FPTree.hpp 42.7 KB
Newer Older
1
/*
2
 * Copyright (C) 2017-2019 DBIS Group - TU Ilmenau, All Rights Reserved.
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
 *
 * This file is part of our NVM-based Data Structure Repository.
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program. If not, see <http://www.gnu.org/licenses/>.
 */

#ifndef DBIS_FPTree_hpp_
#define DBIS_FPTree_hpp_

#include <array>
24
#include <bitset>
25
#include <cmath>
26
27
28
29
30
31
32
33
#include <iostream>

#include <libpmemobj++/make_persistent.hpp>
#include <libpmemobj++/p.hpp>
#include <libpmemobj++/persistent_ptr.hpp>
#include <libpmemobj++/transaction.hpp>
#include <libpmemobj++/utils.hpp>

34
#include "config.h"
35
36
#include "utils/ElementOfRankK.hpp"

37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
#define BRANCH_PADDING  0
#define LEAF_PADDING    0

namespace dbis::fptree {

using pmem::obj::delete_persistent;
using pmem::obj::make_persistent;
using pmem::obj::p;
using pmem::obj::persistent_ptr;
using pmem::obj::transaction;

/**
 * A persistent memory implementation of a FPTree.
 *
 * @tparam KeyType the data type of the key
 * @tparam ValueType the data type of the values associated with the key
 * @tparam N the maximum number of keys on a branch node
 * @tparam M the maximum number of keys on a leaf node
 */
template<typename KeyType, typename ValueType, int N, int M>
class FPTree {
  // we need at least two keys on a branch node to be able to split
  static_assert(N > 2, "number of branch keys has to be >2.");
  // we need at least one key on a leaf node
  static_assert(M > 0, "number of leaf keys should be >0.");

#ifndef UNIT_TESTS
  private:
#else
  public:
#endif

  // Forward declarations
  struct LeafNode;
  struct BranchNode;

73
74
  struct Node {
    Node() : tag(BLANK) {};
75

76
    Node(persistent_ptr<LeafNode> leaf_) : tag(LEAF), leaf(leaf_) {};
77

78
    Node(BranchNode *branch_) : tag(BRANCH), branch(branch_) {};
79

80
    Node(const Node &other) { copy(other); };
81

82
    void copy(const Node &other) throw() {
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
      tag = other.tag;

      switch (tag) {
        case LEAF: {
          leaf = other.leaf;
          break;
        }
        case BRANCH: {
          branch = other.branch;
          break;
        }
        default: break;
      }
    }

98
    Node &operator=(Node other) {
99
100
101
102
103
      copy(other);
      return *this;
    }

    enum NodeType {
104
      BLANK, LEAF, BRANCH
105
106
107
108
109
110
111
    } tag;
    union {
      persistent_ptr<LeafNode> leaf;
      BranchNode *branch;
    };
  };

112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
  /* By Herb Sutter */
  template<typename T>
  struct CacheLineStorage {
    alignas(64) T data;
    char pad[ 64 > sizeof(T) ? 64 - sizeof(T) : 0];
  };
  struct LeafSearch {
    std::bitset<M> b;            //< bitset for valid entries
    std::array<std::byte, M> fp; //< fingerprint array (n & 0xFF)

    unsigned int getFreeZero() const {
      unsigned int idx = 0;
      while (idx < M && b.test(idx)) ++idx;
      return idx;
    }
  };

129
130
131
132
133
134
135
  /**
   * A structure for representing a leaf node of a B+ tree.
   */
  struct LeafNode {
    /**
     * Constructor for creating a new empty leaf node.
     */
136
137
138
139
140
141
142
143
    LeafNode() : nextLeaf(nullptr), prevLeaf(nullptr) {}

    p<CacheLineStorage<LeafSearch>> search;//< helper structure for faster searches
    persistent_ptr<LeafNode> nextLeaf;     //< pointer to the subsequent sibling
    persistent_ptr<LeafNode> prevLeaf;     //< pointer to the preceeding sibling
    p<std::array<KeyType, M>> keys;        //< the actual keys
    p<std::array<ValueType, M>> values;    //< the actual values
    p<unsigned char> pad_[LEAF_PADDING];   //<
144
145
146
147
148
149
150
151
152
153
154
155
156
  };

  /**
   * A structure for representing an branch node (branch node) of a B+ tree.
   */
  struct BranchNode {
    /**
     * Constructor for creating a new empty branch node.
     */
    BranchNode() : numKeys(0) {}

    unsigned int numKeys;                         //< the number of currently stored keys
    std::array<KeyType, N> keys;                  //< the actual keys
157
    std::array<Node, N + 1> children; //< pointers to child nodes (BranchNode or LeafNode)
158
159
160
161
162
163
164
165
166
167
    unsigned char pad_[BRANCH_PADDING];           //<
  };

  /**
   * Create a new empty leaf node
   */
  persistent_ptr<LeafNode> newLeafNode() {
    auto pop = pmem::obj::pool_by_vptr(this);
    persistent_ptr<LeafNode> newNode = nullptr;
    transaction::run(pop, [&] {
168
169
170
171
172
173
174
175
176
177
178
      newNode = make_persistent<LeafNode>();
    });
    return newNode;
  }

  persistent_ptr<LeafNode> newLeafNode(const persistent_ptr<LeafNode> &other) {
    auto pop = pmem::obj::pool_by_vptr(this);
    persistent_ptr<LeafNode> newNode = nullptr;
    transaction::run(pop, [&] {
      newNode = make_persistent<LeafNode>(*other);
    });
179
180
181
    return newNode;
  }

182

183
184
185
  void deleteLeafNode(persistent_ptr<LeafNode> node) {
    auto pop = pmem::obj::pool_by_vptr(this);
    transaction::run(pop, [&] {
186
187
      delete_persistent<LeafNode>(node);
    });
188
189
190
191
192
193
  }

  /**
   * Create a new empty branch node
   */
  BranchNode *newBranchNode() {
194
    return new BranchNode();
195
196
197
  }

  void deleteBranchNode(BranchNode *node) {
198
    delete node;
199
200
201
202
203
204
205
206
  }

  /**
   * A structure for passing information about a node split to
   * the caller.
   */
  struct SplitInfo {
    KeyType key;                 //< the key at which the node was split
207
208
    Node leftChild;  //< the resulting lhs child node
    Node rightChild; //< the resulting rhs child node
209
210
211
212
  };

  unsigned int depth;         //< the depth of the tree, i.e. the number of levels (0 => rootNode is LeafNode)

213
  Node rootNode;     //< pointer to the root node
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
  persistent_ptr<LeafNode> leafList; //<Pointer to the leaf at the most left position. Neccessary for recovery

  PROFILE_DECL

  public:
  /**
   * Typedef for a function passed to the scan method.
   */
  using ScanFunc = std::function<void(const KeyType &key, const ValueType &val)>;
  /**
   * Iterator for iterating over the leaf nodes
   */
  class iterator {
    persistent_ptr<LeafNode> currentNode;
    std::size_t currentPosition;

    public:
    iterator() : currentNode(nullptr), currentPosition(0) {}
232
    iterator(const Node &root, std::size_t d) {
233
234
235
236
237
238
239
240
      // traverse to left-most key
      auto node = root;
      while (d-- > 0) {
        auto n = node.branch;
        node = n->children[0];
      }
      currentNode = node.leaf;
      currentPosition = 0;
241
242
      // Can not overflow as there are at least M/2 entries
      while(!currentNode->search.get_ro().data.b.test(currentPosition)) ++currentPosition;
243
244
245
    }

    iterator& operator++() {
246
      if (currentPosition >= M-1) {
247
248
        currentNode = currentNode->nextLeaf;
        currentPosition = 0;
249
250
251
        if (currentNode == nullptr) return *this;
        while(!currentNode->search.get_ro().data.b.test(currentPosition)) ++currentPosition;
      } else if (!currentNode->search.get_ro().data.b.test(++currentPosition)) ++(*this);
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
      return *this;
    }
    iterator operator++(int) {iterator retval = *this; ++(*this); return retval;}

    bool operator==(iterator other) const {return (currentNode == other.currentNode &&
        currentPosition == other.currentPosition);}
    bool operator!=(iterator other) const {return !(*this == other);}

    std::pair<KeyType, ValueType> operator*() {

      return std::make_pair(currentNode->keys.get_ro()[currentPosition], currentNode->values.get_ro()[currentPosition]);
    }

    // iterator traits
    using difference_type = long;
    using value_type = std::pair<KeyType, ValueType>;
    using pointer = const std::pair<KeyType, ValueType>*;
    using reference = const std::pair<KeyType, ValueType>&;
    using iterator_category = std::forward_iterator_tag;
  };
  iterator begin() { return iterator(rootNode, depth); }
  iterator end() { return iterator(); }
  /**
   * Constructor for creating a new  tree.
   */
  FPTree() {
    rootNode = newLeafNode();
279
280
    leafList = rootNode.leaf;
    depth = 0;
281
    PROFILE_INIT
282
283
    LOG("created new FPTree with sizeof(BranchNode) = " << sizeof(BranchNode)
                            <<  ", sizeof(LeafNode) = " << sizeof(LeafNode));
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
  }

  /**
   * Destructor for the tree. Should delete all allocated nodes.
   */
  ~FPTree() {
    // Nodes are deleted automatically by releasing leafPool and branchPool.
  }

  /**
   * Insert an element (a key-value pair) into the tree. If the key @c key
   * already exists, the corresponding value is replaced by @c val.
   *
   * @param key the key of the element to be inserted
   * @param val the value that is associated with the key
   */
  void insert(const KeyType &key, const ValueType &val) {
    auto pop = pmem::obj::pool_by_vptr(this);
    transaction::run(pop, [&] {
303
			SplitInfo splitInfo;
304

305
306
      bool wasSplit = false;
      if (depth == 0) {
307
308
309
        // the root node is a leaf node
        auto n = rootNode.leaf;
        wasSplit = insertInLeafNode(n, key, val, &splitInfo);
310
      } else {
311
312
313
        // the root node is a branch node
        auto n = rootNode.branch;
        wasSplit = insertInBranchNode(n, depth, key, val, &splitInfo);
314
315
      }
      if (wasSplit) {
316
        // we had an overflow in the node and therefore the node is split
317
318
319
320
321
322
323
324
        auto root = newBranchNode();

        root->keys[0] = splitInfo.key;
        root->children[0] = splitInfo.leftChild;
        root->children[1] = splitInfo.rightChild;
        ++root->numKeys;
        rootNode.branch = root;
        ++depth;
325
      }
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
    });
  }

  /**
   * Find the given @c key in the  tree and if found return the
   * corresponding value.
   *
   * @param key the key we are looking for
   * @param[out] val a pointer to memory where the value is stored
   *                 if the key was found
   * @return true if the key was found, false otherwise
   */
  bool lookup(const KeyType &key, ValueType *val)  {
    assert(val != nullptr);

    bool result = false;
    auto leafNode = findLeafNode(key);
    auto pos = lookupPositionInLeafNode(leafNode, key);
344
    if (pos < M) {
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
      // we found it!
      *val = leafNode->values.get_ro()[pos];
      result = true;
    }
    return result;
  }

  /**
   * Delete the entry with the given key @c key from the tree.
   *
   * @param key the key of the entry to be deleted
   * @return true if the key was found and deleted
   */
  bool erase(const KeyType &key) {
    auto pop = pmem::obj::pool_by_vptr(this);
    bool result;
    transaction::run(pop, [&] {
362
      if (depth == 0) {
363
364
365
366
367
        // special case: the root node is a leaf node and
        // there is no need to handle underflow
        auto node = rootNode.leaf;
        assert(node != nullptr);
        result=eraseFromLeafNode(node, key);
368
      } else {
369
370
371
372
        auto node = rootNode.branch;
        assert(node != nullptr);
        result=eraseFromBranchNode(node, depth, key);

373
374
      }
    });
375
376
377
378
379
    return result;
  }
  /**
   * Recover the FPTree by iterating over the LeafList and using the recoveryInsert method.
   */
380
  void recover() {
381
    LOG("Starting RECOVERY of FPTree");
382
    persistent_ptr<LeafNode> currentLeaf = leafList;
383
    if (leafList == nullptr) {
384
      LOG("No data to recover FPTree");
385
      return;
386
    }
387
388
389
390
391
392
393
394
395
396
397
398
    /* counting leafs */
    auto leafs = 0u;
    while(currentLeaf != nullptr) {
      ++leafs;
      currentLeaf = currentLeaf->nextLeaf;
    }
    float x = std::log(leafs)/std::log(N+1);
    assert(x == int(x) && "Not supported for this amount of leafs, yet");

    /* actual recovery */
    currentLeaf = leafList;
    if (leafList->nextLeaf == nullptr) {
399
      // The index has only one node, so the leaf node becomes the root node
400
401
      rootNode = leafList;
      depth = 0;
402
    } else {
403
      rootNode = newBranchNode();
404
      depth = 1;
405
406
      rootNode.branch->children[0] = currentLeaf;
      currentLeaf = currentLeaf->nextLeaf;
407
408
409
410
411
      while (currentLeaf != nullptr) {
        recoveryInsert(currentLeaf);
        currentLeaf = currentLeaf->nextLeaf;
      }
    }
412
    LOG("RECOVERY Done")
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
  }

  /**
   * Print the structure and content of the tree to stdout.
   */
  void print() const {
    if (depth == 0) {
      printLeafNode(0, rootNode.leaf);
    } else {
      auto n = rootNode;
      printBranchNode(0u, n.branch);
    }
  }

  PROFILE_PRINT

  /**
   * Perform a scan over all key-value pairs stored in the tree.
   * For each entry the given function @func is called.
   *
   * @param func the function called for each entry
   */
435
  void scan(ScanFunc func) const {
436
437
438
    // we traverse to the leftmost leaf node
    auto node = rootNode;
    auto d = depth;
439
    while ( d-- > 0) {
440
      // as long as we aren't at the leaf level we follow the path down
441
      node = node.branch->children[0];
442
443
444
445
446
    }
    auto leaf = node.leaf;
    while (leaf != nullptr) {
      // for each key-value pair call func
      for (auto i = 0u; i < leaf->numKeys.get_ro(); i++) {
447
        if (!leaf->search.get_ro().data.b.test(i)) continue;
448
449
450
451
452
453
454
        const auto &key = leaf->keys.get_ro()[i];
        const auto &val = leaf->values.get_ro()[i];
        func(key, val);
      }
      // move to the next leaf node
      leaf = leaf->nextLeaf;
    }
455
  }
456
457
458
459
460
461
462
463
464

  /**
   * Perform a range scan over all elements within the range [minKey, maxKey]
   * and for each element call the given function @c func.
   *
   * @param minKey the lower boundary of the range
   * @param maxKey the upper boundary of the range
   * @param func the function called for each entry
   */
465
  void scan(const KeyType &minKey, const KeyType &maxKey, ScanFunc func) const {
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
    auto leaf = findLeafNode(minKey);

    bool higherThanMax = false;
    while (!higherThanMax && leaf != nullptr) {
      // for each key-value pair within the range call func
      for (auto i = 0u; i < M; i++) {
        if (!leaf->search.get_ro().data.b.test(i)) continue;
        auto &key = leaf->keys.get_ro()[i];
        if (key < minKey) continue;
        if (key > maxKey) { higherThanMax = true; continue; }

        auto &val = leaf->values.get_ro()[i];
        func(key, val);
      }
      // move to the next leaf node
      leaf = leaf->nextLeaf;
    }
483
  }
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503

#ifndef UNIT_TESTS
  private:
#endif

  /**
   * Insert a (key, value) pair into the corresponding leaf node. It is the
   * responsibility of the caller to make sure that the node @c node is
   * the correct node. The key is inserted at the correct position.
   *
   * @param node the node where the key-value pair is inserted.
   * @param key the key to be inserted
   * @param val the value associated with the key
   * @param splitInfo information about a possible split of the node
   */
  bool insertInLeafNode(persistent_ptr<LeafNode> node, const KeyType &key,
      const ValueType &val, SplitInfo *splitInfo) {
    bool split = false;
    auto pos = lookupPositionInLeafNode(node, key);

504
    if (pos < M) {
505
506
507
      // handle insert of duplicates
      node->values.get_rw()[pos] = val;
      return false;
508
    } 
509

510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
    pos = node->search.get_ro().data.getFreeZero();
    if (pos == M) {
      // the node is full, so we must split it
      // determine the split position by finding median in unsorted array of keys
      auto data = node->keys.get_ro();
      KeyType middle = ElementOfRankK::elementOfRankK((M + 1) / 2, data, 0, M);
      
      // copy leaf
      persistent_ptr<LeafNode> sibling = newLeafNode(node);
      for (auto i = 0u; i < M; i++) {
        KeyType currkey = node->keys.get_ro()[i];
        if (currkey > middle) 
					node->search.get_rw().data.b.reset(i);
        else
					sibling->search.get_rw().data.b.reset(i);
525
526
527
      }

      // insert the new entry
528
529
      const auto rightMin = sibling->keys.get_ro()[findMinKeyAtLeafNode(sibling)];
      if (key < rightMin)
530
        insertInLeafNodeAtPosition(node, node->search.get_ro().data.getFreeZero(), key, val);
531
      else
532
        insertInLeafNodeAtPosition(sibling, sibling->search.get_ro().data.getFreeZero(), key, val);
533
534
535
536
537
538
539
540
541
542
543
544
545

      // setup the list of leaf nodes
      if (node->nextLeaf != nullptr) {
        sibling->nextLeaf = node->nextLeaf;
        node->nextLeaf->prevLeaf = sibling;
      }
      node->nextLeaf = sibling;
      sibling->prevLeaf = node;

      // and inform the caller about the split
      split = true;
      splitInfo->leftChild = node;
      splitInfo->rightChild = sibling;
546
      splitInfo->key = rightMin;
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
    } else {
      // otherwise, we can simply insert the new entry at the given position
      insertInLeafNodeAtPosition(node, pos, key, val);
    }
    return split;
  }

  /**
   * Insert a (key, value) pair at the given position @c pos into the leaf node
   * @c node. The caller has to ensure that
   * - there is enough space to insert the element
   * - the key is inserted at the correct position according to the order of
   * keys
   *
   * @oaram node the leaf node where the element is to be inserted
   * @param pos the position in the leaf node (0 <= pos <= numKeys < M)
   * @param key the key of the element
   * @param val the actual value corresponding to the key
   */
  void insertInLeafNodeAtPosition(persistent_ptr<LeafNode> node, unsigned int pos,
      const KeyType &key, const ValueType &val) {
    assert(pos < M);
569
570
571
    // set bit and hash
    node->search.get_rw().data.b.set(pos);
    node->search.get_rw().data.fp[pos] = fpHash(key);
572

573
    // insert the new entry at the given position
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
    node->keys.get_rw()[pos] = key;
    node->values.get_rw()[pos] = val;
  }

  /**
   * Insert a (key, value) pair into the tree recursively by following the path
   * down to the leaf level starting at node @c node at depth @c depth.
   *
   * @param node the starting node for the insert
   * @param depth the current depth of the tree (0 == leaf level)
   * @param key the key of the element
   * @param val the actual value corresponding to the key
   * @param splitInfo information about the split
   * @return true if a split was performed
   */
  bool insertInBranchNode(BranchNode *node, unsigned int depth,
      const KeyType &key, const ValueType &val,
      SplitInfo *splitInfo) {
    SplitInfo childSplitInfo;
    bool split = false, hasSplit = false;

    auto pos = lookupPositionInBranchNode(node, key);
596
597
598
599
    if (depth == 1) {
      //case #1: our children are leaf nodes
      auto child = node->children[pos].leaf;
      hasSplit = insertInLeafNode(child, key, val, &childSplitInfo);
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
    } else {
      // case #2: our children are branch nodes
      auto child = node->children[pos].branch;
      hasSplit = insertInBranchNode(child, depth - 1, key, val, &childSplitInfo);
    }
    if (hasSplit) {
      BranchNode *host = node;
      // the child node was split, thus we have to add a new entry
      // to our branch node
      if (node->numKeys == N) {
        splitBranchNode(node, childSplitInfo.key, splitInfo);

        host = (key < splitInfo->key ? splitInfo->leftChild
            : splitInfo->rightChild).branch;
        split = true;
        pos = lookupPositionInBranchNode(host, key);
      }
      if (pos < host->numKeys) {
        // if the child isn't inserted at the rightmost position
        // then we have to make space for it
        host->children[host->numKeys + 1] = host->children[host->numKeys];
        for (auto i = host->numKeys; i > pos; i--) {
          host->children[i] = host->children[i - 1];
          host->keys[i] = host->keys[i - 1];
        }
      }
      // finally, add the new entry at the given position
      host->keys[pos] = childSplitInfo.key;
      host->children[pos] = childSplitInfo.leftChild;
      host->children[pos + 1] = childSplitInfo.rightChild;
      host->numKeys = host->numKeys + 1;
    }
    return split;
  }

  /**
   * Split the given branch node @c node in the middle and move
   * half of the keys/children to the new sibling node.
   *
   * @param node the branch node to be split
   * @param splitKey the key on which the split of the child occured
   * @param splitInfo information about the split
   */
  void splitBranchNode(BranchNode *node, const KeyType &splitKey,
      SplitInfo *splitInfo) {
    // we have an overflow at the branch node, let's split it
    // determine the split position
    unsigned int middle = (N + 1) / 2;
    // adjust the middle based on the key we have to insert
    if (splitKey > node->keys[middle]) middle++;
650

651
652
653
654
655
656
657
658
659
    // move all entries behind this position to a new sibling node
    BranchNode *sibling = newBranchNode();
    sibling->numKeys = node->numKeys - middle;
    for (auto i = 0u; i < sibling->numKeys; i++) {
      sibling->keys[i] = node->keys[middle + i];
      sibling->children[i] = node->children[middle + i];
    }
    sibling->children[sibling->numKeys] = node->children[node->numKeys];
    node->numKeys = middle - 1;
660

661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
    splitInfo->key = node->keys[middle - 1];
    splitInfo->leftChild = node;
    splitInfo->rightChild = sibling;
  }

  /**
   * Traverse the tree starting at the root until the leaf node is found that
   * could contain the given @key. Note, that always a leaf node is returned
   * even if the key doesn't exist on this node.
   *
   * @param key the key we are looking for
   * @return the leaf node that would store the key
   */
  persistent_ptr<LeafNode> findLeafNode(const KeyType &key) const {
    auto node = rootNode;

    auto d = depth;
678
    while (d-- > 0) {
679
680
681
682
683
684
685
686
687
      auto n = node.branch;
      auto pos = lookupPositionInBranchNode(n, key);
      node = n->children[pos];
    }
    return node.leaf;
  }
  /**
   * Lookup the search key @c key in the given leaf node and return the
   * position.
688
   * If the search key was not found, then @c M is returned.
689
690
691
   *
   * @param node the leaf node where we search
   * @param key the search key
692
   * @return the position of the key  (or @c M if not found)
693
694
695
696
   */
  unsigned int lookupPositionInLeafNode(persistent_ptr<LeafNode> node,
      const KeyType &key) const {
    unsigned int pos = 0;
697
    const auto hash = fpHash(key);
698
699
    for (; pos < M ; pos++) {
      if(node->search.get_ro().data.b.test(pos) && 
700
         node->search.get_ro().data.fp[pos] == hash && 
701
702
703
         node->keys.get_ro()[pos] == key)
        break;
    }
704
705
706
707
    return pos;
  }

  /**
708
   * Lookup the search key @c key in the given branch node and return the
709
710
711
712
713
714
   * position which is the position in the list of keys + 1. in this way, the
   * position corresponds to the position of the child pointer in the
   * array @children.
   * If the search key is less than the smallest key, then @c 0 is returned.
   * If the key is greater than the largest key, then @c numKeys is returned.
   *
715
   * @param node the branch node where we search
716
717
718
   * @param key the search key
   * @return the position of the key + 1 (or 0 or @c numKey)
   */
719
  unsigned int lookupPositionInBranchNode(BranchNode *node,
720
      const KeyType &key) const {
721
722
    auto pos = 0u;
    for (; pos < node->numKeys && node->keys[pos] <= key; pos++);
723
    return pos;
724
    //return binarySearch(node, 0, node->numKeys-1, key);
725
726
  }

727
728
729
  template<typename Node>
  unsigned int binarySearch(Node *node, int l, int r,
                            KeyType const &key) const {
730
    auto pos = 0u;
731
732
733
734
735
736
    while (l <= r) {
      pos = (l + r) / 2;
      if (node->keys[pos] == key) return ++pos;
      if (node->keys[pos] < key) l = ++pos;
      else r = pos - 1;
    }
737
738
739
    return pos;
  }

740

741
742
743
744
745
746
747
748
749
  /**
   * Delete the element with the given key from the given leaf node.
   *
   * @param node the leaf node from which the element is deleted
   * @param key the key of the element to be deleted
   * @return true of the element was deleted
   */
  bool eraseFromLeafNode(persistent_ptr <LeafNode> node, const KeyType &key) {
    auto pos = lookupPositionInLeafNode(node, key);
750
751
752
    if (pos < M) {
      node->search.get_rw().data.b.reset(pos);
      return true;
753
    }
754
    return false;
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
  }

  /**
   * Delete an entry from the tree by recursively going down to the leaf level
   * and handling the underflows.
   *
   * @param node the current branch node
   * @param d the current depth of the traversal
   * @param key the key to be deleted
   * @return true if the entry was deleted
   */
  bool eraseFromBranchNode(BranchNode *node, unsigned int d, const KeyType &key) {
    assert(d >= 1);
    bool deleted = false;
    // try to find the branch
    auto pos = lookupPositionInBranchNode(node, key);
771
772
773
774
775
    if (d == 1) {
      // the next level is the leaf level
      auto leaf = node->children[pos].leaf;
      assert(leaf != nullptr);
      deleted = eraseFromLeafNode(leaf, key);
776
      unsigned int middle = (M + 1) / 2;
777
      if (leaf->search.get_ro().data.b.count() < middle) {
778
        // handle underflow
779
        underflowAtLeafLevel(node, pos, leaf);
780
781
782
783
784
785
786
787
788
789
790
791
792
      }
    } else {
      auto child = node->children[pos].branch;
      deleted = eraseFromBranchNode(child, d - 1, key);

      pos = lookupPositionInBranchNode(node, key);
      unsigned int middle = (N + 1) / 2;
      if (child->numKeys < middle) {
        // handle underflow
        child = underflowAtBranchLevel(node, pos, child);
        if (d == depth && node->numKeys == 0) {
          // special case: the root node is empty now
          rootNode = child;
793
          --depth;
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
        }
      }
    }
    return deleted;
  }

  /**
   * Handle the case that during a delete operation a underflow at node @c leaf
   * occured. If possible this is handled
   * (1) by rebalancing the elements among the leaf node and one of its siblings
   * (2) if not possible by merging with one of its siblings.
   *
   * @param node the parent node of the node where the underflow occured
   * @param pos the position of the child node @leaf in the @c children array of
   * the lowest branch node
   * @param leaf the node at which the underflow occured
   */
811
812
  void underflowAtLeafLevel(BranchNode *node, unsigned int pos,
      persistent_ptr<LeafNode> leaf) {
813
814
815
816
      assert(pos <= node->numKeys);
      unsigned int middle = (M + 1) / 2;
      // 1. we check whether we can rebalance with one of the siblings
      // but only if both nodes have the same direct parent
817
      if (pos > 0 && leaf->prevLeaf->search.get_ro().data.b.count() > middle) {
818
819
820
        // we have a sibling at the left for rebalancing the keys
        balanceLeafNodes(leaf->prevLeaf, leaf);

821
822
        node->keys[pos - 1] = leaf->keys.get_ro()[findMinKeyAtLeafNode(leaf)];
      } else if (pos < node->numKeys && leaf->nextLeaf->search.get_ro().data.b.count() > middle) {
823
824
825
        // we have a sibling at the right for rebalancing the keys
        balanceLeafNodes(leaf->nextLeaf, leaf);

826
        node->keys[pos] = leaf->nextLeaf->keys.get_ro()[findMinKeyAtLeafNode(leaf->nextLeaf)];
827
828
829
830
      } else {
        // 2. if this fails we have to merge two leaf nodes
        // but only if both nodes have the same direct parent
        persistent_ptr <LeafNode> survivor = nullptr;
831
        if (pos > 0 && leaf->prevLeaf->search.get_ro().data.b.count() <= middle) {
832
833
          survivor = mergeLeafNodes(leaf->prevLeaf, leaf);
          deleteLeafNode(leaf);
834
        } else if (pos < node->numKeys && leaf->nextLeaf->search.get_ro().data.b.count() <= middle) {
835
836
837
          // because we update the pointers in mergeLeafNodes
          // we keep it here
          auto l = leaf->nextLeaf;
838
          survivor = mergeLeafNodes(leaf, l);
839
840
841
842
843
844
845
846
847
848
849
850
851
          deleteLeafNode(l);
        } else {
          // this shouldn't happen?!
          assert(false);
        }
        if (node->numKeys > 1) {
          if (pos > 0) pos--;
          // just remove the child node from the current lowest branch node
          for (auto i = pos; i < node->numKeys - 1; i++) {
            node->keys[i] = node->keys[i + 1];
            node->children[i + 1] = node->children[i + 2];
          }
          node->children[pos] = survivor;
852
          --node->numKeys;
853
854
855
        } else {
          // This is a special case that happens only if
          // the current node is the root node. Now, we have
856
          // to replace the branch root node by a leaf node.
857
          rootNode = survivor;
858
          --depth;
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
        }
      }
    }

  /**
   * Handle the case that during a delete operation a underflow at node @c child
   * occured where @c node is the parent node. If possible this is handled
   * (1) by rebalancing the elements among the node @c child and one of its
   * siblings
   * (2) if not possible by merging with one of its siblings.
   *
   * @param node the parent node of the node where the underflow occured
   * @param pos the position of the child node @child in the @c children array
   * of the branch node
   * @param child the node at which the underflow occured
   * @return the (possibly new) child node (in case of a merge)
   */
  BranchNode* underflowAtBranchLevel(BranchNode *node, unsigned int pos,
877
                                     BranchNode* child) {
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
    assert(node != nullptr);
    assert(child != nullptr);

    BranchNode *newChild = child;
    unsigned int middle = (N + 1) / 2;
    // 1. we check whether we can rebalance with one of the siblings

    if (pos > 0 &&
        node->children[pos - 1].branch->numKeys >middle) {
      // we have a sibling at the left for rebalancing the keys

      BranchNode *sibling = node->children[pos - 1].branch;
      balanceBranchNodes(sibling, child, node, pos - 1);
      // node->keys.get_rw()[pos] = child->keys.get_ro()[0];
      return newChild;
    } else if (pos < node->numKeys && node->children[pos + 1].branch->numKeys > middle) {
      // we have a sibling at the right for rebalancing the keys
      auto sibling = node->children[pos + 1].branch;
      balanceBranchNodes(sibling, child, node, pos);

      return newChild;
    } else {

      // 2. if this fails we have to merge two branch nodes
      BranchNode *lSibling = nullptr, *rSibling = nullptr;
      unsigned int prevKeys = 0, nextKeys = 0;

      if (pos > 0) {

        lSibling = node->children[pos - 1].branch;
        prevKeys = lSibling->numKeys;
      }
      if (pos < node->numKeys) {

        rSibling = node->children[pos + 1].branch;
        nextKeys = rSibling->numKeys;
      }

      BranchNode *witnessNode = nullptr;
      auto ppos = pos;
      if (prevKeys > 0) {

        mergeBranchNodes(lSibling, node->keys[pos - 1], child);
        ppos = pos - 1;
        witnessNode = child;
        newChild = lSibling;
        // pos -= 1;
      } else if (nextKeys > 0) {

        mergeBranchNodes(child, node->keys[pos], rSibling);
        witnessNode = rSibling;
      } else
        // shouldn't happen
        assert(false);

      // remove node->keys.get_ro()[pos] from node
      for (auto i = ppos; i < node->numKeys - 1; i++) {

        node->keys[i] = node->keys[i + 1];
      }
      if (pos == 0) pos++;
      for (auto i = pos; i < node->numKeys; i++) {
        if (i + 1 <= node->numKeys) {


          node->children[i] = node->children[i + 1];
        }
      }
      node->numKeys--;

      deleteBranchNode(witnessNode);
      return newChild;
    }
  }

  /**
   * Redistribute (key, value) pairs from the leaf node @c donor to
   * the leaf node @c receiver such that both nodes have approx. the same
   * number of elements. This method is used in case of an underflow
   * situation of a leaf node.
   *
   * @param donor the leaf node from which the elements are taken
   * @param receiver the sibling leaf node getting the elements from @c donor
   */
  void balanceLeafNodes(persistent_ptr <LeafNode> donor, persistent_ptr <LeafNode> receiver) {
963
964
965
966
967
		const auto dNumKeys = donor->search.get_ro().data.b.count();
		const auto rNumKeys = receiver->search.get_ro().data.b.count();
    assert(dNumKeys > rNumKeys);
    unsigned int balancedNum = (dNumKeys + rNumKeys) / 2;
    unsigned int toMove = dNumKeys - balancedNum;
968
969
970
    if (toMove == 0) return;

    if (donor->keys.get_ro()[0] < receiver->keys.get_ro()[0]) {
971
972
973
974
975
976
977
978
979
980
981
      // move to a node with larger keys
			// move toMove keys/values from donor to receiver
			for (auto i = 0u; i < toMove; i++) {
				const auto max = findMaxKeyAtLeafNode(donor);
				const auto pos = receiver->search.get_ro().data.getFreeZero();
				
				receiver->search.get_rw().data.b.set(pos);
				receiver->search.get_rw().data.fp[pos] = fpHash(donor->keys.get_ro()[max]);
				receiver->keys.get_rw()[pos] = donor->keys.get_ro()[max];
				receiver->values.get_rw()[pos] = donor->values.get_ro()[max];
        donor->search.get_rw().data.b.reset(max);
982
983
      }
    } else {
984
      // move to a node with smaller keys
985
      // move toMove keys/values from donor to receiver
986
987
988
989
990
991
992
993
994
			for (auto i = 0u; i < toMove; i++) {
				const auto min = findMinKeyAtLeafNode(donor);
				const auto pos = receiver->search.get_ro().data.getFreeZero();
				
				receiver->search.get_rw().data.b.set(pos);
				receiver->search.get_rw().data.fp[pos] = fpHash(donor->keys.get_ro()[min]);
				receiver->keys.get_rw()[pos] = donor->keys.get_ro()[min];
				receiver->values.get_rw()[pos] = donor->values.get_ro()[min];
        donor->search.get_rw().data.b.reset(min);
995
      }
996
997
998
999
		}
  }
  
  /**
1000
   * Find position of the minimum key in unsorted leaf
For faster browsing, not all history is shown. View entire blame