScanMs = await time(async () => {
     for (let i = 0; i < scanCount; i++) {
-      await storage.findOne({ email: `user-${i}@test.com` } as Partial<Doc>);
+      await storage.findOne({ email: `user-${i}@test.com` });
     }
   });
   console.log(`  findOne scan         ${findScanMs.toFixed(2)}ms  (${fmtOps((scanCount / findScanMs) * 1000)} ops/sec)  [${scanCount} lookups]`);
 
+  // --- Range queries ---
+  if (supportsRangeOps) {
+    // Wide range: 20% selectivity (10 out of 50 age values).
+    const rangeCount = Math.min(count, 100);
+    let rangeWideTotal = 0;
+    const findRangeWideMs = await time(async () => {
+      for (let i = 0; i < rangeCount; i++) {
+        const results = await storage.find({ age: { $gte: 30, $lt: 40 } });
+        rangeWideTotal += results.length;
+      }
+    });
+    const indexLabel = hasAgeIndex ? 'B+Tree' : 'scan';
+    console.log(`  find wide  [${indexLabel}]  ${findRangeWideMs.toFixed(2)}ms  (${fmtOps((rangeCount / findRangeWideMs) * 1000)} ops/sec)  [${rangeCount}x, ~${Math.round(rangeWideTotal / rangeCount)} hits, 20% sel.]`);
+
+    // Narrow range: 2% selectivity (1 out of 50 age values).
+    let rangeNarrowTotal = 0;
+    const findRangeNarrowMs = await time(async () => {
+      for (let i = 0; i < rangeCount; i++) {
+        const results = await storage.find({ age: { $gte: 42, $lt: 43 } });
+        rangeNarrowTotal += results.length;
+      }
+    });
+    console.log(`  find narrow [${indexLabel}]  ${findRangeNarrowMs.toFixed(2)}ms  (${fmtOps((rangeCount / findRangeNarrowMs) * 1000)} ops/sec)  [${rangeCount}x, ~${Math.round(rangeNarrowTotal / rangeCount)} hits, 2% sel.]`);
+
+    // --- Combined equality + operator ---
+    const comboCount = Math.min(count, 1_000);
+    const findComboMs = await time(async () => {
+      for (let i = 0; i < comboCount; i++) {
+        await storage.find({ id: `id-${i}`, age: { $gte: 20 } });
+      }
+    });
+    console.log(`  find idx+operator    ${findComboMs.toFixed(2)}ms  (${fmtOps((comboCount / findComboMs) * 1000)} ops/sec)  [${comboCount} queries]`);
+  }
+
   // --- Update by indexed field ---
   const updateCount = Math.min(count, 1_000);
   const updateMs = await time(async () => {
     for (let i = 0; i < updateCount; i++) {
-      await storage.updateOne(
+      await storage.updateOne({ id: `id-${i}` }, { name: `updated-${i}` });
-        { id: `id-${i}` } as Partial<Doc>,
-        { age: 99 } as Partial<Doc>,
-      );
     }
   });
   console.log(`  updateOne indexed    ${updateMs.toFixed(2)}ms  (${fmtOps((updateCount / updateMs) * 1000)} ops/sec)  [${updateCount} updates]`);
@@ -101,7 +138,7 @@ async function benchmarkStorage(label: string, storage: BaseStorage<Doc>, docs:
   const deleteCount = Math.min(count, 1_000);
   const deleteMs = await time(async () => {
     for (let i = 0; i < deleteCount; i++) {
-      await storage.deleteOne({ id: `id-${i}` } as Partial<Doc>);
+      await storage.deleteOne({ id: `id-${i}` });
     }
   });
   console.log(`  deleteOne indexed    ${deleteMs.toFixed(2)}ms  (${fmtOps((deleteCount / deleteMs) * 1000)} ops/sec)  [${deleteCount} deletes]`);
@@ -116,7 +153,7 @@ async function benchmarkStorage(label: string, storage: BaseStorage<Doc>, docs:
 // ---------------------------------------------------------------------------
 
 // ---------------------------------------------------------------------------
-// StorageMemory — indexed vs non-indexed
+// StorageMemory — B+ Tree range queries vs full scan
 // ---------------------------------------------------------------------------
 
 const DOC_COUNTS = [1_000, 10_000, 50_000];
@@ -124,32 +161,45 @@ const DOC_COUNTS = [1_000, 10_000, 50_000];
 for (const count of DOC_COUNTS) {
   const docs = generateDocs(count);
 
+  // Indexes on id, name, AND age — range queries on age use B+ Tree.
+  const indexedWithAge = StorageMemory.from<Doc>(['id', 'name', 'age']);
+  await benchmarkStorage('StorageMemory (indexed: id,name,age)', indexedWithAge, docs, { hasAgeIndex: true });
+
+  // Indexes on id, name only — range queries on age fall back to full scan.
   const indexed = StorageMemory.from<Doc>(['id', 'name']);
   await benchmarkStorage('StorageMemory (indexed: id,name)', indexed, docs);
 
+  // No indexes at all.
   const noIndex = StorageMemory.from<Doc>();
   await benchmarkStorage('StorageMemory (no indexes)', noIndex, docs);
 }
 
 // ---------------------------------------------------------------------------
-// EncryptedStorage — crypto overhead dominates, so use smaller counts
+// EncryptedStorage
 // ---------------------------------------------------------------------------
 
-const ENCRYPTED_DOC_COUNTS = [100, 1_000, 10_000];
+const ENCRYPTED_DOC_COUNTS = [100, 1_000];
 const encryptionKey = await AESKey.fromSeed('benchmark-key');
 
 for (const count of ENCRYPTED_DOC_COUNTS) {
   const docs = generateDocs(count);
 
-  // Encrypted + indexed backing store.
+  // Indexed + plaintextKeys (age) — range queries on age use B+ Tree via backing store.
-  const encBase = StorageMemory.from<Record<string, string>>(['id', 'name']);
+  const encBaseA = StorageMemory.from<Record<string, any>>(['id', 'name', 'age']);
-  const encrypted = EncryptedStorage.from<Doc>(encBase, encryptionKey);
+  const encA = EncryptedStorage.from<Doc>(encBaseA, encryptionKey, {
-  await benchmarkStorage('EncryptedStorage (indexed backing store)', encrypted, docs);
+    plaintextKeys: ['age'],
+  });
+  await benchmarkStorage('Encrypted (indexed+age, plaintextKeys: age)', encA, docs, { hasAgeIndex: true });
 
-  // Encrypted + no-index backing store.
+  // Indexed, fully encrypted — no range ops.
-  const encBaseNoIdx = StorageMemory.from<Record<string, string>>();
+  const encBaseB = StorageMemory.from<Record<string, any>>(['id', 'name']);
-  const encryptedNoIdx = EncryptedStorage.from<Doc>(encBaseNoIdx, encryptionKey);
+  const encB = EncryptedStorage.from<Doc>(encBaseB, encryptionKey);
-  await benchmarkStorage('EncryptedStorage (no indexes)', encryptedNoIdx, docs);
+  await benchmarkStorage('Encrypted (indexed, fully encrypted)', encB, docs, { supportsRangeOps: false });
+
+  // No indexes, fully encrypted — worst case.
+  const encBaseC = StorageMemory.from<Record<string, any>>();
+  const encC = EncryptedStorage.from<Doc>(encBaseC, encryptionKey);
+  await benchmarkStorage('Encrypted (no indexes, fully encrypted)', encC, docs, { supportsRangeOps: false });
 }
 
 console.log('\nDone.\n');

package.json

@@ -8,6 +8,9 @@
     "format": "prettier --write .",
     "test": "echo \"Error: no test specified\" && exit 1",
 
+    "benchmark:sha256": "tsx benchmarks/sha256.ts",
+    "benchmark:diffie-helman": "tsx benchmarks/diffie-helman.ts",
+    "benchmark:encryption": "tsx benchmarks/sekp256k1.ts",
     "benchmark:storage": "tsx benchmarks/storage.ts"
   },
   "keywords": [],

src/storage/base-storage.ts

@@ -19,6 +19,54 @@ export type FindOptions = {
  */
 export type IndexDefinition = string[] | string[][];
 
+/**
+ * MongoDB-style comparison operators for a single field value.
+ */
+export type ComparisonOperators<V> = {
+  $eq?: V;
+  $ne?: V;
+  $lt?: V;
+  $lte?: V;
+  $gt?: V;
+  $gte?: V;
+};
+
+/**
+ * A filter value for a single field — either a plain value (equality shorthand)
+ * or an object of comparison operators.
+ */
+export type FieldFilter<V> = V | ComparisonOperators<V>;
+
+/**
+ * Query filter that supports both equality shorthand and comparison operators.
+ *
+ * @example
+ * // Equality shorthand
+ * { name: 'foo' }
+ *
+ * // Comparison operators
+ * { age: { $gte: 18, $lt: 65 } }
+ *
+ * // Combined
+ * { name: 'foo', age: { $gte: 18 } }
+ */
+export type Filter<T extends Record<string, any>> = {
+  [K in keyof T]?: FieldFilter<T[K]>;
+};
+
+/**
+ * Detect whether a filter value is an operator object (e.g. `{ $lt: 50 }`)
+ * rather than a plain value. Guards against Date and Array which are objects
+ * but represent document values, not operators.
+ */
+export function isOperatorObject(value: unknown): value is ComparisonOperators<any> {
+  return value !== null
+    && typeof value === 'object'
+    && !Array.isArray(value)
+    && !(value instanceof Date)
+    && Object.keys(value).some((k) => k.startsWith('$'));
+}
+
 export type StorageEvent<T = Record<string, any>> = {
   insert: {
     value: T;
@@ -54,7 +102,7 @@ export abstract class BaseStorage<
    * Find a single document that matches the filter
    * @param filter MongoDB-like query filter
    */
-  async findOne(filter?: Partial<T>): Promise<T | null> {
+  async findOne(filter?: Filter<T>): Promise<T | null> {
     const results = await this.find(filter);
     return results.length > 0 ? results[0] : null;
   }
@@ -64,7 +112,7 @@ export abstract class BaseStorage<
    * @param filter MongoDB-like query filter
    * @param options Query options (limit, skip, sort)
    */
-  abstract find(filter?: Partial<T>, options?: FindOptions): Promise<T[]>;
+  abstract find(filter?: Filter<T>, options?: FindOptions): Promise<T[]>;
 
   /**
    * Update a document that matches the filter
@@ -72,7 +120,7 @@ export abstract class BaseStorage<
    * @param update Document or fields to update
    * @returns True if a document was updated, false otherwise
    */
-  async updateOne(filter: Partial<T>, update?: Partial<T>): Promise<boolean> {
+  async updateOne(filter: Filter<T>, update?: Partial<T>): Promise<boolean> {
     const results = await this.updateMany(filter, update, { limit: 1 });
     return results > 0;
   }
@@ -85,7 +133,7 @@ export abstract class BaseStorage<
    * @returns Number of documents updated
    */
   abstract updateMany(
-    filter: Partial<T>,
+    filter: Filter<T>,
     update: Partial<T>,
     options?: Partial<FindOptions>,
   ): Promise<number>;
@@ -95,7 +143,7 @@ export abstract class BaseStorage<
    * @param filter Query to match the document to delete
    * @returns True if a document was deleted, false otherwise
    */
-  async deleteOne(filter: Partial<T>): Promise<boolean> {
+  async deleteOne(filter: Filter<T>): Promise<boolean> {
     const results = await this.deleteMany(filter, { limit: 1 });
     return results > 0;
   }
@@ -107,7 +155,7 @@ export abstract class BaseStorage<
    * @returns Number of documents deleted
    */
   abstract deleteMany(
-    filter: Partial<T>,
+    filter: Filter<T>,
     options: Partial<FindOptions>,
   ): Promise<number>;
 

src/storage/encrypted-storage.ts

@@ -3,15 +3,29 @@ import { Packr } from 'msgpackr';
 import { AESKey } from 'src/crypto/aes-key.js';
 import { Bytes } from 'src/crypto/bytes.js';
 
-import { BaseStorage, type FindOptions } from './base-storage.js';
+import { BaseStorage, type FindOptions, type Filter, isOperatorObject } from './base-storage.js';
 
-import { encodeExtendedJson, decodeExtendedJson, encodeExtendedJsonObject, decodeExtendedJsonObject } from 'src/utils/ext-json.js';
+import { encodeExtendedJsonObject, decodeExtendedJsonObject } from 'src/utils/ext-json.js';
+
+export type EncryptedStorageOptions = {
+  /**
+   * Fields that should be stored in plaintext (not encrypted).
+   * These fields retain their original types in the backing store, which
+   * allows comparison operators ($lt, $gt, etc.) to work on them.
+   * All other fields are encrypted.
+   */
+  plaintextKeys?: string[];
+};
 
 export class EncryptedStorage<
   T extends Record<string, any> = Record<string, any>,
 > extends BaseStorage<T> {
-  static from<T>(storage: BaseStorage<Record<string, string>>, key: AESKey) {
+  static from<T>(
-    return new EncryptedStorage<T>(storage, key);
+    storage: BaseStorage<Record<string, any>>,
+    key: AESKey,
+    options?: EncryptedStorageOptions,
+  ) {
+    return new EncryptedStorage<T>(storage, key, options);
   }
 
   private readonly msgpackr = new Packr({
@@ -33,34 +47,32 @@ export class EncryptedStorage<
    */
   private readonly decryptCache = new Map<string, any>();
 
+  /** Set of field names that are stored in plaintext (not encrypted). */
+  private readonly plaintextKeys: Set<string>;
+
   constructor(
-    private readonly storage: BaseStorage<Record<string, string>>,
+    private readonly storage: BaseStorage<Record<string, any>>,
     private readonly key: AESKey,
+    options?: EncryptedStorageOptions,
   ) {
     super();
 
-    // Forward events from the underlying storage, decrypting the data
+    this.plaintextKeys = new Set(options?.plaintextKeys ?? []);
-    this.storage.on('insert', async (event) => {
-      // De-crypt the value before emitting the event.
-      const decryptedValue = await this.convertToDecrypted(event.value as Record<string, string>);
     
-      // Re-emit the insert event with the original payload.
+    // Forward events from the underlying storage, converting data back.
+    this.storage.on('insert', async (event) => {
+      const decryptedValue = await this.convertFromStorage(event.value);
       this.emit('insert', { value: decryptedValue });
     });
     
     this.storage.on('update', async (event) => {
-      // Decrypt both old and new values before re-emitting.
+      const decryptedOldValue = await this.convertFromStorage(event.oldValue);
-      const decryptedOldValue = await this.convertToDecrypted(event.oldValue as Record<string, string>);
+      const decryptedValue = await this.convertFromStorage(event.value);
-      const decryptedValue = await this.convertToDecrypted(event.value as Record<string, string>);
-
       this.emit('update', { oldValue: decryptedOldValue, value: decryptedValue });
     });
     
     this.storage.on('delete', async (event) => {
-      // De-crypt the value before emitting the event.
+      const decryptedValue = await this.convertFromStorage(event.value);
-      const decryptedValue = await this.convertToDecrypted(event.value as Record<string, string>);
-
-      // Re-emit the delete event with the original payload.
       this.emit('delete', { value: decryptedValue });
     });
     
@@ -70,53 +82,83 @@ export class EncryptedStorage<
   }
 
   async insertMany(documents: Array<T>): Promise<void> {
-    // Encrypt all documents in parallel.
+    const converted = await Promise.all(
-    const encrypted = await Promise.all(
+      documents.map((doc) => this.convertForStorage(doc)),
-      documents.map((doc) => this.convertToEncrypted(doc)),
     );
-    await this.storage.insertMany(encrypted);
+    await this.storage.insertMany(converted);
   }
 
-  async find(filter?: Partial<T>, options?: FindOptions): Promise<T[]> {
+  async find(filter?: Filter<T>, options?: FindOptions): Promise<T[]> {
-    const encryptedFilter = filter ? await this.convertToEncrypted(filter) : undefined;
+    const convertedFilter = filter
-    const documents = await this.storage.find(encryptedFilter, options);
+      ? await this.convertFilterForStorage(filter)
+      : undefined;
+    const documents = await this.storage.find(convertedFilter, options);
     return Promise.all(
-      documents.map(async (document) => this.convertToDecrypted(document)),
+      documents.map((doc) => this.convertFromStorage(doc)),
     );
   }
 
   async updateMany(
-    filter: Partial<T>,
+    filter: Filter<T>,
     update: Partial<T>,
     options: Partial<FindOptions> = {},
   ): Promise<number> {
-    const encryptedFilter = await this.convertToEncrypted(filter);
+    const convertedFilter = await this.convertFilterForStorage(filter);
-    const encryptedUpdate = await this.convertToEncrypted(update);
+    const convertedUpdate = await this.convertForStorage(update);
-    return this.storage.updateMany(encryptedFilter, encryptedUpdate, options);
+    return this.storage.updateMany(convertedFilter, convertedUpdate, options);
   }
 
   async deleteMany(
-    filter: Partial<T>,
+    filter: Filter<T>,
     options: Partial<FindOptions> = {},
   ): Promise<number> {
-    const encryptedFilter = await this.convertToEncrypted(filter);
+    const convertedFilter = await this.convertFilterForStorage(filter);
-    return this.storage.deleteMany(encryptedFilter, options);
+    return this.storage.deleteMany(convertedFilter, options);
   }
 
   deriveChild<C>(path: string): BaseStorage<C> {
-    return EncryptedStorage.from(this.storage.deriveChild(path), this.key);
+    return EncryptedStorage.from<C>(
+      this.storage.deriveChild(path),
+      this.key,
+      { plaintextKeys: [...this.plaintextKeys] },
+    );
   }
 
-  private async convertToEncrypted(
+  // ---------------------------------------------------------------------------
+  // Storage conversion — documents (insert/update values)
+  // ---------------------------------------------------------------------------
+
+  /**
+   * Convert a document for storage. Encrypted fields are encrypted;
+   * plaintext fields are passed through with value formatting only.
+   */
+  private async convertForStorage(
     document: Partial<T>,
-  ): Promise<Record<string, string>> {
+  ): Promise<Record<string, any>> {
-    const encrypted: Record<string, string> = {};
+    const result: Record<string, any> = {};
     const formattedDocument = this.formatDocumentForEncryption(document);
     const entries = Object.entries(formattedDocument);
 
-    // Encrypt all fields in parallel, using the cache when possible.
+    // Split into plaintext and encrypted fields.
-    const results = await Promise.all(
+    const plaintextEntries: Array<[string, any]> = [];
-      entries.map(async ([key, value]) => {
+    const encryptedEntries: Array<[string, any]> = [];
+
+    for (const entry of entries) {
+      if (this.plaintextKeys.has(entry[0])) {
+        plaintextEntries.push(entry);
+      } else {
+        encryptedEntries.push(entry);
+      }
+    }
+
+    // Plaintext fields pass through directly.
+    for (const [key, value] of plaintextEntries) {
+      result[key] = value;
+    }
+
+    // Encrypt fields in parallel, with memoization.
+    const encrypted = await Promise.all(
+      encryptedEntries.map(async ([key, value]) => {
         const bin = this.msgpackr.pack(value);
         const cacheKey = Bytes.from(bin).toBase64();
 
@@ -131,21 +173,36 @@ export class EncryptedStorage<
       }),
     );
 
-    for (const [key, ciphertext] of results) {
+    for (const [key, ciphertext] of encrypted) {
-      encrypted[key] = ciphertext;
+      result[key] = ciphertext;
     }
 
-    return encrypted;
+    return result;
   }
 
-  private async convertToDecrypted(
+  /**
-    document: Record<string, string>,
+   * Convert a stored document back to its original form. Encrypted fields
+   * are decrypted; plaintext fields are passed through with value formatting.
+   */
+  private async convertFromStorage(
+    document: Record<string, any>,
   ): Promise<T> {
     const entries = Object.entries(document);
 
-    // Decrypt all fields in parallel, using the cache when possible.
+    const plaintextEntries: Array<[string, any]> = [];
-    const results = await Promise.all(
+    const encryptedEntries: Array<[string, any]> = [];
-      entries.map(async ([key, ciphertext]) => {
+
+    for (const entry of entries) {
+      if (this.plaintextKeys.has(entry[0])) {
+        plaintextEntries.push(entry);
+      } else {
+        encryptedEntries.push(entry);
+      }
+    }
+
+    // Decrypt encrypted fields in parallel, with memoization.
+    const decrypted = await Promise.all(
+      encryptedEntries.map(async ([key, ciphertext]) => {
         let value = this.decryptCache.get(ciphertext);
         if (value === undefined) {
           const bin = await this.key.decrypt(Bytes.fromBase64(ciphertext));
@@ -156,70 +213,122 @@ export class EncryptedStorage<
       }),
     );
 
-    const decrypted: Record<string, any> = {};
+    const result: Record<string, any> = {};
-    for (const [key, value] of results) {
+
-      decrypted[key] = value;
+    for (const [key, value] of plaintextEntries) {
+      result[key] = value;
+    }
+    for (const [key, value] of decrypted) {
+      result[key] = value;
     }
 
-    const decodedDocument = this.formatDocumentFromDecryption(decrypted);
+    const decodedDocument = this.formatDocumentFromDecryption(result);
     return decodedDocument as T;
   }
 
-  private formatDocumentForEncryption(document: any): any {
+  // ---------------------------------------------------------------------------
-    // First, iterate through each key and value in the document and format the value for encryption.
+  // Storage conversion — filters (may contain operator objects)
-    const formattedDocument: any = {};
+  // ---------------------------------------------------------------------------
 
+  /**
+   * Convert a query filter for storage. Handles both plain equality values
+   * and operator objects.
+   *
+   * - Plaintext fields: values and operator objects pass through as-is.
+   * - Encrypted fields: plain values are encrypted. Operator objects throw
+   *   because range comparisons are meaningless on ciphertext.
+   */
+  private async convertFilterForStorage(
+    filter: Filter<T>,
+  ): Promise<Filter<Record<string, any>>> {
+    const result: Record<string, any> = {};
+    const entries = Object.entries(filter);
+
+    const encryptionTasks: Array<Promise<readonly [string, any]>> = [];
+
+    for (const [key, value] of entries) {
+      if (this.plaintextKeys.has(key)) {
+        // Plaintext field — pass through (including operator objects).
+        result[key] = isOperatorObject(value)
+          ? value
+          : this.formatValueForEncryption(value);
+      } else if (isOperatorObject(value)) {
+        // Encrypted field with an operator — not supported.
+        throw new Error(
+          `Range operators ($lt, $gt, etc.) cannot be used on encrypted field '${key}'. ` +
+          `Add '${key}' to plaintextKeys if you need range queries on this field.`,
+        );
+      } else {
+        // Encrypted field with a plain equality value — encrypt it.
+        const formatted = this.formatValueForEncryption(value);
+        encryptionTasks.push(
+          (async () => {
+            const bin = this.msgpackr.pack(formatted);
+            const cacheKey = Bytes.from(bin).toBase64();
+
+            let ciphertext = this.encryptCache.get(cacheKey);
+            if (ciphertext === undefined) {
+              const encryptedValue = await this.key.encrypt(bin, true);
+              ciphertext = encryptedValue.toBase64();
+              this.encryptCache.set(cacheKey, ciphertext);
+            }
+
+            return [key, ciphertext] as const;
+          })(),
+        );
+      }
+    }
+
+    const encryptedResults = await Promise.all(encryptionTasks);
+    for (const [key, ciphertext] of encryptedResults) {
+      result[key] = ciphertext;
+    }
+
+    return result;
+  }
+
+  // ---------------------------------------------------------------------------
+  // Value formatting
+  // ---------------------------------------------------------------------------
+
+  private formatDocumentForEncryption(document: any): any {
+    const formattedDocument: any = {};
     for (const [key, value] of Object.entries(document)) {
       formattedDocument[key] = this.formatValueForEncryption(value);
     }
-
+    return encodeExtendedJsonObject(formattedDocument);
-    // Then, encode the document to extended JSON.
-    const encodedDocument = encodeExtendedJsonObject(formattedDocument);
-
-    return encodedDocument;
   }
 
   private formatDocumentFromDecryption(document: any): any {
-    // First, decode the document from extended JSON.
     const decodedDocument = decodeExtendedJsonObject(document);
-
-    // Then, iterate through each key and value in the document and format the value from decryption.
     for (const [key, value] of Object.entries(decodedDocument)) {
       decodedDocument[key] = this.formatValueFromDecryption(value);
     }
-
     return decodedDocument;
   }
 
+  /**
+   * Format a value before encryption. Converts types that msgpackr
+   * doesn't natively support (e.g. Date) into serialisable forms.
+   */
   private formatValueForEncryption(value: any): any {
-    // msgpackr doesnt support Date, so we need to convert it to a string.
     if (value instanceof Date) {
       return `<Date: ${value.getTime()}>`;
     }
-
     return value;
   }
 
+  /**
+   * Restore a value after decryption. Reverses the transformations
+   * applied by `formatValueForEncryption`.
+   */
   private formatValueFromDecryption(value: any): any {
-    // msgpackr doesnt support Date, so we need to convert it to a Date.
     if (typeof value === 'string') {
-      // Check if this value matches an Extended JSON encoded date.
-      // TODO: Do this without a regex for performance reasons.
-      // const dateMatch = value.match(/<Date: (?<time>[0-9]+)>/);
-
-      // Without regex
       if (value.startsWith('<Date: ') && value.endsWith('>')) {
         const time = value.slice(7, -1);
         return new Date(parseInt(time));
       }
-
-      // If it does, convert it to a Date.
-      // if (dateMatch) {
-      //   const { time } = dateMatch.groups!;
-      //   return new Date(parseInt(time));
-      // }
     }
-
     return value;
   }
 }

src/storage/storage-localstorage.ts

@@ -1,4 +1,12 @@
-import { BaseStorage, FindOptions, type IndexDefinition } from './base-storage.js';
+import {
+  BaseStorage,
+  FindOptions,
+  type IndexDefinition,
+  type Filter,
+  type ComparisonOperators,
+  isOperatorObject,
+} from './base-storage.js';
+import { BPlusTree, type BPlusTreeEntry } from 'src/utils/btree.js';
 
 /**
  * Key prefix separator used to namespace documents within localStorage.
@@ -18,7 +26,7 @@ const MANIFEST_SUFFIX = '__keys__';
 const COUNTER_SUFFIX = '__next__';
 
 /**
- * Separator used when joining multiple field values into a single index key.
+ * Separator used when joining field names to create the index map key.
  */
 const INDEX_KEY_SEP = '\x00';
 
@@ -34,6 +42,18 @@ function normalizeIndexes(indexes?: IndexDefinition): string[][] {
   return indexes as string[][];
 }
 
+/**
+ * Comparator for compound index keys (arrays of raw values).
+ */
+function tupleCompare(a: any[], b: any[]): number {
+  const len = Math.min(a.length, b.length);
+  for (let i = 0; i < len; i++) {
+    if (a[i] < b[i]) return -1;
+    if (a[i] > b[i]) return 1;
+  }
+  return a.length - b.length;
+}
+
 /**
  * Implementation of BaseStorage using the browser's localStorage API.
  *
@@ -43,9 +63,9 @@ function normalizeIndexes(indexes?: IndexDefinition): string[][] {
  * tracks all internal keys so that read operations avoid scanning every
  * key in localStorage.
  *
- * Optional indexes provide fast lookups when a query filter matches
+ * Optional indexes are backed by B+ Trees, providing O(log n) equality
- * an index exactly. Indexes are held in memory and rebuilt only when a
+ * lookups and O(log n + k) range queries. Indexes are held in memory and
- * cross-tab manifest change is detected.
+ * rebuilt only when a cross-tab manifest change is detected.
  *
  * Because localStorage is synchronous and string-only, all values are
  * JSON-serialised on write and parsed on read.
@@ -84,12 +104,11 @@ export class StorageLocalStorage<
   private indexDefs: string[][];
 
   /**
-   * Secondary index maps (same structure as StorageMemory).
+   * Secondary indexes backed by B+ Trees.
-   * Outer key  = index name (joined field names).
+   * Map key = index name (joined field names).
-   * Inner key  = index value (joined field values from a document).
+   * Map value = B+ Tree mapping index keys to sets of internal document keys.
-   * Inner value = set of internal numeric keys.
    */
-  private indexes: Map<string, Map<string, Set<number>>>;
+  private indexes: Map<string, BPlusTree<any, number>>;
 
   /** Lazily-created child storage instances. */
   private children: Map<string, StorageLocalStorage<any>>;
@@ -104,7 +123,9 @@ export class StorageLocalStorage<
     this.indexDefs = normalizeIndexes(indexes);
     this.indexes = new Map();
     for (const fields of this.indexDefs) {
-      this.indexes.set(fields.join(INDEX_KEY_SEP), new Map());
+      const name = fields.join(INDEX_KEY_SEP);
+      const comparator = fields.length > 1 ? tupleCompare : undefined;
+      this.indexes.set(name, new BPlusTree<any, number>(32, comparator));
     }
 
     // Bootstrap from localStorage.
@@ -132,23 +153,25 @@ export class StorageLocalStorage<
     this.persistManifest();
   }
 
-  async find(filter?: Partial<T>, options?: FindOptions): Promise<T[]> {
+  async find(filter?: Filter<T>, options?: FindOptions): Promise<T[]> {
     this.refreshManifest();
 
     let results: T[];
-    const indexedKeys = this.resolveIndexKeys(filter);
+    const resolution = this.resolveIndexKeys(filter);
+
+    if (resolution !== null) {
+      const { keys, resolvedFields } = resolution;
+      const filterKeys = filter ? Object.keys(filter) : [];
+      const needsVerification = filterKeys.some((k) => !resolvedFields.includes(k));
 
-    if (indexedKeys !== null) {
-      // Use the index to narrow which documents we read from localStorage.
       results = [];
-      for (const key of indexedKeys) {
+      for (const key of keys) {
         const raw = localStorage.getItem(this.docKey(key));
         if (raw === null) continue;
         const doc = JSON.parse(raw) as T;
-        if (this.matchesFilter(doc, filter)) {
+        if (needsVerification && !this.matchesFilter(doc, filter)) continue;
         results.push(doc);
       }
-      }
     } else {
       // Full scan over all documents in the manifest.
       results = [];
@@ -175,7 +198,7 @@ export class StorageLocalStorage<
   }
 
   async updateMany(
-    filter: Partial<T>,
+    filter: Filter<T>,
     update: Partial<T>,
     options: Partial<FindOptions> = {},
   ): Promise<number> {
@@ -207,7 +230,7 @@ export class StorageLocalStorage<
   }
 
   async deleteMany(
-    filter: Partial<T>,
+    filter: Filter<T>,
     options: Partial<FindOptions> = {},
   ): Promise<number> {
     this.refreshManifest();
@@ -251,12 +274,30 @@ export class StorageLocalStorage<
 
   /**
    * Checks whether a document satisfies every field in the filter.
+   * Supports both plain equality values and comparison operator objects.
    */
-  private matchesFilter(item: T, filter?: Partial<T>): boolean {
+  private matchesFilter(item: T, filter?: Filter<T>): boolean {
     if (!filter || Object.keys(filter).length === 0) return true;
     for (const [key, value] of Object.entries(filter)) {
+      if (isOperatorObject(value)) {
+        if (!this.matchesOperators(item[key], value)) return false;
+      } else {
         if (item[key] !== value) return false;
       }
+    }
+    return true;
+  }
+
+  /**
+   * Evaluate a set of comparison operators against a single field value.
+   */
+  private matchesOperators(fieldValue: any, ops: ComparisonOperators<any>): boolean {
+    if (ops.$eq !== undefined && fieldValue !== ops.$eq) return false;
+    if (ops.$ne !== undefined && fieldValue === ops.$ne) return false;
+    if (ops.$lt !== undefined && !(fieldValue < ops.$lt)) return false;
+    if (ops.$lte !== undefined && !(fieldValue <= ops.$lte)) return false;
+    if (ops.$gt !== undefined && !(fieldValue > ops.$gt)) return false;
+    if (ops.$gte !== undefined && !(fieldValue >= ops.$gte)) return false;
     return true;
   }
 
@@ -264,12 +305,24 @@ export class StorageLocalStorage<
    * Collect all [internalKey, document] pairs that match a filter.
    * Uses an index when possible, otherwise falls back to a full scan.
    */
-  private collectMatches(filter?: Partial<T>): Array<[number, T]> {
+  private collectMatches(filter?: Filter<T>): Array<[number, T]> {
-    const indexKeys = this.resolveIndexKeys(filter);
+    const resolution = this.resolveIndexKeys(filter);
-    const keysToScan = indexKeys ?? this.manifest;
     const results: Array<[number, T]> = [];
 
-    for (const key of keysToScan) {
+    if (resolution !== null) {
+      const { keys, resolvedFields } = resolution;
+      const filterKeys = filter ? Object.keys(filter) : [];
+      const needsVerification = filterKeys.some((k) => !resolvedFields.includes(k));
+
+      for (const key of keys) {
+        const raw = localStorage.getItem(this.docKey(key));
+        if (raw === null) continue;
+        const doc = JSON.parse(raw) as T;
+        if (needsVerification && !this.matchesFilter(doc, filter)) continue;
+        results.push([key, doc]);
+      }
+    } else {
+      for (const key of this.manifest) {
         const raw = localStorage.getItem(this.docKey(key));
         if (raw === null) continue;
         const doc = JSON.parse(raw) as T;
@@ -277,6 +330,7 @@ export class StorageLocalStorage<
           results.push([key, doc]);
         }
       }
+    }
 
     return results;
   }
@@ -300,82 +354,149 @@ export class StorageLocalStorage<
   // ---------------------------------------------------------------------------
 
   /**
-   * Build the index value string for a given document and set of fields.
+   * Build the B+ Tree key for a document and a set of index fields.
-   * Returns `null` if any field is missing from the document.
+   * - Single-field indexes return the raw field value.
+   * - Compound indexes return an array of raw field values.
+   * Returns `null` if any required field is missing from the document.
    */
-  private buildIndexValue(doc: Record<string, any>, fields: string[]): string | null {
+  private buildIndexKey(doc: Record<string, any>, fields: string[]): any | null {
-    const parts: string[] = [];
+    if (fields.length === 1) {
+      if (!(fields[0] in doc)) return null;
+      return doc[fields[0]];
+    }
+
+    const parts: any[] = [];
     for (const field of fields) {
       if (!(field in doc)) return null;
-      parts.push(String(doc[field]));
+      parts.push(doc[field]);
     }
-    return parts.join(INDEX_KEY_SEP);
+    return parts;
   }
 
   /** Register a document in all applicable indexes. */
   private addToIndexes(internalKey: number, doc: T): void {
     for (const fields of this.indexDefs) {
-      const indexName = fields.join(INDEX_KEY_SEP);
+      const indexKey = this.buildIndexKey(doc, fields);
-      const indexValue = this.buildIndexValue(doc, fields);
+      if (indexKey === null) continue;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      const name = fields.join(INDEX_KEY_SEP);
-      let bucket = indexMap.get(indexValue);
+      this.indexes.get(name)!.insert(indexKey, internalKey);
-      if (!bucket) {
-        bucket = new Set();
-        indexMap.set(indexValue, bucket);
-      }
-      bucket.add(internalKey);
     }
   }
 
   /** Remove a document from all applicable indexes. */
   private removeFromIndexes(internalKey: number, doc: T): void {
     for (const fields of this.indexDefs) {
-      const indexName = fields.join(INDEX_KEY_SEP);
+      const indexKey = this.buildIndexKey(doc, fields);
-      const indexValue = this.buildIndexValue(doc, fields);
+      if (indexKey === null) continue;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      const name = fields.join(INDEX_KEY_SEP);
-      const bucket = indexMap.get(indexValue);
+      this.indexes.get(name)!.delete(indexKey, internalKey);
-      if (bucket) {
-        bucket.delete(internalKey);
-        if (bucket.size === 0) indexMap.delete(indexValue);
-      }
     }
   }
 
   /**
    * Attempt to resolve candidate internal keys from the indexes.
    * Returns `null` if no index can serve the query.
+   *
+   * Supports three resolution strategies:
+   * 1. Equality lookup via B+ Tree `.get()` — O(log n)
+   * 2. Range scan via B+ Tree `.range()` — O(log n + k)
+   * 3. Compound equality — B+ Tree `.get()` with a tuple key
    */
-  private resolveIndexKeys(filter?: Partial<T>): Set<number> | null {
+  private resolveIndexKeys(
+    filter?: Filter<T>,
+  ): { keys: Iterable<number>; resolvedFields: string[] } | null {
     if (!filter) return null;
     const filterKeys = Object.keys(filter);
     if (filterKeys.length === 0) return null;
 
     for (const fields of this.indexDefs) {
-      if (!fields.every((f) => f in filter)) continue;
-
       const indexName = fields.join(INDEX_KEY_SEP);
-      const indexValue = this.buildIndexValue(filter, fields);
+      const btree = this.indexes.get(indexName)!;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      if (fields.length === 1) {
-      const bucket = indexMap.get(indexValue);
+        // --- Single-field index ---
-      return bucket ?? new Set();
+        const field = fields[0];
+        if (!(field in filter)) continue;
+
+        const filterValue = (filter as any)[field];
+
+        if (isOperatorObject(filterValue)) {
+          const keys = this.resolveOperatorViaTree(btree, filterValue);
+          if (keys !== null) return { keys, resolvedFields: [field] };
+          continue;
+        }
+
+        // Plain equality.
+        return { keys: btree.get(filterValue) ?? [], resolvedFields: [field] };
+      } else {
+        // --- Compound index — all fields must be plain equality ---
+        if (!fields.every((f) => f in filter && !isOperatorObject((filter as any)[f]))) {
+          continue;
+        }
+
+        const tupleKey = fields.map((f) => (filter as any)[f]);
+        return { keys: btree.get(tupleKey) ?? [], resolvedFields: [...fields] };
+      }
     }
 
     return null;
   }
 
   /**
-   * Rebuild all in-memory index maps by reading every document from
+   * Try to resolve an operator filter against a single-field B+ Tree index.
+   * Returns a flat array of matching internal keys, or null if the
+   * operators can't be served by the tree ($ne).
+   */
+  private resolveOperatorViaTree(
+    btree: BPlusTree<any, number>,
+    ops: ComparisonOperators<any>,
+  ): Iterable<number> | null {
+    if (ops.$ne !== undefined) return null;
+
+    if (ops.$eq !== undefined) {
+      return btree.get(ops.$eq) ?? [];
+    }
+
+    let min: any = undefined;
+    let max: any = undefined;
+    let lowerInclusive = true;
+    let upperInclusive = false;
+
+    if (ops.$gt !== undefined) { min = ops.$gt; lowerInclusive = false; }
+    if (ops.$gte !== undefined) { min = ops.$gte; lowerInclusive = true; }
+    if (ops.$lt !== undefined) { max = ops.$lt; upperInclusive = false; }
+    if (ops.$lte !== undefined) { max = ops.$lte; upperInclusive = true; }
+
+    if (min === undefined && max === undefined) return null;
+
+    const entries = btree.range(min, max, { lowerInclusive, upperInclusive });
+    return this.flattenEntryKeys(entries);
+  }
+
+  /**
+   * Flatten B+ Tree range results into a flat array of internal keys.
+   * Uses an array instead of a Set — no hash overhead, no deduplication
+   * needed because each internal key only appears under one index key.
+   */
+  private flattenEntryKeys(entries: BPlusTreeEntry<any, number>[]): number[] {
+    const result: number[] = [];
+    for (const entry of entries) {
+      for (const key of entry.values) {
+        result.push(key);
+      }
+    }
+    return result;
+  }
+
+  /**
+   * Rebuild all in-memory index B+ Trees by reading every document from
    * localStorage. Called only when a cross-tab manifest change is detected.
    */
   private rebuildIndexes(): void {
-    for (const [, indexMap] of this.indexes) {
+    for (const [, btree] of this.indexes) {
-      indexMap.clear();
+      btree.clear();
     }
 
     for (const key of this.manifest) {

src/storage/storage-memory-synced.ts

@@ -1,4 +1,4 @@
-import { BaseStorage, FindOptions } from './base-storage.js';
+import { BaseStorage, FindOptions, type Filter } from './base-storage.js';
 import { StorageMemory } from './storage-memory.js';
 
 /**
@@ -65,19 +65,19 @@ export class StorageMemorySynced<T extends Record<string, any> = Record<string,
     await this.store.insertMany(documents);
   }
 
-  async find(filter?: Partial<T>, options?: FindOptions): Promise<T[]> {
+  async find(filter?: Filter<T>, options?: FindOptions): Promise<T[]> {
     return await this.inMemoryCache.find(filter, options);
   }
 
   async updateMany(
-    filter: Partial<T>,
+    filter: Filter<T>,
     update: Partial<T>,
     options: FindOptions = {} as FindOptions
   ): Promise<number> {
     return await this.store.updateMany(filter, update, options);
   }
 
-  async deleteMany(filter: Partial<T>, options: FindOptions = {} as FindOptions): Promise<number> {
+  async deleteMany(filter: Filter<T>, options: FindOptions = {} as FindOptions): Promise<number> {
     return await this.store.deleteMany(filter, options);
   }
 

src/storage/storage-memory.ts

@@ -1,8 +1,15 @@
-import { BaseStorage, FindOptions, type IndexDefinition } from './base-storage.js';
+import {
+  BaseStorage,
+  FindOptions,
+  type IndexDefinition,
+  type Filter,
+  type ComparisonOperators,
+  isOperatorObject,
+} from './base-storage.js';
+import { BPlusTree, type BPlusTreeEntry } from 'src/utils/btree.js';
 
 /**
- * Separator used when joining multiple field values into a single index key.
+ * Separator used when joining field names to create the index map key.
- * Chosen to be unlikely to appear in real field values.
  */
 const INDEX_KEY_SEP = '\x00';
 
@@ -22,13 +29,26 @@ function normalizeIndexes(indexes?: IndexDefinition): string[][] {
   return indexes as string[][];
 }
 
+/**
+ * Comparator for compound index keys (arrays of raw values).
+ * Compares element-by-element using native `<` / `>` operators.
+ */
+function tupleCompare(a: any[], b: any[]): number {
+  const len = Math.min(a.length, b.length);
+  for (let i = 0; i < len; i++) {
+    if (a[i] < b[i]) return -1;
+    if (a[i] > b[i]) return 1;
+  }
+  return a.length - b.length;
+}
+
 /**
  * Implementation of BaseStore using Memory as the storage backend.
  *
  * @remarks
  * Documents are keyed internally by an auto-incrementing numeric key.
- * Optional indexes provide O(1) lookups when a query filter matches
+ * Optional indexes are backed by B+ Trees, providing O(log n) equality
- * an index exactly.
+ * lookups and O(log n + k) range queries.
  */
 export class StorageMemory<
   T extends Record<string, any> = Record<string, any>,
@@ -46,12 +66,11 @@ export class StorageMemory<
   private store: Map<number, T>;
 
   /**
-   * Secondary index maps.
+   * Secondary indexes backed by B+ Trees.
-   * Outer key  = index name (joined field names).
+   * Map key = index name (joined field names).
-   * Inner key  = index value (joined field values from a document).
+   * Map value = B+ Tree mapping index keys to sets of internal document keys.
-   * Inner value = set of internal keys that share this index value.
    */
-  private indexes: Map<string, Map<string, Set<number>>>;
+  private indexes: Map<string, BPlusTree<any, number>>;
 
   /** The normalized index definitions supplied at construction time. */
   private indexDefs: string[][];
@@ -66,10 +85,12 @@ export class StorageMemory<
     this.children = new Map();
     this.indexDefs = normalizeIndexes(indexes);
 
-    // Initialise an empty map for each index definition.
+    // Create a B+ Tree for each index definition.
     this.indexes = new Map();
     for (const fields of this.indexDefs) {
-      this.indexes.set(fields.join(INDEX_KEY_SEP), new Map());
+      const name = fields.join(INDEX_KEY_SEP);
+      const comparator = fields.length > 1 ? tupleCompare : undefined;
+      this.indexes.set(name, new BPlusTree<any, number>(32, comparator));
     }
   }
 
@@ -86,7 +107,7 @@ export class StorageMemory<
     }
   }
 
-  async find(filter?: Partial<T>, options?: FindOptions): Promise<T[]> {
+  async find(filter?: Filter<T>, options?: FindOptions): Promise<T[]> {
     let results: T[];
 
     // Attempt to satisfy the query via an index.
@@ -118,7 +139,7 @@ export class StorageMemory<
   }
 
   async updateMany(
-    filter: Partial<T>,
+    filter: Filter<T>,
     update: Partial<T>,
     options: Partial<FindOptions> = {},
   ): Promise<number> {
@@ -147,7 +168,7 @@ export class StorageMemory<
   }
 
   async deleteMany(
-    filter: Partial<T>,
+    filter: Filter<T>,
     options: Partial<FindOptions> = {},
   ): Promise<number> {
     const rowsToDelete = this.collectMatches(filter);
@@ -182,37 +203,56 @@ export class StorageMemory<
 
   /**
    * Checks whether a document satisfies every field in the filter.
-   * An empty or undefined filter matches everything.
+   * Supports both plain equality values and comparison operator objects.
    */
-  private matchesFilter(item: T, filter?: Partial<T>): boolean {
+  private matchesFilter(item: T, filter?: Filter<T>): boolean {
     if (!filter || Object.keys(filter).length === 0) {
       return true;
     }
 
     for (const [key, value] of Object.entries(filter)) {
-      if (item[key] !== value) {
+      if (isOperatorObject(value)) {
-        return false;
+        if (!this.matchesOperators(item[key], value)) return false;
+      } else {
+        if (item[key] !== value) return false;
       }
     }
     return true;
   }
 
+  /**
+   * Evaluate a set of comparison operators against a single field value.
+   * All operators must pass for the field to match.
+   */
+  private matchesOperators(fieldValue: any, ops: ComparisonOperators<any>): boolean {
+    if (ops.$eq !== undefined && fieldValue !== ops.$eq) return false;
+    if (ops.$ne !== undefined && fieldValue === ops.$ne) return false;
+    if (ops.$lt !== undefined && !(fieldValue < ops.$lt)) return false;
+    if (ops.$lte !== undefined && !(fieldValue <= ops.$lte)) return false;
+    if (ops.$gt !== undefined && !(fieldValue > ops.$gt)) return false;
+    if (ops.$gte !== undefined && !(fieldValue >= ops.$gte)) return false;
+    return true;
+  }
+
   /**
    * Collect all [internalKey, document] pairs that match a filter.
    * Uses an index when possible, otherwise falls back to a full scan.
    */
-  private collectMatches(filter?: Partial<T>): Array<[number, T]> {
+  private collectMatches(filter?: Filter<T>): Array<[number, T]> {
-    const indexKeys = this.resolveIndexKeys(filter);
+    const resolution = this.resolveIndexKeys(filter);
+
+    if (resolution !== null) {
+      const { keys, resolvedFields } = resolution;
+      const filterKeys = filter ? Object.keys(filter) : [];
+      const needsVerification = filterKeys.some((k) => !resolvedFields.includes(k));
 
-    if (indexKeys !== null) {
-      // We have candidate internal keys from the index — fetch and verify.
       const results: Array<[number, T]> = [];
-      for (const key of indexKeys) {
+      for (const key of keys) {
         const doc = this.store.get(key);
-        if (doc && this.matchesFilter(doc, filter)) {
+        if (!doc) continue;
+        if (needsVerification && !this.matchesFilter(doc, filter)) continue;
         results.push([key, doc]);
       }
-      }
       return results;
     }
 
@@ -246,97 +286,166 @@ export class StorageMemory<
   // ---------------------------------------------------------------------------
 
   /**
-   * Build the index value string for a given document and set of fields.
+   * Build the B+ Tree key for a document and a set of index fields.
-   * Returns `null` if any of the fields are missing from the document,
+   * - Single-field indexes return the raw field value.
-   * since we can't meaningfully index a partial key.
+   * - Compound indexes return an array of raw field values.
+   * Returns `null` if any required field is missing from the document.
    */
-  private buildIndexValue(doc: Record<string, any>, fields: string[]): string | null {
+  private buildIndexKey(doc: Record<string, any>, fields: string[]): any | null {
-    const parts: string[] = [];
+    if (fields.length === 1) {
+      if (!(fields[0] in doc)) return null;
+      return doc[fields[0]];
+    }
+
+    const parts: any[] = [];
     for (const field of fields) {
       if (!(field in doc)) return null;
-      parts.push(String(doc[field]));
+      parts.push(doc[field]);
     }
-    return parts.join(INDEX_KEY_SEP);
+    return parts;
   }
 
   /** Register a document in all applicable indexes. */
   private addToIndexes(internalKey: number, doc: T): void {
     for (const fields of this.indexDefs) {
-      const indexName = fields.join(INDEX_KEY_SEP);
+      const indexKey = this.buildIndexKey(doc, fields);
-      const indexValue = this.buildIndexValue(doc, fields);
+      if (indexKey === null) continue;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      const name = fields.join(INDEX_KEY_SEP);
-      let bucket = indexMap.get(indexValue);
+      this.indexes.get(name)!.insert(indexKey, internalKey);
-      if (!bucket) {
-        bucket = new Set();
-        indexMap.set(indexValue, bucket);
-      }
-      bucket.add(internalKey);
     }
   }
 
   /** Remove a document from all applicable indexes. */
   private removeFromIndexes(internalKey: number, doc: T): void {
     for (const fields of this.indexDefs) {
-      const indexName = fields.join(INDEX_KEY_SEP);
+      const indexKey = this.buildIndexKey(doc, fields);
-      const indexValue = this.buildIndexValue(doc, fields);
+      if (indexKey === null) continue;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      const name = fields.join(INDEX_KEY_SEP);
-      const bucket = indexMap.get(indexValue);
+      this.indexes.get(name)!.delete(indexKey, internalKey);
-      if (bucket) {
-        bucket.delete(internalKey);
-        if (bucket.size === 0) indexMap.delete(indexValue);
-      }
     }
   }
 
   /**
-   * Attempt to resolve a set of candidate internal keys from the indexes.
+   * Result of an index resolution attempt.
-   * Returns `null` if no index can serve the query.
+   * `keys` is an iterable of candidate internal keys.
-   *
+   * `resolvedFields` lists the filter fields fully satisfied by the index,
-   * An index is used when the filter fields are a superset of (or equal to)
+   * so callers can skip re-verifying those conditions in matchesFilter.
-   * an index's fields — meaning the index value can be fully constructed
-   * from the filter.
    */
-  private resolveIndexKeys(filter?: Partial<T>): Set<number> | null {
+  private resolveIndexKeys(
+    filter?: Filter<T>,
+  ): { keys: Iterable<number>; resolvedFields: string[] } | null {
     if (!filter) return null;
     const filterKeys = Object.keys(filter);
     if (filterKeys.length === 0) return null;
 
     for (const fields of this.indexDefs) {
-      // Every field in the index must be present in the filter.
-      if (!fields.every((f) => f in filter)) continue;
-
       const indexName = fields.join(INDEX_KEY_SEP);
-      const indexValue = this.buildIndexValue(filter, fields);
+      const btree = this.indexes.get(indexName)!;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      if (fields.length === 1) {
-      const bucket = indexMap.get(indexValue);
+        // --- Single-field index ---
-      return bucket ?? new Set();
+        const field = fields[0];
+        if (!(field in filter)) continue;
+
+        const filterValue = (filter as any)[field];
+
+        if (isOperatorObject(filterValue)) {
+          const keys = this.resolveOperatorViaTree(btree, filterValue);
+          if (keys !== null) return { keys, resolvedFields: [field] };
+          continue;
+        }
+
+        // Plain equality.
+        return { keys: btree.get(filterValue) ?? [], resolvedFields: [field] };
+      } else {
+        // --- Compound index — all fields must be plain equality ---
+        if (!fields.every((f) => f in filter && !isOperatorObject((filter as any)[f]))) {
+          continue;
+        }
+
+        const tupleKey = fields.map((f) => (filter as any)[f]);
+        return { keys: btree.get(tupleKey) ?? [], resolvedFields: [...fields] };
+      }
     }
 
     return null;
   }
 
+  /**
+   * Try to resolve an operator filter against a single-field B+ Tree index.
+   * Returns a flat array of matching internal keys, or null if the
+   * operators can't be served by the tree ($ne).
+   */
+  private resolveOperatorViaTree(
+    btree: BPlusTree<any, number>,
+    ops: ComparisonOperators<any>,
+  ): Iterable<number> | null {
+    // $ne prevents efficient index use.
+    if (ops.$ne !== undefined) return null;
+
+    // $eq is a point lookup.
+    if (ops.$eq !== undefined) {
+      return btree.get(ops.$eq) ?? [];
+    }
+
+    // Extract range bounds from the remaining operators.
+    let min: any = undefined;
+    let max: any = undefined;
+    let lowerInclusive = true;
+    let upperInclusive = false;
+
+    if (ops.$gt !== undefined) { min = ops.$gt; lowerInclusive = false; }
+    if (ops.$gte !== undefined) { min = ops.$gte; lowerInclusive = true; }
+    if (ops.$lt !== undefined) { max = ops.$lt; upperInclusive = false; }
+    if (ops.$lte !== undefined) { max = ops.$lte; upperInclusive = true; }
+
+    if (min === undefined && max === undefined) return null;
+
+    const entries = btree.range(min, max, { lowerInclusive, upperInclusive });
+    return this.flattenEntryKeys(entries);
+  }
+
+  /**
+   * Flatten B+ Tree range results into a flat array of internal keys.
+   * Uses an array instead of a Set — no hash overhead, no deduplication
+   * needed because each internal key only appears under one index key.
+   */
+  private flattenEntryKeys(entries: BPlusTreeEntry<any, number>[]): number[] {
+    const result: number[] = [];
+    for (const entry of entries) {
+      for (const key of entry.values) {
+        result.push(key);
+      }
+    }
+    return result;
+  }
+
   /**
    * Try to answer a `find` query entirely through an index.
    * Returns `null` when no index can serve the filter, signalling
    * the caller to fall back to a full scan.
+   *
+   * When the index covers every field in the filter, matchesFilter
+   * is skipped entirely — the B+ Tree has already ensured the
+   * conditions are met.
    */
-  private findViaIndex(filter?: Partial<T>): T[] | null {
+  private findViaIndex(filter?: Filter<T>): T[] | null {
-    const keys = this.resolveIndexKeys(filter);
+    const resolution = this.resolveIndexKeys(filter);
-    if (keys === null) return null;
+    if (resolution === null) return null;
+
+    const { keys, resolvedFields } = resolution;
+    const filterKeys = filter ? Object.keys(filter) : [];
+    const needsVerification = filterKeys.some((k) => !resolvedFields.includes(k));
 
     const results: T[] = [];
     for (const key of keys) {
       const doc = this.store.get(key);
-      if (doc && this.matchesFilter(doc, filter)) {
+      if (!doc) continue;
+      if (needsVerification && !this.matchesFilter(doc, filter)) continue;
       results.push(doc);
     }
-    }
     return results;
   }
 }

src/utils/btree.test.ts

@@ -0,0 +1,391 @@
+import { describe, it, expect, beforeEach } from 'vitest';
+import { BPlusTree } from './btree.js';
+
+describe('BPlusTree', () => {
+  let tree: BPlusTree<number, string>;
+
+  beforeEach(() => {
+    tree = new BPlusTree<number, string>();
+  });
+
+  // -------------------------------------------------------------------------
+  // Construction
+  // -------------------------------------------------------------------------
+
+  describe('constructor', () => {
+    it('should create an empty tree', () => {
+      expect(tree.size).toBe(0);
+    });
+
+    it('should reject order < 3', () => {
+      expect(() => new BPlusTree(2)).toThrow('order must be at least 3');
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Insert & Get
+  // -------------------------------------------------------------------------
+
+  describe('insert and get', () => {
+    it('should insert and retrieve a single entry', () => {
+      tree.insert(10, 'a');
+      expect(tree.get(10)).toEqual(new Set(['a']));
+      expect(tree.size).toBe(1);
+    });
+
+    it('should handle multiple distinct keys', () => {
+      tree.insert(10, 'a');
+      tree.insert(20, 'b');
+      tree.insert(5, 'c');
+      expect(tree.get(10)).toEqual(new Set(['a']));
+      expect(tree.get(20)).toEqual(new Set(['b']));
+      expect(tree.get(5)).toEqual(new Set(['c']));
+      expect(tree.size).toBe(3);
+    });
+
+    it('should return undefined for missing keys', () => {
+      tree.insert(10, 'a');
+      expect(tree.get(99)).toBeUndefined();
+    });
+
+    it('should accumulate duplicate keys into a Set', () => {
+      tree.insert(10, 'a');
+      tree.insert(10, 'b');
+      tree.insert(10, 'c');
+      expect(tree.get(10)).toEqual(new Set(['a', 'b', 'c']));
+      expect(tree.size).toBe(3);
+    });
+
+    it('should not double-count duplicate values for the same key', () => {
+      tree.insert(10, 'a');
+      tree.insert(10, 'a');
+      expect(tree.get(10)).toEqual(new Set(['a']));
+      expect(tree.size).toBe(1);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Delete
+  // -------------------------------------------------------------------------
+
+  describe('delete', () => {
+    it('should delete a specific value from a key', () => {
+      tree.insert(10, 'a');
+      tree.insert(10, 'b');
+      expect(tree.delete(10, 'a')).toBe(true);
+      expect(tree.get(10)).toEqual(new Set(['b']));
+      expect(tree.size).toBe(1);
+    });
+
+    it('should remove the key entry when its last value is deleted', () => {
+      tree.insert(10, 'a');
+      expect(tree.delete(10, 'a')).toBe(true);
+      expect(tree.get(10)).toBeUndefined();
+      expect(tree.size).toBe(0);
+    });
+
+    it('should delete all values for a key when value is omitted', () => {
+      tree.insert(10, 'a');
+      tree.insert(10, 'b');
+      expect(tree.delete(10)).toBe(true);
+      expect(tree.get(10)).toBeUndefined();
+      expect(tree.size).toBe(0);
+    });
+
+    it('should return false for non-existent key', () => {
+      expect(tree.delete(99)).toBe(false);
+    });
+
+    it('should return false for non-existent value', () => {
+      tree.insert(10, 'a');
+      expect(tree.delete(10, 'z')).toBe(false);
+      expect(tree.size).toBe(1);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Range queries
+  // -------------------------------------------------------------------------
+
+  describe('range', () => {
+    beforeEach(() => {
+      for (let i = 0; i < 100; i++) {
+        tree.insert(i, `v${i}`);
+      }
+    });
+
+    it('should return all entries when no bounds given', () => {
+      const result = tree.range();
+      expect(result.length).toBe(100);
+      expect(result[0].key).toBe(0);
+      expect(result[99].key).toBe(99);
+    });
+
+    it('should return entries in key order', () => {
+      const keys = tree.range().map((e) => e.key);
+      for (let i = 1; i < keys.length; i++) {
+        expect(keys[i]).toBeGreaterThan(keys[i - 1]);
+      }
+    });
+
+    it('should respect lower bound (inclusive by default)', () => {
+      const result = tree.range(50);
+      expect(result.length).toBe(50);
+      expect(result[0].key).toBe(50);
+    });
+
+    it('should respect upper bound (exclusive by default)', () => {
+      const result = tree.range(undefined, 10);
+      expect(result.length).toBe(10);
+      expect(result[result.length - 1].key).toBe(9);
+    });
+
+    it('should support inclusive upper bound', () => {
+      const result = tree.range(undefined, 10, { upperInclusive: true });
+      expect(result.length).toBe(11);
+      expect(result[result.length - 1].key).toBe(10);
+    });
+
+    it('should support exclusive lower bound', () => {
+      const result = tree.range(50, undefined, { lowerInclusive: false });
+      expect(result.length).toBe(49);
+      expect(result[0].key).toBe(51);
+    });
+
+    it('should handle combined bounds', () => {
+      const result = tree.range(20, 30);
+      expect(result.length).toBe(10);
+      expect(result[0].key).toBe(20);
+      expect(result[result.length - 1].key).toBe(29);
+    });
+
+    it('should return empty array for no-result range', () => {
+      const result = tree.range(200, 300);
+      expect(result).toEqual([]);
+    });
+
+    it('should return empty for inverted bounds', () => {
+      const result = tree.range(50, 10);
+      expect(result).toEqual([]);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Edge cases
+  // -------------------------------------------------------------------------
+
+  describe('edge cases', () => {
+    it('should handle get on empty tree', () => {
+      expect(tree.get(1)).toBeUndefined();
+    });
+
+    it('should handle range on empty tree', () => {
+      expect(tree.range()).toEqual([]);
+    });
+
+    it('should handle delete on empty tree', () => {
+      expect(tree.delete(1)).toBe(false);
+    });
+
+    it('should handle insert-then-delete-all back to empty', () => {
+      for (let i = 0; i < 50; i++) {
+        tree.insert(i, `v${i}`);
+      }
+      for (let i = 0; i < 50; i++) {
+        expect(tree.delete(i, `v${i}`)).toBe(true);
+      }
+      expect(tree.size).toBe(0);
+      expect(tree.range()).toEqual([]);
+      // Verify we can still insert after emptying.
+      tree.insert(1, 'new');
+      expect(tree.get(1)).toEqual(new Set(['new']));
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Clear
+  // -------------------------------------------------------------------------
+
+  describe('clear', () => {
+    it('should reset the tree to empty', () => {
+      for (let i = 0; i < 100; i++) tree.insert(i, `v${i}`);
+      expect(tree.size).toBe(100);
+      tree.clear();
+      expect(tree.size).toBe(0);
+      expect(tree.get(0)).toBeUndefined();
+      expect(tree.range()).toEqual([]);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Entries iterator
+  // -------------------------------------------------------------------------
+
+  describe('entries', () => {
+    it('should yield all entries in key order', () => {
+      tree.insert(30, 'c');
+      tree.insert(10, 'a');
+      tree.insert(20, 'b');
+
+      const result = [...tree.entries()];
+      expect(result.map((e) => e.key)).toEqual([10, 20, 30]);
+    });
+
+    it('should yield nothing for empty tree', () => {
+      expect([...tree.entries()]).toEqual([]);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Large dataset
+  // -------------------------------------------------------------------------
+
+  describe('large dataset', () => {
+    const N = 10_000;
+
+    it('should correctly store and retrieve N items', () => {
+      for (let i = 0; i < N; i++) {
+        tree.insert(i, `v${i}`);
+      }
+      expect(tree.size).toBe(N);
+
+      // Spot-check some values.
+      expect(tree.get(0)).toEqual(new Set(['v0']));
+      expect(tree.get(N - 1)).toEqual(new Set([`v${N - 1}`]));
+      expect(tree.get(Math.floor(N / 2))).toEqual(new Set([`v${Math.floor(N / 2)}`]));
+    });
+
+    it('should produce correct range results on large dataset', () => {
+      for (let i = 0; i < N; i++) {
+        tree.insert(i, `v${i}`);
+      }
+
+      const result = tree.range(5000, 5010);
+      expect(result.length).toBe(10);
+      expect(result[0].key).toBe(5000);
+      expect(result[9].key).toBe(5009);
+    });
+
+    it('should survive inserting and deleting many items', () => {
+      for (let i = 0; i < N; i++) {
+        tree.insert(i, `v${i}`);
+      }
+
+      // Delete the first half.
+      for (let i = 0; i < N / 2; i++) {
+        expect(tree.delete(i, `v${i}`)).toBe(true);
+      }
+
+      expect(tree.size).toBe(N / 2);
+      expect(tree.get(0)).toBeUndefined();
+      expect(tree.get(N / 2)).toEqual(new Set([`v${N / 2}`]));
+
+      // Remaining range should start at N/2.
+      const remaining = tree.range();
+      expect(remaining.length).toBe(N / 2);
+      expect(remaining[0].key).toBe(N / 2);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Custom comparator
+  // -------------------------------------------------------------------------
+
+  describe('custom comparator', () => {
+    it('should support reverse ordering', () => {
+      const reverseTree = new BPlusTree<number, string>(32, (a, b) => b - a);
+      reverseTree.insert(1, 'a');
+      reverseTree.insert(2, 'b');
+      reverseTree.insert(3, 'c');
+
+      const entries = [...reverseTree.entries()];
+      expect(entries.map((e) => e.key)).toEqual([3, 2, 1]);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Node splitting (small order to force splits)
+  // -------------------------------------------------------------------------
+
+  describe('node splitting with small order', () => {
+    let smallTree: BPlusTree<number, string>;
+
+    beforeEach(() => {
+      smallTree = new BPlusTree<number, string>(4);
+    });
+
+    it('should handle splits correctly', () => {
+      // Order 4 means max 3 keys per node — splits after the 4th insert.
+      for (let i = 0; i < 20; i++) {
+        smallTree.insert(i, `v${i}`);
+      }
+      expect(smallTree.size).toBe(20);
+
+      // All values should be retrievable.
+      for (let i = 0; i < 20; i++) {
+        expect(smallTree.get(i)).toEqual(new Set([`v${i}`]));
+      }
+    });
+
+    it('should maintain sorted order after many splits', () => {
+      // Insert in random order to stress split logic.
+      const values = Array.from({ length: 50 }, (_, i) => i);
+      for (let i = values.length - 1; i > 0; i--) {
+        const j = Math.floor(Math.random() * (i + 1));
+        [values[i], values[j]] = [values[j], values[i]];
+      }
+
+      for (const v of values) {
+        smallTree.insert(v, `v${v}`);
+      }
+
+      const entries = [...smallTree.entries()];
+      const keys = entries.map((e) => e.key);
+      expect(keys).toEqual([...keys].sort((a, b) => a - b));
+    });
+
+    it('should handle delete with merging at small order', () => {
+      for (let i = 0; i < 20; i++) {
+        smallTree.insert(i, `v${i}`);
+      }
+
+      // Delete enough to trigger merges.
+      for (let i = 0; i < 15; i++) {
+        expect(smallTree.delete(i, `v${i}`)).toBe(true);
+      }
+
+      expect(smallTree.size).toBe(5);
+
+      // Remaining keys should be intact.
+      for (let i = 15; i < 20; i++) {
+        expect(smallTree.get(i)).toEqual(new Set([`v${i}`]));
+      }
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // String keys
+  // -------------------------------------------------------------------------
+
+  describe('string keys', () => {
+    it('should work with string keys using default comparator', () => {
+      const strTree = new BPlusTree<string, number>();
+      strTree.insert('banana', 1);
+      strTree.insert('apple', 2);
+      strTree.insert('cherry', 3);
+
+      const entries = [...strTree.entries()];
+      expect(entries.map((e) => e.key)).toEqual(['apple', 'banana', 'cherry']);
+      expect(strTree.get('banana')).toEqual(new Set([1]));
+    });
+
+    it('should support string range queries', () => {
+      const strTree = new BPlusTree<string, number>();
+      const words = ['apple', 'banana', 'cherry', 'date', 'elderberry', 'fig'];
+      words.forEach((w, i) => strTree.insert(w, i));
+
+      const result = strTree.range('banana', 'elderberry');
+      expect(result.map((e) => e.key)).toEqual(['banana', 'cherry', 'date']);
+    });
+  });
+});

src/utils/btree.ts

@@ -0,0 +1,553 @@
+/**
+ * Generic comparator function. Returns negative if a < b, positive if a > b, 0 if equal.
+ */
+export type Comparator<K> = (a: K, b: K) => number;
+
+/**
+ * Options for range queries.
+ */
+export type RangeOptions = {
+  /** Whether the lower bound is inclusive (default: true). */
+  lowerInclusive?: boolean;
+  /** Whether the upper bound is inclusive (default: false). */
+  upperInclusive?: boolean;
+};
+
+/**
+ * A single entry returned by range queries and iteration.
+ */
+export type BPlusTreeEntry<K, V> = {
+  key: K;
+  values: Set<V>;
+};
+
+// ---------------------------------------------------------------------------
+// Node types
+// ---------------------------------------------------------------------------
+
+/**
+ * Internal (non-leaf) node. Stores keys that guide searches and pointers
+ * to child nodes. Does NOT store values — all values live in leaves.
+ */
+class InternalNode<K, V> {
+  keys: K[] = [];
+  children: Array<InternalNode<K, V> | LeafNode<K, V>> = [];
+}
+
+/**
+ * Leaf node. Stores key/value-set pairs and maintains a doubly-linked
+ * list across all leaves for efficient range scans.
+ */
+class LeafNode<K, V> {
+  keys: K[] = [];
+  values: Array<Set<V>> = [];
+  next: LeafNode<K, V> | null = null;
+  prev: LeafNode<K, V> | null = null;
+}
+
+type Node<K, V> = InternalNode<K, V> | LeafNode<K, V>;
+
+function isLeaf<K, V>(node: Node<K, V>): node is LeafNode<K, V> {
+  return node instanceof LeafNode;
+}
+
+// ---------------------------------------------------------------------------
+// Default comparator
+// ---------------------------------------------------------------------------
+
+/**
+ * Default comparator using native `<` / `>` operators.
+ * Works correctly for numbers, strings, and Dates.
+ */
+function defaultComparator<K>(a: K, b: K): number {
+  if (a < b) return -1;
+  if (a > b) return 1;
+  return 0;
+}
+
+// ---------------------------------------------------------------------------
+// B+ Tree
+// ---------------------------------------------------------------------------
+
+/**
+ * In-memory B+ Tree with duplicate-key support.
+ *
+ * Each unique key maps to a `Set<V>`, allowing multiple values to share
+ * the same key (e.g. many documents with the same indexed field value).
+ *
+ * Leaf nodes are linked in a doubly-linked list so range scans are O(k)
+ * after the initial O(log n) descent.
+ *
+ * @typeParam K - Key type (must be comparable via the provided comparator)
+ * @typeParam V - Value type stored in each key's Set
+ */
+export class BPlusTree<K, V> {
+  /** Maximum number of keys per node. A node splits when it exceeds this. */
+  private readonly maxKeys: number;
+
+  /** Minimum number of keys a non-root node must hold after deletion. */
+  private readonly minKeys: number;
+
+  private readonly compare: Comparator<K>;
+
+  private root: Node<K, V>;
+
+  /** Total number of individual values across all keys. */
+  private _size = 0;
+
+  constructor(order = 32, comparator?: Comparator<K>) {
+    if (order < 3) throw new Error('B+ Tree order must be at least 3');
+    this.maxKeys = order - 1;
+    this.minKeys = Math.ceil(order / 2) - 1;
+    this.compare = comparator ?? defaultComparator;
+    this.root = new LeafNode<K, V>();
+  }
+
+  // -------------------------------------------------------------------------
+  // Public API
+  // -------------------------------------------------------------------------
+
+  /** Total number of individual values stored in the tree. */
+  get size(): number {
+    return this._size;
+  }
+
+  /** Remove all entries from the tree. */
+  clear(): void {
+    this.root = new LeafNode<K, V>();
+    this._size = 0;
+  }
+
+  /**
+   * Insert a value under the given key. If the key already exists the
+   * value is added to its Set; otherwise a new key entry is created.
+   */
+  insert(key: K, value: V): void {
+    const leaf = this.findLeaf(key);
+    const idx = this.leafKeyIndex(leaf, key);
+
+    if (idx < leaf.keys.length && this.compare(leaf.keys[idx], key) === 0) {
+      // Key exists — add to its value set.
+      const before = leaf.values[idx].size;
+      leaf.values[idx].add(value);
+      this._size += leaf.values[idx].size - before;
+    } else {
+      // New key — splice into position.
+      leaf.keys.splice(idx, 0, key);
+      leaf.values.splice(idx, 0, new Set([value]));
+      this._size++;
+    }
+
+    // Split if the leaf overflows.
+    if (leaf.keys.length > this.maxKeys) {
+      this.splitLeaf(leaf);
+    }
+  }
+
+  /**
+   * Look up all values associated with the exact key.
+   * Returns `undefined` if the key is not present.
+   */
+  get(key: K): Set<V> | undefined {
+    const leaf = this.findLeaf(key);
+    const idx = this.leafKeyIndex(leaf, key);
+    if (idx < leaf.keys.length && this.compare(leaf.keys[idx], key) === 0) {
+      return leaf.values[idx];
+    }
+    return undefined;
+  }
+
+  /**
+   * Delete a value (or all values) for the given key.
+   *
+   * - If `value` is provided, only that value is removed from the key's Set.
+   *   The key entry is removed when its Set becomes empty.
+   * - If `value` is omitted, the entire key entry (with all values) is removed.
+   *
+   * @returns `true` if something was removed, `false` if the key/value wasn't found.
+   */
+  delete(key: K, value?: V): boolean {
+    const leaf = this.findLeaf(key);
+    const idx = this.leafKeyIndex(leaf, key);
+
+    if (idx >= leaf.keys.length || this.compare(leaf.keys[idx], key) !== 0) {
+      return false;
+    }
+
+    if (value !== undefined) {
+      const set = leaf.values[idx];
+      if (!set.has(value)) return false;
+      set.delete(value);
+      this._size--;
+
+      if (set.size > 0) return true;
+      // Set empty — fall through to remove the key entry entirely.
+    } else {
+      this._size -= leaf.values[idx].size;
+    }
+
+    leaf.keys.splice(idx, 1);
+    leaf.values.splice(idx, 1);
+
+    // Rebalance if needed (skip for root leaf).
+    if (leaf !== this.root && leaf.keys.length < this.minKeys) {
+      this.rebalanceLeaf(leaf);
+    }
+
+    // Shrink tree height if the root internal node has a single child.
+    if (!isLeaf(this.root) && this.root.children.length === 1) {
+      this.root = this.root.children[0];
+    }
+
+    return true;
+  }
+
+  /**
+   * Range query. Returns all entries whose keys fall within `[min, max]`
+   * (bounds configurable via `opts`).
+   *
+   * - Omit `min` for an unbounded lower end.
+   * - Omit `max` for an unbounded upper end.
+   * - Omit both to iterate the entire tree in key order.
+   *
+   * Default bounds: lower inclusive, upper exclusive (half-open interval).
+   */
+  range(
+    min?: K,
+    max?: K,
+    opts?: RangeOptions,
+  ): BPlusTreeEntry<K, V>[] {
+    const lowerInc = opts?.lowerInclusive ?? true;
+    const upperInc = opts?.upperInclusive ?? false;
+
+    const results: BPlusTreeEntry<K, V>[] = [];
+
+    // Find the starting leaf.
+    let leaf: LeafNode<K, V>;
+    let startIdx: number;
+
+    if (min !== undefined) {
+      leaf = this.findLeaf(min);
+      startIdx = this.leafKeyIndex(leaf, min);
+      // Adjust for exclusive lower bound.
+      if (!lowerInc && startIdx < leaf.keys.length && this.compare(leaf.keys[startIdx], min) === 0) {
+        startIdx++;
+      }
+    } else {
+      leaf = this.firstLeaf();
+      startIdx = 0;
+    }
+
+    // Walk the leaf chain collecting matching entries.
+    let currentLeaf: LeafNode<K, V> | null = leaf;
+    let i = startIdx;
+
+    while (currentLeaf) {
+      while (i < currentLeaf.keys.length) {
+        const key = currentLeaf.keys[i];
+
+        if (max !== undefined) {
+          const cmp = this.compare(key, max);
+          if (cmp > 0 || (cmp === 0 && !upperInc)) {
+            return results;
+          }
+        }
+
+        results.push({ key, values: currentLeaf.values[i] });
+        i++;
+      }
+
+      currentLeaf = currentLeaf.next;
+      i = 0;
+    }
+
+    return results;
+  }
+
+  /**
+   * Iterate over all entries in key order.
+   */
+  *entries(): IterableIterator<BPlusTreeEntry<K, V>> {
+    let leaf: LeafNode<K, V> | null = this.firstLeaf();
+    while (leaf) {
+      for (let i = 0; i < leaf.keys.length; i++) {
+        yield { key: leaf.keys[i], values: leaf.values[i] };
+      }
+      leaf = leaf.next;
+    }
+  }
+
+  // -------------------------------------------------------------------------
+  // Tree navigation
+  // -------------------------------------------------------------------------
+
+  /**
+   * Descend to the leaf node that should contain the given key.
+   */
+  private findLeaf(key: K): LeafNode<K, V> {
+    let node: Node<K, V> = this.root;
+    while (!isLeaf(node)) {
+      const internal = node as InternalNode<K, V>;
+      let childIdx = internal.keys.length;
+      for (let i = 0; i < internal.keys.length; i++) {
+        if (this.compare(key, internal.keys[i]) < 0) {
+          childIdx = i;
+          break;
+        }
+      }
+      node = internal.children[childIdx];
+    }
+    return node;
+  }
+
+  /** Get the leftmost leaf in the tree. */
+  private firstLeaf(): LeafNode<K, V> {
+    let node: Node<K, V> = this.root;
+    while (!isLeaf(node)) {
+      node = (node as InternalNode<K, V>).children[0];
+    }
+    return node;
+  }
+
+  /**
+   * Binary search within a leaf for the insertion position of `key`.
+   * Returns the index of the first key >= `key`.
+   */
+  private leafKeyIndex(leaf: LeafNode<K, V>, key: K): number {
+    let lo = 0;
+    let hi = leaf.keys.length;
+    while (lo < hi) {
+      const mid = (lo + hi) >>> 1;
+      if (this.compare(leaf.keys[mid], key) < 0) {
+        lo = mid + 1;
+      } else {
+        hi = mid;
+      }
+    }
+    return lo;
+  }
+
+  // -------------------------------------------------------------------------
+  // Splitting
+  // -------------------------------------------------------------------------
+
+  /**
+   * Split an overflowing leaf node. The right half becomes a new leaf,
+   * and a copy of its first key is promoted to the parent.
+   */
+  private splitLeaf(leaf: LeafNode<K, V>): void {
+    const mid = Math.ceil(leaf.keys.length / 2);
+    const newLeaf = new LeafNode<K, V>();
+
+    newLeaf.keys = leaf.keys.splice(mid);
+    newLeaf.values = leaf.values.splice(mid);
+
+    // Maintain the doubly-linked list.
+    newLeaf.next = leaf.next;
+    newLeaf.prev = leaf;
+    if (leaf.next) leaf.next.prev = newLeaf;
+    leaf.next = newLeaf;
+
+    const promotedKey = newLeaf.keys[0];
+    this.insertIntoParent(leaf, promotedKey, newLeaf);
+  }
+
+  /**
+   * Split an overflowing internal node. The middle key is pushed up
+   * to the parent (not copied — it's removed from this level).
+   */
+  private splitInternal(node: InternalNode<K, V>): void {
+    const mid = Math.floor(node.keys.length / 2);
+    const promotedKey = node.keys[mid];
+
+    const newNode = new InternalNode<K, V>();
+    newNode.keys = node.keys.splice(mid + 1);
+    newNode.children = node.children.splice(mid + 1);
+    node.keys.splice(mid, 1); // remove the promoted key
+
+    this.insertIntoParent(node, promotedKey, newNode);
+  }
+
+  /**
+   * Insert a promoted key and new right child into the parent of `left`.
+   * If `left` is the root, a new root is created.
+   */
+  private insertIntoParent(
+    left: Node<K, V>,
+    key: K,
+    right: Node<K, V>,
+  ): void {
+    if (left === this.root) {
+      const newRoot = new InternalNode<K, V>();
+      newRoot.keys = [key];
+      newRoot.children = [left, right];
+      this.root = newRoot;
+      return;
+    }
+
+    const parent = this.findParent(this.root, left) as InternalNode<K, V>;
+    const idx = parent.children.indexOf(left);
+
+    parent.keys.splice(idx, 0, key);
+    parent.children.splice(idx + 1, 0, right);
+
+    if (parent.keys.length > this.maxKeys) {
+      this.splitInternal(parent);
+    }
+  }
+
+  // -------------------------------------------------------------------------
+  // Rebalancing (deletion)
+  // -------------------------------------------------------------------------
+
+  /**
+   * Rebalance a leaf that has fewer than `minKeys` entries after deletion.
+   * Tries to borrow from a sibling first; if neither sibling can spare
+   * a key, merges with a sibling.
+   */
+  private rebalanceLeaf(leaf: LeafNode<K, V>): void {
+    const parent = this.findParent(this.root, leaf) as InternalNode<K, V>;
+    const idx = parent.children.indexOf(leaf);
+
+    // Try borrowing from the right sibling.
+    if (idx < parent.children.length - 1) {
+      const rightSibling = parent.children[idx + 1] as LeafNode<K, V>;
+      if (rightSibling.keys.length > this.minKeys) {
+        leaf.keys.push(rightSibling.keys.shift()!);
+        leaf.values.push(rightSibling.values.shift()!);
+        parent.keys[idx] = rightSibling.keys[0];
+        return;
+      }
+    }
+
+    // Try borrowing from the left sibling.
+    if (idx > 0) {
+      const leftSibling = parent.children[idx - 1] as LeafNode<K, V>;
+      if (leftSibling.keys.length > this.minKeys) {
+        leaf.keys.unshift(leftSibling.keys.pop()!);
+        leaf.values.unshift(leftSibling.values.pop()!);
+        parent.keys[idx - 1] = leaf.keys[0];
+        return;
+      }
+    }
+
+    // Merge with a sibling.
+    if (idx < parent.children.length - 1) {
+      this.mergeLeaves(leaf, parent.children[idx + 1] as LeafNode<K, V>, parent, idx);
+    } else {
+      this.mergeLeaves(parent.children[idx - 1] as LeafNode<K, V>, leaf, parent, idx - 1);
+    }
+  }
+
+  /**
+   * Merge `right` leaf into `left` leaf and remove the separator key
+   * from the parent.
+   */
+  private mergeLeaves(
+    left: LeafNode<K, V>,
+    right: LeafNode<K, V>,
+    parent: InternalNode<K, V>,
+    separatorIdx: number,
+  ): void {
+    left.keys.push(...right.keys);
+    left.values.push(...right.values);
+
+    // Fix linked list pointers.
+    left.next = right.next;
+    if (right.next) right.next.prev = left;
+
+    // Remove the separator key and right child from the parent.
+    parent.keys.splice(separatorIdx, 1);
+    parent.children.splice(separatorIdx + 1, 1);
+
+    // Recursively rebalance the parent if needed.
+    if (parent !== this.root && parent.keys.length < this.minKeys) {
+      this.rebalanceInternal(parent);
+    }
+  }
+
+  /**
+   * Rebalance an internal node that has too few keys after a merge.
+   */
+  private rebalanceInternal(node: InternalNode<K, V>): void {
+    const parent = this.findParent(this.root, node) as InternalNode<K, V>;
+    const idx = parent.children.indexOf(node);
+
+    // Try borrowing from the right sibling.
+    if (idx < parent.children.length - 1) {
+      const rightSibling = parent.children[idx + 1] as InternalNode<K, V>;
+      if (rightSibling.keys.length > this.minKeys) {
+        node.keys.push(parent.keys[idx]);
+        parent.keys[idx] = rightSibling.keys.shift()!;
+        node.children.push(rightSibling.children.shift()!);
+        return;
+      }
+    }
+
+    // Try borrowing from the left sibling.
+    if (idx > 0) {
+      const leftSibling = parent.children[idx - 1] as InternalNode<K, V>;
+      if (leftSibling.keys.length > this.minKeys) {
+        node.keys.unshift(parent.keys[idx - 1]);
+        parent.keys[idx - 1] = leftSibling.keys.pop()!;
+        node.children.unshift(leftSibling.children.pop()!);
+        return;
+      }
+    }
+
+    // Merge with a sibling.
+    if (idx < parent.children.length - 1) {
+      const rightSibling = parent.children[idx + 1] as InternalNode<K, V>;
+      this.mergeInternal(node, rightSibling, parent, idx);
+    } else {
+      const leftSibling = parent.children[idx - 1] as InternalNode<K, V>;
+      this.mergeInternal(leftSibling, node, parent, idx - 1);
+    }
+  }
+
+  /**
+   * Merge two internal nodes by pulling down the separator key from the
+   * parent and concatenating children.
+   */
+  private mergeInternal(
+    left: InternalNode<K, V>,
+    right: InternalNode<K, V>,
+    parent: InternalNode<K, V>,
+    separatorIdx: number,
+  ): void {
+    left.keys.push(parent.keys[separatorIdx]);
+    left.keys.push(...right.keys);
+    left.children.push(...right.children);
+
+    parent.keys.splice(separatorIdx, 1);
+    parent.children.splice(separatorIdx + 1, 1);
+
+    if (parent !== this.root && parent.keys.length < this.minKeys) {
+      this.rebalanceInternal(parent);
+    }
+  }
+
+  // -------------------------------------------------------------------------
+  // Utilities
+  // -------------------------------------------------------------------------
+
+  /**
+   * Walk the tree from `current` downward to find the parent of `target`.
+   * Returns `null` if `target` is the root or not found.
+   */
+  private findParent(
+    current: Node<K, V>,
+    target: Node<K, V>,
+  ): InternalNode<K, V> | null {
+    if (isLeaf(current)) return null;
+    const internal = current as InternalNode<K, V>;
+
+    for (const child of internal.children) {
+      if (child === target) return internal;
+      const found = this.findParent(child, target);
+      if (found) return found;
+    }
+
+    return null;
+  }
+}

src/utils/index.ts

@@ -1,3 +1,4 @@
 export * from './event-emitter.js';
 export * from './exponential-backoff.js';
 export * from './sse-session.js';
+export * from './btree.js';