1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
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
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
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
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
|
#pragma once
#ifdef __GNUC__
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-parameter"
#endif
//===- llvm/ADT/SparseMultiSet.h - Sparse multiset --------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
///
/// \file
/// This file defines the SparseMultiSet class, which adds multiset behavior to
/// the SparseSet.
///
/// A sparse multiset holds a small number of objects identified by integer keys
/// from a moderately sized universe. The sparse multiset uses more memory than
/// other containers in order to provide faster operations. Any key can map to
/// multiple values. A SparseMultiSetNode class is provided, which serves as a
/// convenient base class for the contents of a SparseMultiSet.
///
//===----------------------------------------------------------------------===//
#ifndef LLVM_ADT_SPARSEMULTISET_H
#define LLVM_ADT_SPARSEMULTISET_H
#include "llvm/ADT/identity.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/SparseSet.h"
#include <cassert>
#include <cstdint>
#include <cstdlib>
#include <iterator>
#include <limits>
#include <utility>
namespace llvm {
/// Fast multiset implementation for objects that can be identified by small
/// unsigned keys.
///
/// SparseMultiSet allocates memory proportional to the size of the key
/// universe, so it is not recommended for building composite data structures.
/// It is useful for algorithms that require a single set with fast operations.
///
/// Compared to DenseSet and DenseMap, SparseMultiSet provides constant-time
/// fast clear() as fast as a vector. The find(), insert(), and erase()
/// operations are all constant time, and typically faster than a hash table.
/// The iteration order doesn't depend on numerical key values, it only depends
/// on the order of insert() and erase() operations. Iteration order is the
/// insertion order. Iteration is only provided over elements of equivalent
/// keys, but iterators are bidirectional.
///
/// Compared to BitVector, SparseMultiSet<unsigned> uses 8x-40x more memory, but
/// offers constant-time clear() and size() operations as well as fast iteration
/// independent on the size of the universe.
///
/// SparseMultiSet contains a dense vector holding all the objects and a sparse
/// array holding indexes into the dense vector. Most of the memory is used by
/// the sparse array which is the size of the key universe. The SparseT template
/// parameter provides a space/speed tradeoff for sets holding many elements.
///
/// When SparseT is uint32_t, find() only touches up to 3 cache lines, but the
/// sparse array uses 4 x Universe bytes.
///
/// When SparseT is uint8_t (the default), find() touches up to 3+[N/256] cache
/// lines, but the sparse array is 4x smaller. N is the number of elements in
/// the set.
///
/// For sets that may grow to thousands of elements, SparseT should be set to
/// uint16_t or uint32_t.
///
/// Multiset behavior is provided by providing doubly linked lists for values
/// that are inlined in the dense vector. SparseMultiSet is a good choice when
/// one desires a growable number of entries per key, as it will retain the
/// SparseSet algorithmic properties despite being growable. Thus, it is often a
/// better choice than a SparseSet of growable containers or a vector of
/// vectors. SparseMultiSet also keeps iterators valid after erasure (provided
/// the iterators don't point to the element erased), allowing for more
/// intuitive and fast removal.
///
/// @tparam ValueT The type of objects in the set.
/// @tparam KeyFunctorT A functor that computes an unsigned index from KeyT.
/// @tparam SparseT An unsigned integer type. See above.
///
template<typename ValueT,
typename KeyFunctorT = identity<unsigned>,
typename SparseT = uint8_t>
class SparseMultiSet {
static_assert(std::numeric_limits<SparseT>::is_integer &&
!std::numeric_limits<SparseT>::is_signed,
"SparseT must be an unsigned integer type");
/// The actual data that's stored, as a doubly-linked list implemented via
/// indices into the DenseVector. The doubly linked list is implemented
/// circular in Prev indices, and INVALID-terminated in Next indices. This
/// provides efficient access to list tails. These nodes can also be
/// tombstones, in which case they are actually nodes in a single-linked
/// freelist of recyclable slots.
struct SMSNode {
static constexpr unsigned INVALID = ~0U;
ValueT Data;
unsigned Prev;
unsigned Next;
SMSNode(ValueT D, unsigned P, unsigned N) : Data(D), Prev(P), Next(N) {}
/// List tails have invalid Nexts.
bool isTail() const {
return Next == INVALID;
}
/// Whether this node is a tombstone node, and thus is in our freelist.
bool isTombstone() const {
return Prev == INVALID;
}
/// Since the list is circular in Prev, all non-tombstone nodes have a valid
/// Prev.
bool isValid() const { return Prev != INVALID; }
};
using KeyT = typename KeyFunctorT::argument_type;
using DenseT = SmallVector<SMSNode, 8>;
DenseT Dense;
SparseT *Sparse = nullptr;
unsigned Universe = 0;
KeyFunctorT KeyIndexOf;
SparseSetValFunctor<KeyT, ValueT, KeyFunctorT> ValIndexOf;
/// We have a built-in recycler for reusing tombstone slots. This recycler
/// puts a singly-linked free list into tombstone slots, allowing us quick
/// erasure, iterator preservation, and dense size.
unsigned FreelistIdx = SMSNode::INVALID;
unsigned NumFree = 0;
unsigned sparseIndex(const ValueT &Val) const {
assert(ValIndexOf(Val) < Universe &&
"Invalid key in set. Did object mutate?");
return ValIndexOf(Val);
}
unsigned sparseIndex(const SMSNode &N) const { return sparseIndex(N.Data); }
/// Whether the given entry is the head of the list. List heads's previous
/// pointers are to the tail of the list, allowing for efficient access to the
/// list tail. D must be a valid entry node.
bool isHead(const SMSNode &D) const {
assert(D.isValid() && "Invalid node for head");
return Dense[D.Prev].isTail();
}
/// Whether the given entry is a singleton entry, i.e. the only entry with
/// that key.
bool isSingleton(const SMSNode &N) const {
assert(N.isValid() && "Invalid node for singleton");
// Is N its own predecessor?
return &Dense[N.Prev] == &N;
}
/// Add in the given SMSNode. Uses a free entry in our freelist if
/// available. Returns the index of the added node.
unsigned addValue(const ValueT& V, unsigned Prev, unsigned Next) {
if (NumFree == 0) {
Dense.push_back(SMSNode(V, Prev, Next));
return Dense.size() - 1;
}
// Peel off a free slot
unsigned Idx = FreelistIdx;
unsigned NextFree = Dense[Idx].Next;
assert(Dense[Idx].isTombstone() && "Non-tombstone free?");
Dense[Idx] = SMSNode(V, Prev, Next);
FreelistIdx = NextFree;
--NumFree;
return Idx;
}
/// Make the current index a new tombstone. Pushes it onto the freelist.
void makeTombstone(unsigned Idx) {
Dense[Idx].Prev = SMSNode::INVALID;
Dense[Idx].Next = FreelistIdx;
FreelistIdx = Idx;
++NumFree;
}
public:
using value_type = ValueT;
using reference = ValueT &;
using const_reference = const ValueT &;
using pointer = ValueT *;
using const_pointer = const ValueT *;
using size_type = unsigned;
SparseMultiSet() = default;
SparseMultiSet(const SparseMultiSet &) = delete;
SparseMultiSet &operator=(const SparseMultiSet &) = delete;
~SparseMultiSet() { free(Sparse); }
/// Set the universe size which determines the largest key the set can hold.
/// The universe must be sized before any elements can be added.
///
/// @param U Universe size. All object keys must be less than U.
///
void setUniverse(unsigned U) {
// It's not hard to resize the universe on a non-empty set, but it doesn't
// seem like a likely use case, so we can add that code when we need it.
assert(empty() && "Can only resize universe on an empty map");
// Hysteresis prevents needless reallocations.
if (U >= Universe/4 && U <= Universe)
return;
free(Sparse);
// The Sparse array doesn't actually need to be initialized, so malloc
// would be enough here, but that will cause tools like valgrind to
// complain about branching on uninitialized data.
Sparse = static_cast<SparseT*>(safe_calloc(U, sizeof(SparseT)));
Universe = U;
}
/// Our iterators are iterators over the collection of objects that share a
/// key.
template <typename SMSPtrTy> class iterator_base {
friend class SparseMultiSet;
public:
using iterator_category = std::bidirectional_iterator_tag;
using value_type = ValueT;
using difference_type = std::ptrdiff_t;
using pointer = value_type *;
using reference = value_type &;
private:
SMSPtrTy SMS;
unsigned Idx;
unsigned SparseIdx;
iterator_base(SMSPtrTy P, unsigned I, unsigned SI)
: SMS(P), Idx(I), SparseIdx(SI) {}
/// Whether our iterator has fallen outside our dense vector.
bool isEnd() const {
if (Idx == SMSNode::INVALID)
return true;
assert(Idx < SMS->Dense.size() && "Out of range, non-INVALID Idx?");
return false;
}
/// Whether our iterator is properly keyed, i.e. the SparseIdx is valid
bool isKeyed() const { return SparseIdx < SMS->Universe; }
unsigned Prev() const { return SMS->Dense[Idx].Prev; }
unsigned Next() const { return SMS->Dense[Idx].Next; }
void setPrev(unsigned P) { SMS->Dense[Idx].Prev = P; }
void setNext(unsigned N) { SMS->Dense[Idx].Next = N; }
public:
reference operator*() const {
assert(isKeyed() && SMS->sparseIndex(SMS->Dense[Idx].Data) == SparseIdx &&
"Dereferencing iterator of invalid key or index");
return SMS->Dense[Idx].Data;
}
pointer operator->() const { return &operator*(); }
/// Comparison operators
bool operator==(const iterator_base &RHS) const {
// end compares equal
if (SMS == RHS.SMS && Idx == RHS.Idx) {
assert((isEnd() || SparseIdx == RHS.SparseIdx) &&
"Same dense entry, but different keys?");
return true;
}
return false;
}
bool operator!=(const iterator_base &RHS) const {
return !operator==(RHS);
}
/// Increment and decrement operators
iterator_base &operator--() { // predecrement - Back up
assert(isKeyed() && "Decrementing an invalid iterator");
assert((isEnd() || !SMS->isHead(SMS->Dense[Idx])) &&
"Decrementing head of list");
// If we're at the end, then issue a new find()
if (isEnd())
Idx = SMS->findIndex(SparseIdx).Prev();
else
Idx = Prev();
return *this;
}
iterator_base &operator++() { // preincrement - Advance
assert(!isEnd() && isKeyed() && "Incrementing an invalid/end iterator");
Idx = Next();
return *this;
}
iterator_base operator--(int) { // postdecrement
iterator_base I(*this);
--*this;
return I;
}
iterator_base operator++(int) { // postincrement
iterator_base I(*this);
++*this;
return I;
}
};
using iterator = iterator_base<SparseMultiSet *>;
using const_iterator = iterator_base<const SparseMultiSet *>;
// Convenience types
using RangePair = std::pair<iterator, iterator>;
/// Returns an iterator past this container. Note that such an iterator cannot
/// be decremented, but will compare equal to other end iterators.
iterator end() { return iterator(this, SMSNode::INVALID, SMSNode::INVALID); }
const_iterator end() const {
return const_iterator(this, SMSNode::INVALID, SMSNode::INVALID);
}
/// Returns true if the set is empty.
///
/// This is not the same as BitVector::empty().
///
bool empty() const { return size() == 0; }
/// Returns the number of elements in the set.
///
/// This is not the same as BitVector::size() which returns the size of the
/// universe.
///
size_type size() const {
assert(NumFree <= Dense.size() && "Out-of-bounds free entries");
return Dense.size() - NumFree;
}
/// Clears the set. This is a very fast constant time operation.
///
void clear() {
// Sparse does not need to be cleared, see find().
Dense.clear();
NumFree = 0;
FreelistIdx = SMSNode::INVALID;
}
/// Find an element by its index.
///
/// @param Idx A valid index to find.
/// @returns An iterator to the element identified by key, or end().
///
iterator findIndex(unsigned Idx) {
assert(Idx < Universe && "Key out of range");
const unsigned Stride = std::numeric_limits<SparseT>::max() + 1u;
for (unsigned i = Sparse[Idx], e = Dense.size(); i < e; i += Stride) {
const unsigned FoundIdx = sparseIndex(Dense[i]);
// Check that we're pointing at the correct entry and that it is the head
// of a valid list.
if (Idx == FoundIdx && Dense[i].isValid() && isHead(Dense[i]))
return iterator(this, i, Idx);
// Stride is 0 when SparseT >= unsigned. We don't need to loop.
if (!Stride)
break;
}
return end();
}
/// Find an element by its key.
///
/// @param Key A valid key to find.
/// @returns An iterator to the element identified by key, or end().
///
iterator find(const KeyT &Key) {
return findIndex(KeyIndexOf(Key));
}
const_iterator find(const KeyT &Key) const {
iterator I = const_cast<SparseMultiSet*>(this)->findIndex(KeyIndexOf(Key));
return const_iterator(I.SMS, I.Idx, KeyIndexOf(Key));
}
/// Returns the number of elements identified by Key. This will be linear in
/// the number of elements of that key.
size_type count(const KeyT &Key) const {
unsigned Ret = 0;
for (const_iterator It = find(Key); It != end(); ++It)
++Ret;
return Ret;
}
/// Returns true if this set contains an element identified by Key.
bool contains(const KeyT &Key) const {
return find(Key) != end();
}
/// Return the head and tail of the subset's list, otherwise returns end().
iterator getHead(const KeyT &Key) { return find(Key); }
iterator getTail(const KeyT &Key) {
iterator I = find(Key);
if (I != end())
I = iterator(this, I.Prev(), KeyIndexOf(Key));
return I;
}
/// The bounds of the range of items sharing Key K. First member is the head
/// of the list, and the second member is a decrementable end iterator for
/// that key.
RangePair equal_range(const KeyT &K) {
iterator B = find(K);
iterator E = iterator(this, SMSNode::INVALID, B.SparseIdx);
return std::make_pair(B, E);
}
/// Insert a new element at the tail of the subset list. Returns an iterator
/// to the newly added entry.
iterator insert(const ValueT &Val) {
unsigned Idx = sparseIndex(Val);
iterator I = findIndex(Idx);
unsigned NodeIdx = addValue(Val, SMSNode::INVALID, SMSNode::INVALID);
if (I == end()) {
// Make a singleton list
Sparse[Idx] = NodeIdx;
Dense[NodeIdx].Prev = NodeIdx;
return iterator(this, NodeIdx, Idx);
}
// Stick it at the end.
unsigned HeadIdx = I.Idx;
unsigned TailIdx = I.Prev();
Dense[TailIdx].Next = NodeIdx;
Dense[HeadIdx].Prev = NodeIdx;
Dense[NodeIdx].Prev = TailIdx;
return iterator(this, NodeIdx, Idx);
}
/// Erases an existing element identified by a valid iterator.
///
/// This invalidates iterators pointing at the same entry, but erase() returns
/// an iterator pointing to the next element in the subset's list. This makes
/// it possible to erase selected elements while iterating over the subset:
///
/// tie(I, E) = Set.equal_range(Key);
/// while (I != E)
/// if (test(*I))
/// I = Set.erase(I);
/// else
/// ++I;
///
/// Note that if the last element in the subset list is erased, this will
/// return an end iterator which can be decremented to get the new tail (if it
/// exists):
///
/// tie(B, I) = Set.equal_range(Key);
/// for (bool isBegin = B == I; !isBegin; /* empty */) {
/// isBegin = (--I) == B;
/// if (test(I))
/// break;
/// I = erase(I);
/// }
iterator erase(iterator I) {
assert(I.isKeyed() && !I.isEnd() && !Dense[I.Idx].isTombstone() &&
"erasing invalid/end/tombstone iterator");
// First, unlink the node from its list. Then swap the node out with the
// dense vector's last entry
iterator NextI = unlink(Dense[I.Idx]);
// Put in a tombstone.
makeTombstone(I.Idx);
return NextI;
}
/// Erase all elements with the given key. This invalidates all
/// iterators of that key.
void eraseAll(const KeyT &K) {
for (iterator I = find(K); I != end(); /* empty */)
I = erase(I);
}
private:
/// Unlink the node from its list. Returns the next node in the list.
iterator unlink(const SMSNode &N) {
if (isSingleton(N)) {
// Singleton is already unlinked
assert(N.Next == SMSNode::INVALID && "Singleton has next?");
return iterator(this, SMSNode::INVALID, ValIndexOf(N.Data));
}
if (isHead(N)) {
// If we're the head, then update the sparse array and our next.
Sparse[sparseIndex(N)] = N.Next;
Dense[N.Next].Prev = N.Prev;
return iterator(this, N.Next, ValIndexOf(N.Data));
}
if (N.isTail()) {
// If we're the tail, then update our head and our previous.
findIndex(sparseIndex(N)).setPrev(N.Prev);
Dense[N.Prev].Next = N.Next;
// Give back an end iterator that can be decremented
iterator I(this, N.Prev, ValIndexOf(N.Data));
return ++I;
}
// Otherwise, just drop us
Dense[N.Next].Prev = N.Prev;
Dense[N.Prev].Next = N.Next;
return iterator(this, N.Next, ValIndexOf(N.Data));
}
};
} // end namespace llvm
#endif // LLVM_ADT_SPARSEMULTISET_H
#ifdef __GNUC__
#pragma GCC diagnostic pop
#endif
|