/js/src/v8/splay.js

  1// Copyright 2009 the V8 project authors. All rights reserved.
  2// Redistribution and use in source and binary forms, with or without
  3// modification, are permitted provided that the following conditions are
  4// met:
  5//
  6//     * Redistributions of source code must retain the above copyright
  7//       notice, this list of conditions and the following disclaimer.
  8//     * Redistributions in binary form must reproduce the above
  9//       copyright notice, this list of conditions and the following
 10//       disclaimer in the documentation and/or other materials provided
 11//       with the distribution.
 12//     * Neither the name of Google Inc. nor the names of its
 13//       contributors may be used to endorse or promote products derived
 14//       from this software without specific prior written permission.
 15//
 16// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 17// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 18// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 19// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 20// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 21// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 22// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 23// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 24// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 25// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 26// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 27
 28// This benchmark is based on a JavaScript log processing module used
 29// by the V8 profiler to generate execution time profiles for runs of
 30// JavaScript applications, and it effectively measures how fast the
 31// JavaScript engine is at allocating nodes and reclaiming the memory
 32// used for old nodes. Because of the way splay trees work, the engine
 33// also has to deal with a lot of changes to the large tree object
 34// graph.
 35
 36var Splay = new BenchmarkSuite('Splay', 81491, [
 37  new Benchmark("Splay", SplayRun, SplaySetup, SplayTearDown)
 38]);
 39
 40
 41// Configuration.
 42var kSplayTreeSize = 8000;
 43var kSplayTreeModifications = 80;
 44var kSplayTreePayloadDepth = 5;
 45
 46var splayTree = null;
 47
 48
 49function GeneratePayloadTree(depth, tag) {
 50  if (depth == 0) {
 51    return {
 52      array  : [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ],
 53      string : 'String for key ' + tag + ' in leaf node'
 54    };
 55  } else {
 56    return {
 57      left:  GeneratePayloadTree(depth - 1, tag),
 58      right: GeneratePayloadTree(depth - 1, tag)
 59    };
 60  }
 61}
 62
 63
 64function GenerateKey() {
 65  // The benchmark framework guarantees that Math.random is
 66  // deterministic; see base.js.
 67  return Math.random();
 68}
 69
 70
 71function InsertNewNode() {
 72  // Insert new node with a unique key.
 73  var key;
 74  do {
 75    key = GenerateKey();
 76  } while (splayTree.find(key) != null);
 77  var payload = GeneratePayloadTree(kSplayTreePayloadDepth, String(key));
 78  splayTree.insert(key, payload);
 79  return key;
 80}
 81
 82
 83
 84function SplaySetup() {
 85  splayTree = new SplayTree();
 86  for (var i = 0; i < kSplayTreeSize; i++) InsertNewNode();
 87}
 88
 89
 90function SplayTearDown() {
 91  // Allow the garbage collector to reclaim the memory
 92  // used by the splay tree no matter how we exit the
 93  // tear down function.
 94  var keys = splayTree.exportKeys();
 95  splayTree = null;
 96
 97  // Verify that the splay tree has the right size.
 98  var length = keys.length;
 99  if (length != kSplayTreeSize) {
100    throw new Error("Splay tree has wrong size");
101  }
102
103  // Verify that the splay tree has sorted, unique keys.
104  for (var i = 0; i < length - 1; i++) {
105    if (keys[i] >= keys[i + 1]) {
106      throw new Error("Splay tree not sorted");
107    }
108  }
109}
110
111
112function SplayRun() {
113  // Replace a few nodes in the splay tree.
114  for (var i = 0; i < kSplayTreeModifications; i++) {
115    var key = InsertNewNode();
116    var greatest = splayTree.findGreatestLessThan(key);
117    if (greatest == null) splayTree.remove(key);
118    else splayTree.remove(greatest.key);
119  }
120}
121
122
123/**
124 * Constructs a Splay tree.  A splay tree is a self-balancing binary
125 * search tree with the additional property that recently accessed
126 * elements are quick to access again. It performs basic operations
127 * such as insertion, look-up and removal in O(log(n)) amortized time.
128 *
129 * @constructor
130 */
131function SplayTree() {
132};
133
134
135/**
136 * Pointer to the root node of the tree.
137 *
138 * @type {SplayTree.Node}
139 * @private
140 */
141SplayTree.prototype.root_ = null;
142
143
144/**
145 * @return {boolean} Whether the tree is empty.
146 */
147SplayTree.prototype.isEmpty = function() {
148  return !this.root_;
149};
150
151
152/**
153 * Inserts a node into the tree with the specified key and value if
154 * the tree does not already contain a node with the specified key. If
155 * the value is inserted, it becomes the root of the tree.
156 *
157 * @param {number} key Key to insert into the tree.
158 * @param {*} value Value to insert into the tree.
159 */
160SplayTree.prototype.insert = function(key, value) {
161  if (this.isEmpty()) {
162    this.root_ = new SplayTree.Node(key, value);
163    return;
164  }
165  // Splay on the key to move the last node on the search path for
166  // the key to the root of the tree.
167  this.splay_(key);
168  if (this.root_.key == key) {
169    return;
170  }
171  var node = new SplayTree.Node(key, value);
172  if (key > this.root_.key) {
173    node.left = this.root_;
174    node.right = this.root_.right;
175    this.root_.right = null;
176  } else {
177    node.right = this.root_;
178    node.left = this.root_.left;
179    this.root_.left = null;
180  }
181  this.root_ = node;
182};
183
184
185/**
186 * Removes a node with the specified key from the tree if the tree
187 * contains a node with this key. The removed node is returned. If the
188 * key is not found, an exception is thrown.
189 *
190 * @param {number} key Key to find and remove from the tree.
191 * @return {SplayTree.Node} The removed node.
192 */
193SplayTree.prototype.remove = function(key) {
194  if (this.isEmpty()) {
195    throw Error('Key not found: ' + key);
196  }
197  this.splay_(key);
198  if (this.root_.key != key) {
199    throw Error('Key not found: ' + key);
200  }
201  var removed = this.root_;
202  if (!this.root_.left) {
203    this.root_ = this.root_.right;
204  } else {
205    var right = this.root_.right;
206    this.root_ = this.root_.left;
207    // Splay to make sure that the new root has an empty right child.
208    this.splay_(key);
209    // Insert the original right child as the right child of the new
210    // root.
211    this.root_.right = right;
212  }
213  return removed;
214};
215
216
217/**
218 * Returns the node having the specified key or null if the tree doesn't contain
219 * a node with the specified key.
220 *
221 * @param {number} key Key to find in the tree.
222 * @return {SplayTree.Node} Node having the specified key.
223 */
224SplayTree.prototype.find = function(key) {
225  if (this.isEmpty()) {
226    return null;
227  }
228  this.splay_(key);
229  return this.root_.key == key ? this.root_ : null;
230};
231
232
233/**
234 * @return {SplayTree.Node} Node having the maximum key value.
235 */
236SplayTree.prototype.findMax = function(opt_startNode) {
237  if (this.isEmpty()) {
238    return null;
239  }
240  var current = opt_startNode || this.root_;
241  while (current.right) {
242    current = current.right;
243  }
244  return current;
245};
246
247
248/**
249 * @return {SplayTree.Node} Node having the maximum key value that
250 *     is less than the specified key value.
251 */
252SplayTree.prototype.findGreatestLessThan = function(key) {
253  if (this.isEmpty()) {
254    return null;
255  }
256  // Splay on the key to move the node with the given key or the last
257  // node on the search path to the top of the tree.
258  this.splay_(key);
259  // Now the result is either the root node or the greatest node in
260  // the left subtree.
261  if (this.root_.key < key) {
262    return this.root_;
263  } else if (this.root_.left) {
264    return this.findMax(this.root_.left);
265  } else {
266    return null;
267  }
268};
269
270
271/**
272 * @return {Array<*>} An array containing all the keys of tree's nodes.
273 */
274SplayTree.prototype.exportKeys = function() {
275  var result = [];
276  if (!this.isEmpty()) {
277    this.root_.traverse_(function(node) { result.push(node.key); });
278  }
279  return result;
280};
281
282
283/**
284 * Perform the splay operation for the given key. Moves the node with
285 * the given key to the top of the tree.  If no node has the given
286 * key, the last node on the search path is moved to the top of the
287 * tree. This is the simplified top-down splaying algorithm from:
288 * "Self-adjusting Binary Search Trees" by Sleator and Tarjan
289 *
290 * @param {number} key Key to splay the tree on.
291 * @private
292 */
293SplayTree.prototype.splay_ = function(key) {
294  if (this.isEmpty()) {
295    return;
296  }
297  // Create a dummy node.  The use of the dummy node is a bit
298  // counter-intuitive: The right child of the dummy node will hold
299  // the L tree of the algorithm.  The left child of the dummy node
300  // will hold the R tree of the algorithm.  Using a dummy node, left
301  // and right will always be nodes and we avoid special cases.
302  var dummy, left, right;
303  dummy = left = right = new SplayTree.Node(null, null);
304  var current = this.root_;
305  while (true) {
306    if (key < current.key) {
307      if (!current.left) {
308        break;
309      }
310      if (key < current.left.key) {
311        // Rotate right.
312        var tmp = current.left;
313        current.left = tmp.right;
314        tmp.right = current;
315        current = tmp;
316        if (!current.left) {
317          break;
318        }
319      }
320      // Link right.
321      right.left = current;
322      right = current;
323      current = current.left;
324    } else if (key > current.key) {
325      if (!current.right) {
326        break;
327      }
328      if (key > current.right.key) {
329        // Rotate left.
330        var tmp = current.right;
331        current.right = tmp.left;
332        tmp.left = current;
333        current = tmp;
334        if (!current.right) {
335          break;
336        }
337      }
338      // Link left.
339      left.right = current;
340      left = current;
341      current = current.right;
342    } else {
343      break;
344    }
345  }
346  // Assemble.
347  left.right = current.left;
348  right.left = current.right;
349  current.left = dummy.right;
350  current.right = dummy.left;
351  this.root_ = current;
352};
353
354
355/**
356 * Constructs a Splay tree node.
357 *
358 * @param {number} key Key.
359 * @param {*} value Value.
360 */
361SplayTree.Node = function(key, value) {
362  this.key = key;
363  this.value = value;
364};
365
366
367/**
368 * @type {SplayTree.Node}
369 */
370SplayTree.Node.prototype.left = null;
371
372
373/**
374 * @type {SplayTree.Node}
375 */
376SplayTree.Node.prototype.right = null;
377
378
379/**
380 * Performs an ordered traversal of the subtree starting at
381 * this SplayTree.Node.
382 *
383 * @param {function(SplayTree.Node)} f Visitor function.
384 * @private
385 */
386SplayTree.Node.prototype.traverse_ = function(f) {
387  var current = this;
388  while (current) {
389    var left = current.left;
390    if (left) left.traverse_(f);
391    f(current);
392    current = current.right;
393  }
394};