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1 : : // Copyright (c) The Bitcoin Core developers
2 : : // Distributed under the MIT software license, see the accompanying
3 : : // file COPYING or http://www.opensource.org/licenses/mit-license.php.
4 : :
5 : : #ifndef BITCOIN_CLUSTER_LINEARIZE_H
6 : : #define BITCOIN_CLUSTER_LINEARIZE_H
7 : :
8 : : #include <algorithm>
9 : : #include <cstdint>
10 : : #include <numeric>
11 : : #include <optional>
12 : : #include <utility>
13 : : #include <vector>
14 : :
15 : : #include <memusage.h>
16 : : #include <random.h>
17 : : #include <span.h>
18 : : #include <util/feefrac.h>
19 : : #include <util/vecdeque.h>
20 : :
21 : : namespace cluster_linearize {
22 : :
23 : : /** Data type to represent transaction indices in DepGraphs and the clusters they represent. */
24 : : using DepGraphIndex = uint32_t;
25 : :
26 : : /** Data structure that holds a transaction graph's preprocessed data (fee, size, ancestors,
27 : : * descendants). */
28 : : template<typename SetType>
29 [ + + + - : 5653 : class DepGraph
+ - ][ + -
+ - + - +
- + - ]
30 : : {
31 : : /** Information about a single transaction. */
32 : : struct Entry
33 : : {
34 : : /** Fee and size of transaction itself. */
35 : 50090 : FeeFrac feerate;
36 : : /** All ancestors of the transaction (including itself). */
37 : 50090 : SetType ancestors;
38 : : /** All descendants of the transaction (including itself). */
39 : 50090 : SetType descendants;
40 : :
41 : : /** Equality operator (primarily for for testing purposes). */
42 [ + - + - : 100180 : friend bool operator==(const Entry&, const Entry&) noexcept = default;
- + ]
43 : :
44 : : /** Construct an empty entry. */
45 : 75582 : Entry() noexcept = default;
46 : : /** Construct an entry with a given feerate, ancestor set, descendant set. */
47 : 77239 : Entry(const FeeFrac& f, const SetType& a, const SetType& d) noexcept : feerate(f), ancestors(a), descendants(d) {}
48 : : };
49 : :
50 : : /** Data for each transaction. */
51 : : std::vector<Entry> entries;
52 : :
53 : : /** Which positions are used. */
54 : : SetType m_used;
55 : :
56 : : public:
57 : : /** Equality operator (primarily for testing purposes). */
58 : 1883 : friend bool operator==(const DepGraph& a, const DepGraph& b) noexcept
59 : : {
60 [ + - ]: 1883 : if (a.m_used != b.m_used) return false;
61 : : // Only compare the used positions within the entries vector.
62 [ + + + + ]: 52695 : for (auto idx : a.m_used) {
63 [ + - ]: 50090 : if (a.entries[idx] != b.entries[idx]) return false;
64 : : }
65 : : return true;
66 : : }
67 : :
68 : : // Default constructors.
69 : 184 : DepGraph() noexcept = default;
70 : : DepGraph(const DepGraph&) noexcept = default;
71 : : DepGraph(DepGraph&&) noexcept = default;
72 : 13 : DepGraph& operator=(const DepGraph&) noexcept = default;
73 : 3777 : DepGraph& operator=(DepGraph&&) noexcept = default;
74 : :
75 : : /** Construct a DepGraph object given another DepGraph and a mapping from old to new.
76 : : *
77 : : * @param depgraph The original DepGraph that is being remapped.
78 : : *
79 : : * @param mapping A span such that mapping[i] gives the position in the new DepGraph
80 : : * for position i in the old depgraph. Its size must be equal to
81 : : * depgraph.PositionRange(). The value of mapping[i] is ignored if
82 : : * position i is a hole in depgraph (i.e., if !depgraph.Positions()[i]).
83 : : *
84 : : * @param pos_range The PositionRange() for the new DepGraph. It must equal the largest
85 : : * value in mapping for any used position in depgraph plus 1, or 0 if
86 : : * depgraph.TxCount() == 0.
87 : : *
88 : : * Complexity: O(N^2) where N=depgraph.TxCount().
89 : : */
90 [ - + ]: 2814 : DepGraph(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> mapping, DepGraphIndex pos_range) noexcept : entries(pos_range)
91 : : {
92 [ - + ]: 2814 : Assume(mapping.size() == depgraph.PositionRange());
93 : 2814 : Assume((pos_range == 0) == (depgraph.TxCount() == 0));
94 [ + + ]: 77919 : for (DepGraphIndex i : depgraph.Positions()) {
95 : 75105 : auto new_idx = mapping[i];
96 : 75105 : Assume(new_idx < pos_range);
97 : : // Add transaction.
98 : 75105 : entries[new_idx].ancestors = SetType::Singleton(new_idx);
99 : 75105 : entries[new_idx].descendants = SetType::Singleton(new_idx);
100 : 75105 : m_used.Set(new_idx);
101 : : // Fill in fee and size.
102 : 75105 : entries[new_idx].feerate = depgraph.entries[i].feerate;
103 : : }
104 [ + + ]: 77919 : for (DepGraphIndex i : depgraph.Positions()) {
105 : : // Fill in dependencies by mapping direct parents.
106 : 75105 : SetType parents;
107 [ + + + + ]: 321075 : for (auto j : depgraph.GetReducedParents(i)) parents.Set(mapping[j]);
108 : 75105 : AddDependencies(parents, mapping[i]);
109 : : }
110 : : // Verify that the provided pos_range was correct (no unused positions at the end).
111 [ + - ]: 4551 : Assume(m_used.None() ? (pos_range == 0) : (pos_range == m_used.Last() + 1));
112 : 2814 : }
113 : :
114 : : /** Get the set of transactions positions in use. Complexity: O(1). */
115 [ + + + + : 33484 : const SetType& Positions() const noexcept { return m_used; }
+ - + - +
+ + + + +
+ - + + +
+ + - + -
+ - + - +
- + - ]
116 : : /** Get the range of positions in this DepGraph. All entries in Positions() are in [0, PositionRange() - 1]. */
117 [ - + - + : 5668 : DepGraphIndex PositionRange() const noexcept { return entries.size(); }
- + - + -
+ ][ - + -
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+ ]
118 : : /** Get the number of transactions in the graph. Complexity: O(1). */
119 [ - + - + ]: 452210 : auto TxCount() const noexcept { return m_used.Count(); }
[ + - + -
+ + + - +
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+ - + - +
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+ ]
120 : : /** Get the feerate of a given transaction i. Complexity: O(1). */
121 [ + - + + : 76119 : const FeeFrac& FeeRate(DepGraphIndex i) const noexcept { return entries[i].feerate; }
+ - + + +
- + + + -
+ + + - +
+ ]
122 : : /** Get the mutable feerate of a given transaction i. Complexity: O(1). */
123 [ + - + - ]: 121 : FeeFrac& FeeRate(DepGraphIndex i) noexcept { return entries[i].feerate; }
124 : : /** Get the ancestors of a given transaction i. Complexity: O(1). */
125 [ - - - - : 28855127 : const SetType& Ancestors(DepGraphIndex i) const noexcept { return entries[i].ancestors; }
- + ][ + +
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+ + - ]
126 : : /** Get the descendants of a given transaction i. Complexity: O(1). */
127 [ - - ][ + + : 1845590 : const SetType& Descendants(DepGraphIndex i) const noexcept { return entries[i].descendants; }
+ + + - +
- - + - +
- + - + -
+ - + - +
- + - + -
+ - + -
+ ]
128 : :
129 : : /** Add a new unconnected transaction to this transaction graph (in the first available
130 : : * position), and return its DepGraphIndex.
131 : : *
132 : : * Complexity: O(1) (amortized, due to resizing of backing vector).
133 : : */
134 : 77239 : DepGraphIndex AddTransaction(const FeeFrac& feefrac) noexcept
135 : : {
136 : : static constexpr auto ALL_POSITIONS = SetType::Fill(SetType::Size());
137 [ + - ]: 77239 : auto available = ALL_POSITIONS - m_used;
138 [ + - ]: 125164 : Assume(available.Any());
139 : 77239 : DepGraphIndex new_idx = available.First();
140 [ - + + - ]: 77239 : if (new_idx == entries.size()) {
141 : 77239 : entries.emplace_back(feefrac, SetType::Singleton(new_idx), SetType::Singleton(new_idx));
142 : : } else {
143 : 0 : entries[new_idx] = Entry(feefrac, SetType::Singleton(new_idx), SetType::Singleton(new_idx));
144 : : }
145 : 77239 : m_used.Set(new_idx);
146 : 77239 : return new_idx;
147 : : }
148 : :
149 : : /** Remove the specified positions from this DepGraph.
150 : : *
151 : : * The specified positions will no longer be part of Positions(), and dependencies with them are
152 : : * removed. Note that due to DepGraph only tracking ancestors/descendants (and not direct
153 : : * dependencies), if a parent is removed while a grandparent remains, the grandparent will
154 : : * remain an ancestor.
155 : : *
156 : : * Complexity: O(N) where N=TxCount().
157 : : */
158 : 28 : void RemoveTransactions(const SetType& del) noexcept
159 : : {
160 : 28 : m_used -= del;
161 : : // Remove now-unused trailing entries.
162 [ + + - + : 67 : while (!entries.empty() && !m_used[entries.size() - 1]) {
+ + ]
163 : 39 : entries.pop_back();
164 : : }
165 : : // Remove the deleted transactions from ancestors/descendants of other transactions. Note
166 : : // that the deleted positions will retain old feerate and dependency information. This does
167 : : // not matter as they will be overwritten by AddTransaction if they get used again.
168 [ + + ]: 175 : for (auto& entry : entries) {
169 : 147 : entry.ancestors &= m_used;
170 : 147 : entry.descendants &= m_used;
171 : : }
172 : 28 : }
173 : :
174 : : /** Modify this transaction graph, adding multiple parents to a specified child.
175 : : *
176 : : * Complexity: O(N) where N=TxCount().
177 : : */
178 : 154233 : void AddDependencies(const SetType& parents, DepGraphIndex child) noexcept
179 : : {
180 [ + + ]: 154233 : Assume(m_used[child]);
181 : 250083 : Assume(parents.IsSubsetOf(m_used));
182 : : // Compute the ancestors of parents that are not already ancestors of child.
183 [ + + ]: 154233 : SetType par_anc;
184 [ + + + + ]: 834475 : for (auto par : parents - Ancestors(child)) {
185 : 1045631 : par_anc |= Ancestors(par);
186 : : }
187 [ + + ]: 154233 : par_anc -= Ancestors(child);
188 : : // Bail out if there are no such ancestors.
189 [ + + ]: 154233 : if (par_anc.None()) return;
190 : : // To each such ancestor, add as descendants the descendants of the child.
191 : 120257 : const auto& chl_des = entries[child].descendants;
192 [ + + ]: 958600 : for (auto anc_of_par : par_anc) {
193 : 1367525 : entries[anc_of_par].descendants |= chl_des;
194 : : }
195 : : // To each descendant of the child, add those ancestors.
196 [ + + + + ]: 285189 : for (auto dec_of_chl : Descendants(child)) {
197 : 195839 : entries[dec_of_chl].ancestors |= par_anc;
198 : : }
199 : : }
200 : :
201 : : /** Compute the (reduced) set of parents of node i in this graph.
202 : : *
203 : : * This returns the minimal subset of the parents of i whose ancestors together equal all of
204 : : * i's ancestors (unless i is part of a cycle of dependencies). Note that DepGraph does not
205 : : * store the set of parents; this information is inferred from the ancestor sets.
206 : : *
207 : : * Complexity: O(N) where N=Ancestors(i).Count() (which is bounded by TxCount()).
208 : : */
209 [ + + ]: 5156757 : SetType GetReducedParents(DepGraphIndex i) const noexcept
210 : : {
211 [ + + ]: 5156757 : SetType parents = Ancestors(i);
212 : 5156757 : parents.Reset(i);
213 [ + + + + : 32339291 : for (auto parent : parents) {
+ + ]
214 [ + + ]: 25697423 : if (parents[parent]) {
215 : 21634185 : parents -= Ancestors(parent);
216 : 21634185 : parents.Set(parent);
217 : : }
218 : : }
219 : 5156757 : return parents;
220 : : }
221 : :
222 : : /** Compute the (reduced) set of children of node i in this graph.
223 : : *
224 : : * This returns the minimal subset of the children of i whose descendants together equal all of
225 : : * i's descendants (unless i is part of a cycle of dependencies). Note that DepGraph does not
226 : : * store the set of children; this information is inferred from the descendant sets.
227 : : *
228 : : * Complexity: O(N) where N=Descendants(i).Count() (which is bounded by TxCount()).
229 : : */
230 [ + + ]: 50070 : SetType GetReducedChildren(DepGraphIndex i) const noexcept
231 : : {
232 [ + + ]: 50070 : SetType children = Descendants(i);
233 : 50070 : children.Reset(i);
234 [ + + + + : 293106 : for (auto child : children) {
+ + ]
235 [ + + ]: 233772 : if (children[child]) {
236 : 167192 : children -= Descendants(child);
237 : 167192 : children.Set(child);
238 : : }
239 : : }
240 : 50070 : return children;
241 : : }
242 : :
243 : : /** Compute the aggregate feerate of a set of nodes in this graph.
244 : : *
245 : : * Complexity: O(N) where N=elems.Count().
246 : : **/
247 : : FeeFrac FeeRate(const SetType& elems) const noexcept
248 : : {
249 : : FeeFrac ret;
250 : : for (auto pos : elems) ret += entries[pos].feerate;
251 : : return ret;
252 : : }
253 : :
254 : : /** Get the connected component within the subset "todo" that contains tx (which must be in
255 : : * todo).
256 : : *
257 : : * Two transactions are considered connected if they are both in `todo`, and one is an ancestor
258 : : * of the other in the entire graph (so not just within `todo`), or transitively there is a
259 : : * path of transactions connecting them. This does mean that if `todo` contains a transaction
260 : : * and a grandparent, but misses the parent, they will still be part of the same component.
261 : : *
262 : : * Complexity: O(ret.Count()).
263 : : */
264 : 119 : SetType GetConnectedComponent(const SetType& todo, DepGraphIndex tx) const noexcept
265 : : {
266 : 119 : Assume(todo[tx]);
267 : 119 : Assume(todo.IsSubsetOf(m_used));
268 : 119 : auto to_add = SetType::Singleton(tx);
269 : 119 : SetType ret;
270 : : do {
271 : 238 : SetType old = ret;
272 [ + - + + ]: 740 : for (auto add : to_add) {
273 : 264 : ret |= Descendants(add);
274 : 264 : ret |= Ancestors(add);
275 : : }
276 [ + + ]: 238 : ret &= todo;
277 : 238 : to_add = ret - old;
278 [ + + ]: 238 : } while (to_add.Any());
279 : 119 : return ret;
280 : : }
281 : :
282 : : /** Find some connected component within the subset "todo" of this graph.
283 : : *
284 : : * Specifically, this finds the connected component which contains the first transaction of
285 : : * todo (if any).
286 : : *
287 : : * Complexity: O(ret.Count()).
288 : : */
289 [ - + ]: 119 : SetType FindConnectedComponent(const SetType& todo) const noexcept
290 : : {
291 [ - + ]: 119 : if (todo.None()) return todo;
292 : 119 : return GetConnectedComponent(todo, todo.First());
293 : : }
294 : :
295 : : /** Determine if a subset is connected.
296 : : *
297 : : * Complexity: O(subset.Count()).
298 : : */
299 : 11 : bool IsConnected(const SetType& subset) const noexcept
300 : : {
301 [ - + ]: 11 : return FindConnectedComponent(subset) == subset;
302 : : }
303 : :
304 : : /** Determine if this entire graph is connected.
305 : : *
306 : : * Complexity: O(TxCount()).
307 : : */
308 : : bool IsConnected() const noexcept { return IsConnected(m_used); }
309 : :
310 : : /** Append the entries of select to list in a topologically valid order.
311 : : *
312 : : * Complexity: O(select.Count() * log(select.Count())).
313 : : */
314 : : void AppendTopo(std::vector<DepGraphIndex>& list, const SetType& select) const noexcept
315 : : {
316 : : DepGraphIndex old_len = list.size();
317 : : for (auto i : select) list.push_back(i);
318 : : std::sort(list.begin() + old_len, list.end(), [&](DepGraphIndex a, DepGraphIndex b) noexcept {
319 : : const auto a_anc_count = entries[a].ancestors.Count();
320 : : const auto b_anc_count = entries[b].ancestors.Count();
321 : : if (a_anc_count != b_anc_count) return a_anc_count < b_anc_count;
322 : : return a < b;
323 : : });
324 : : }
325 : :
326 : : /** Check if this graph is acyclic. */
327 : 942 : bool IsAcyclic() const noexcept
328 : : {
329 [ + + + - : 26350 : for (auto i : Positions()) {
+ + ]
330 [ + - ]: 25046 : if ((Ancestors(i) & Descendants(i)) != SetType::Singleton(i)) {
331 : : return false;
332 : : }
333 : : }
334 : : return true;
335 : : }
336 : :
337 : : unsigned CountDependencies() const noexcept
338 : : {
339 : : unsigned ret = 0;
340 : : for (auto i : Positions()) {
341 : : ret += GetReducedParents(i).Count();
342 : : }
343 : : return ret;
344 : : }
345 : :
346 : : /** Reduce memory usage if possible. No observable effect. */
347 : 1911 : void Compact() noexcept
348 : : {
349 : 1911 : entries.shrink_to_fit();
350 : : }
351 : :
352 : 3699 : size_t DynamicMemoryUsage() const noexcept
353 : : {
354 [ - + ]: 3699 : return memusage::DynamicUsage(entries);
355 : : }
356 : : };
357 : :
358 : : /** A set of transactions together with their aggregate feerate. */
359 : : template<typename SetType>
360 : : struct SetInfo
361 : : {
362 : : /** The transactions in the set. */
363 : : SetType transactions;
364 : : /** Their combined fee and size. */
365 : : FeeFrac feerate;
366 : :
367 : : /** Construct a SetInfo for the empty set. */
368 : 1848267 : SetInfo() noexcept = default;
369 : :
370 : : /** Construct a SetInfo for a specified set and feerate. */
371 : 1034734 : SetInfo(const SetType& txn, const FeeFrac& fr) noexcept : transactions(txn), feerate(fr) {}
372 : :
373 : : /** Construct a SetInfo for a given transaction in a depgraph. */
374 : 28471 : explicit SetInfo(const DepGraph<SetType>& depgraph, DepGraphIndex pos) noexcept :
375 : 28471 : transactions(SetType::Singleton(pos)), feerate(depgraph.FeeRate(pos)) {}
376 : :
377 : : /** Construct a SetInfo for a set of transactions in a depgraph. */
378 : : explicit SetInfo(const DepGraph<SetType>& depgraph, const SetType& txn) noexcept :
379 : : transactions(txn), feerate(depgraph.FeeRate(txn)) {}
380 : :
381 : : /** Add a transaction to this SetInfo (which must not yet be in it). */
382 : : void Set(const DepGraph<SetType>& depgraph, DepGraphIndex pos) noexcept
383 : : {
384 : : Assume(!transactions[pos]);
385 : : transactions.Set(pos);
386 : : feerate += depgraph.FeeRate(pos);
387 : : }
388 : :
389 : : /** Add the transactions of other to this SetInfo (no overlap allowed). */
390 : 34064869 : SetInfo& operator|=(const SetInfo& other) noexcept
391 : : {
392 : 56059375 : Assume(!transactions.Overlaps(other.transactions));
393 : 34064869 : transactions |= other.transactions;
394 : 34064869 : feerate += other.feerate;
395 : 34064869 : return *this;
396 : : }
397 : :
398 : : /** Remove the transactions of other from this SetInfo (which must be a subset). */
399 : 12169945 : SetInfo& operator-=(const SetInfo& other) noexcept
400 : : {
401 : 20144613 : Assume(other.transactions.IsSubsetOf(transactions));
402 : 12169945 : transactions -= other.transactions;
403 : 12169945 : feerate -= other.feerate;
404 : 12169945 : return *this;
405 : : }
406 : :
407 : : /** Compute the difference between this and other SetInfo (which must be a subset). */
408 : 1034734 : SetInfo operator-(const SetInfo& other) const noexcept
409 : : {
410 : 1034734 : Assume(other.transactions.IsSubsetOf(transactions));
411 : 1034734 : return {transactions - other.transactions, feerate - other.feerate};
412 : : }
413 : :
414 : : /** Swap two SetInfo objects. */
415 : : friend void swap(SetInfo& a, SetInfo& b) noexcept
416 : : {
417 : : swap(a.transactions, b.transactions);
418 : : swap(a.feerate, b.feerate);
419 : : }
420 : :
421 : : /** Permit equality testing. */
422 : : friend bool operator==(const SetInfo&, const SetInfo&) noexcept = default;
423 : : };
424 : :
425 : : /** Compute the chunks of linearization as SetInfos. */
426 : : template<typename SetType>
427 : 1900 : std::vector<SetInfo<SetType>> ChunkLinearizationInfo(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> linearization) noexcept
428 : : {
429 : 1900 : std::vector<SetInfo<SetType>> ret;
430 [ + + ]: 30371 : for (DepGraphIndex i : linearization) {
431 : : /** The new chunk to be added, initially a singleton. */
432 : 28471 : SetInfo<SetType> new_chunk(depgraph, i);
433 : : // As long as the new chunk has a higher feerate than the last chunk so far, absorb it.
434 [ + + + + ]: 32456 : while (!ret.empty() && new_chunk.feerate >> ret.back().feerate) {
435 : 3985 : new_chunk |= ret.back();
436 : 3985 : ret.pop_back();
437 : : }
438 : : // Actually move that new chunk into the chunking.
439 : 28471 : ret.emplace_back(std::move(new_chunk));
440 : : }
441 : 1900 : return ret;
442 : : }
443 : :
444 : : /** Compute the feerates of the chunks of linearization. Identical to ChunkLinearizationInfo, but
445 : : * only returns the chunk feerates, not the corresponding transaction sets. */
446 : : template<typename SetType>
447 : 186221 : std::vector<FeeFrac> ChunkLinearization(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> linearization) noexcept
448 : : {
449 : 186221 : std::vector<FeeFrac> ret;
450 [ + + ]: 5189264 : for (DepGraphIndex i : linearization) {
451 : : /** The new chunk to be added, initially a singleton. */
452 : 5003043 : auto new_chunk = depgraph.FeeRate(i);
453 : : // As long as the new chunk has a higher feerate than the last chunk so far, absorb it.
454 [ + + + + ]: 8275662 : while (!ret.empty() && new_chunk >> ret.back()) {
455 : 3272619 : new_chunk += ret.back();
456 : 3272619 : ret.pop_back();
457 : : }
458 : : // Actually move that new chunk into the chunking.
459 : 5003043 : ret.push_back(std::move(new_chunk));
460 : : }
461 : 186221 : return ret;
462 : : }
463 : :
464 : : /** Class to represent the internal state of the spanning-forest linearization (SFL) algorithm.
465 : : *
466 : : * At all times, each dependency is marked as either "active" or "inactive". The subset of active
467 : : * dependencies is the state of the SFL algorithm. The implementation maintains several other
468 : : * values to speed up operations, but everything is ultimately a function of what that subset of
469 : : * active dependencies is.
470 : : *
471 : : * Given such a subset, define a chunk as the set of transactions that are connected through active
472 : : * dependencies (ignoring their parent/child direction). Thus, every state implies a particular
473 : : * partitioning of the graph into chunks (including potential singletons). In the extreme, each
474 : : * transaction may be in its own chunk, or in the other extreme all transactions may form a single
475 : : * chunk. A chunk's feerate is its total fee divided by its total size.
476 : : *
477 : : * The algorithm consists of switching dependencies between active and inactive. The final
478 : : * linearization that is produced at the end consists of these chunks, sorted from high to low
479 : : * feerate, each individually sorted in an arbitrary but topological (= no child before parent)
480 : : * way.
481 : : *
482 : : * We define three quality properties the state can have, each being stronger than the previous:
483 : : *
484 : : * - acyclic: The state is acyclic whenever no cycle of active dependencies exists within the
485 : : * graph, ignoring the parent/child direction. This is equivalent to saying that within
486 : : * each chunk the set of active dependencies form a tree, and thus the overall set of
487 : : * active dependencies in the graph form a spanning forest, giving the algorithm its
488 : : * name. Being acyclic is also equivalent to every chunk of N transactions having
489 : : * exactly N-1 active dependencies.
490 : : *
491 : : * For example in a diamond graph, D->{B,C}->A, the 4 dependencies cannot be
492 : : * simultaneously active. If at least one is inactive, the state is acyclic.
493 : : *
494 : : * The algorithm maintains an acyclic state at *all* times as an invariant. This implies
495 : : * that activating a dependency always corresponds to merging two chunks, and that
496 : : * deactivating one always corresponds to splitting two chunks.
497 : : *
498 : : * - topological: We say the state is topological whenever it is acyclic and no inactive dependency
499 : : * exists between two distinct chunks such that the child chunk has higher or equal
500 : : * feerate than the parent chunk.
501 : : *
502 : : * The relevance is that whenever the state is topological, the produced output
503 : : * linearization will be topological too (i.e., not have children before parents).
504 : : * Note that the "or equal" part of the definition matters: if not, one can end up
505 : : * in a situation with mutually-dependent equal-feerate chunks that cannot be
506 : : * linearized. For example C->{A,B} and D->{A,B}, with C->A and D->B active. The AC
507 : : * chunk depends on DB through C->B, and the BD chunk depends on AC through D->A.
508 : : * Merging them into a single ABCD chunk fixes this.
509 : : *
510 : : * The algorithm attempts to keep the state topological as much as possible, so it
511 : : * can be interrupted to produce an output whenever, but will sometimes need to
512 : : * temporarily deviate from it when improving the state.
513 : : *
514 : : * - optimal: For every active dependency, define its top and bottom set as the set of transactions
515 : : * in the chunks that would result if the dependency were deactivated; the top being the
516 : : * one with the dependency's parent, and the bottom being the one with the child. Note
517 : : * that due to acyclicity, every deactivation splits a chunk exactly in two.
518 : : *
519 : : * We say the state is optimal whenever it is topological and it has no active
520 : : * dependency whose top feerate is strictly higher than its bottom feerate. The
521 : : * relevance is that it can be proven that whenever the state is optimal, the produced
522 : : * linearization will also be optimal (in the convexified feerate diagram sense). It can
523 : : * also be proven that for every graph at least one optimal state exists.
524 : : *
525 : : * Note that it is possible for the SFL state to not be optimal, but the produced
526 : : * linearization to still be optimal. This happens when the chunks of a state are
527 : : * identical to those of an optimal state, but the exact set of active dependencies
528 : : * within a chunk differ in such a way that the state optimality condition is not
529 : : * satisfied. Thus, the state being optimal is more a "the eventual output is *known*
530 : : * to be optimal".
531 : : *
532 : : * The algorithm terminates whenever an optimal state is reached.
533 : : *
534 : : *
535 : : * This leads to the following high-level algorithm:
536 : : * - Start with all dependencies inactive, and thus all transactions in their own chunk. This is
537 : : * definitely acyclic.
538 : : * - Activate dependencies (merging chunks) until the state is topological.
539 : : * - Loop until optimal (no dependencies with higher-feerate top than bottom), or time runs out:
540 : : * - Deactivate a violating dependency, potentially making the state non-topological.
541 : : * - Activate other dependencies to make the state topological again.
542 : : * - Output the chunks from high to low feerate, each internally sorted topologically.
543 : : *
544 : : * When merging, we always either:
545 : : * - Merge upwards: merge a chunk with the lowest-feerate other chunk it depends on, among those
546 : : * with lower or equal feerate than itself.
547 : : * - Merge downwards: merge a chunk with the highest-feerate other chunk that depends on it, among
548 : : * those with higher or equal feerate than itself.
549 : : *
550 : : * Using these strategies in the improvement loop above guarantees that the output linearization
551 : : * after a deactivate + merge step is never worse or incomparable (in the convexified feerate
552 : : * diagram sense) than the output linearization that would be produced before the step. With that,
553 : : * we can refine the high-level algorithm to:
554 : : * - Start with all dependencies inactive.
555 : : * - Perform merges as described until none are possible anymore, making the state topological.
556 : : * - Loop until optimal or time runs out:
557 : : * - Pick a dependency D to deactivate among those with higher feerate top than bottom.
558 : : * - Deactivate D, causing the chunk it is in to split into top T and bottom B.
559 : : * - Do an upwards merge of T, if possible. If so, repeat the same with the merged result.
560 : : * - Do a downwards merge of B, if possible. If so, repeat the same with the merged result.
561 : : * - Output the chunks from high to low feerate, each internally sorted topologically.
562 : : *
563 : : * Instead of performing merges arbitrarily to make the initial state topological, it is possible
564 : : * to do so guided by an existing linearization. This has the advantage that the state's would-be
565 : : * output linearization is immediately as good as the existing linearization it was based on:
566 : : * - Start with all dependencies inactive.
567 : : * - For each transaction t in the existing linearization:
568 : : * - Find the chunk C that transaction is in (which will be singleton).
569 : : * - Do an upwards merge of C, if possible. If so, repeat the same with the merged result.
570 : : * No downwards merges are needed in this case.
571 : : *
572 : : * What remains to be specified are a number of heuristics:
573 : : *
574 : : * - How to decide which chunks to merge:
575 : : * - The merge upwards and downward rules specify that the lowest-feerate respectively
576 : : * highest-feerate candidate chunk is merged with, but if there are multiple equal-feerate
577 : : * candidates, a uniformly random one among them is picked.
578 : : *
579 : : * - How to decide what dependency to activate (when merging chunks):
580 : : * - After picking two chunks to be merged (see above), a uniformly random dependency between the
581 : : * two chunks is activated.
582 : : *
583 : : * - How to decide which chunk to find a dependency to split in:
584 : : * - A round-robin queue of chunks to improve is maintained. The initial ordering of this queue
585 : : * is uniformly randomly permuted.
586 : : *
587 : : * - How to decide what dependency to deactivate (when splitting chunks):
588 : : * - Inside the selected chunk (see above), among the dependencies whose top feerate is strictly
589 : : * higher than its bottom feerate in the selected chunk, if any, a uniformly random dependency
590 : : * is deactivated.
591 : : *
592 : : * - How to decide the exact output linearization:
593 : : * - When there are multiple equal-feerate chunks with no dependencies between them, output a
594 : : * uniformly random one among the ones with no missing dependent chunks first.
595 : : * - Within chunks, repeatedly pick a uniformly random transaction among those with no missing
596 : : * dependencies.
597 : : */
598 : : template<typename SetType>
599 : : class SpanningForestState
600 : : {
601 : : private:
602 : : /** Internal RNG. */
603 : : InsecureRandomContext m_rng;
604 : :
605 : : /** Data type to represent indexing into m_tx_data. */
606 : : using TxIdx = uint32_t;
607 : : /** Data type to represent indexing into m_dep_data. */
608 : : using DepIdx = uint32_t;
609 : :
610 : : /** Structure with information about a single transaction. For transactions that are the
611 : : * representative for the chunk they are in, this also stores chunk information. */
612 : 6909734 : struct TxData {
613 : : /** The dependencies to children of this transaction. Immutable after construction. */
614 : : std::vector<DepIdx> child_deps;
615 : : /** The set of parent transactions of this transaction. Immutable after construction. */
616 : : SetType parents;
617 : : /** The set of child transactions of this transaction. Immutable after construction. */
618 : : SetType children;
619 : : /** Which transaction holds the chunk_setinfo for the chunk this transaction is in
620 : : * (the representative for the chunk). */
621 : : TxIdx chunk_rep;
622 : : /** (Only if this transaction is the representative for the chunk it is in) the total
623 : : * chunk set and feerate. */
624 : : SetInfo<SetType> chunk_setinfo;
625 : : };
626 : :
627 : : /** Structure with information about a single dependency. */
628 : 14996170 : struct DepData {
629 : : /** Whether this dependency is active. */
630 : : bool active;
631 : : /** What the parent and child transactions are. Immutable after construction. */
632 : : TxIdx parent, child;
633 : : /** (Only if this dependency is active) the would-be top chunk and its feerate that would
634 : : * be formed if this dependency were to be deactivated. */
635 : : SetInfo<SetType> top_setinfo;
636 : : };
637 : :
638 : : /** The set of all TxIdx's of transactions in the cluster indexing into m_tx_data. */
639 : : SetType m_transaction_idxs;
640 : : /** Information about each transaction (and chunks). Keeps the "holes" from DepGraph during
641 : : * construction. Indexed by TxIdx. */
642 : : std::vector<TxData> m_tx_data;
643 : : /** Information about each dependency. Indexed by DepIdx. */
644 : : std::vector<DepData> m_dep_data;
645 : : /** A FIFO of chunk representatives of chunks that may be improved still. */
646 : : VecDeque<TxIdx> m_suboptimal_chunks;
647 : :
648 : : /** The number of updated transactions in activations/deactivations. */
649 : : uint64_t m_cost{0};
650 : :
651 : : /** Update a chunk:
652 : : * - All transactions have their chunk representative set to `chunk_rep`.
653 : : * - All dependencies which have `query` in their top_setinfo get `dep_change` added to it
654 : : * (if `!Subtract`) or removed from it (if `Subtract`).
655 : : */
656 : : template<bool Subtract>
657 : 11202206 : void UpdateChunk(const SetType& chunk, TxIdx query, TxIdx chunk_rep, const SetInfo<SetType>& dep_change) noexcept
658 : : {
659 : : // Iterate over all the chunk's transactions.
660 [ + + + + ]: 96773394 : for (auto tx_idx : chunk) {
661 [ - + ]: 81507702 : auto& tx_data = m_tx_data[tx_idx];
662 : : // Update the chunk representative.
663 : 81507702 : tx_data.chunk_rep = chunk_rep;
664 : : // Iterate over all active dependencies with tx_idx as parent. Combined with the outer
665 : : // loop this iterates over all internal active dependencies of the chunk.
666 [ - + ]: 81507702 : auto child_deps = std::span{tx_data.child_deps};
667 [ + + ]: 565874180 : for (auto dep_idx : child_deps) {
668 [ + + ]: 484366478 : auto& dep_entry = m_dep_data[dep_idx];
669 [ + + ]: 484366478 : Assume(dep_entry.parent == tx_idx);
670 : : // Skip inactive dependencies.
671 [ + + ]: 484366478 : if (!dep_entry.active) continue;
672 : : // If this dependency's top_setinfo contains query, update it to add/remove
673 : : // dep_change.
674 [ + + ]: 70305496 : if (dep_entry.top_setinfo.transactions[query]) {
675 : : if constexpr (Subtract) {
676 : 12169945 : dep_entry.top_setinfo -= dep_change;
677 : : } else {
678 : 29494515 : dep_entry.top_setinfo |= dep_change;
679 : : }
680 : : }
681 : : }
682 : : }
683 : 11202206 : }
684 : :
685 : : /** Make a specified inactive dependency active. Returns the merged chunk representative. */
686 : 4566369 : TxIdx Activate(DepIdx dep_idx) noexcept
687 : : {
688 : 4566369 : auto& dep_data = m_dep_data[dep_idx];
689 : 4566369 : Assume(!dep_data.active);
690 : 4566369 : auto& child_tx_data = m_tx_data[dep_data.child];
691 : 4566369 : auto& parent_tx_data = m_tx_data[dep_data.parent];
692 : :
693 : : // Gather information about the parent and child chunks.
694 : 4566369 : Assume(parent_tx_data.chunk_rep != child_tx_data.chunk_rep);
695 : 4566369 : auto& par_chunk_data = m_tx_data[parent_tx_data.chunk_rep];
696 : 4566369 : auto& chl_chunk_data = m_tx_data[child_tx_data.chunk_rep];
697 : 4566369 : TxIdx top_rep = parent_tx_data.chunk_rep;
698 : 4566369 : auto top_part = par_chunk_data.chunk_setinfo;
699 : 4566369 : auto bottom_part = chl_chunk_data.chunk_setinfo;
700 : : // Update the parent chunk to also contain the child.
701 : 4566369 : par_chunk_data.chunk_setinfo |= bottom_part;
702 : 4566369 : m_cost += par_chunk_data.chunk_setinfo.transactions.Count();
703 : :
704 : : // Consider the following example:
705 : : //
706 : : // A A There are two chunks, ABC and DEF, and the inactive E->C dependency
707 : : // / \ / \ is activated, resulting in a single chunk ABCDEF.
708 : : // B C B C
709 : : // : ==> | Dependency | top set before | top set after | change
710 : : // D E D E B->A | AC | ACDEF | +DEF
711 : : // \ / \ / C->A | AB | AB |
712 : : // F F F->D | D | D |
713 : : // F->E | E | ABCE | +ABC
714 : : //
715 : : // The common pattern here is that any dependency which has the parent or child of the
716 : : // dependency being activated (E->C here) in its top set, will have the opposite part added
717 : : // to it. This is true for B->A and F->E, but not for C->A and F->D.
718 : : //
719 : : // Let UpdateChunk traverse the old parent chunk top_part (ABC in example), and add
720 : : // bottom_part (DEF) to every dependency's top_set which has the parent (C) in it. The
721 : : // representative of each of these transactions was already top_rep, so that is not being
722 : : // changed here.
723 : 4566369 : UpdateChunk<false>(/*chunk=*/top_part.transactions, /*query=*/dep_data.parent,
724 : : /*chunk_rep=*/top_rep, /*dep_change=*/bottom_part);
725 : : // Let UpdateChunk traverse the old child chunk bottom_part (DEF in example), and add
726 : : // top_part (ABC) to every dependency's top_set which has the child (E) in it. At the same
727 : : // time, change the representative of each of these transactions to be top_rep, which
728 : : // becomes the representative for the merged chunk.
729 : 4566369 : UpdateChunk<false>(/*chunk=*/bottom_part.transactions, /*query=*/dep_data.child,
730 : : /*chunk_rep=*/top_rep, /*dep_change=*/top_part);
731 : : // Make active.
732 : 4566369 : dep_data.active = true;
733 : 4566369 : dep_data.top_setinfo = top_part;
734 : 4566369 : return top_rep;
735 : : }
736 : :
737 : : /** Make a specified active dependency inactive. */
738 : 1034734 : void Deactivate(DepIdx dep_idx) noexcept
739 : : {
740 : 1034734 : auto& dep_data = m_dep_data[dep_idx];
741 : 1034734 : Assume(dep_data.active);
742 : 1034734 : auto& parent_tx_data = m_tx_data[dep_data.parent];
743 : : // Make inactive.
744 : 1034734 : dep_data.active = false;
745 : : // Update representatives.
746 : 1034734 : auto& chunk_data = m_tx_data[parent_tx_data.chunk_rep];
747 : 1034734 : m_cost += chunk_data.chunk_setinfo.transactions.Count();
748 : 1034734 : auto top_part = dep_data.top_setinfo;
749 : 1034734 : auto bottom_part = chunk_data.chunk_setinfo - top_part;
750 : 1034734 : TxIdx bottom_rep = dep_data.child;
751 : 1034734 : auto& bottom_chunk_data = m_tx_data[bottom_rep];
752 : 1034734 : bottom_chunk_data.chunk_setinfo = bottom_part;
753 : 1034734 : TxIdx top_rep = dep_data.parent;
754 : 1034734 : auto& top_chunk_data = m_tx_data[top_rep];
755 : 1034734 : top_chunk_data.chunk_setinfo = top_part;
756 : :
757 : : // See the comment above in Activate(). We perform the opposite operations here,
758 : : // removing instead of adding.
759 : : //
760 : : // Let UpdateChunk traverse the old parent chunk top_part, and remove bottom_part from
761 : : // every dependency's top_set which has the parent in it. At the same time, change the
762 : : // representative of each of these transactions to be top_rep.
763 : 1034734 : UpdateChunk<true>(/*chunk=*/top_part.transactions, /*query=*/dep_data.parent,
764 : : /*chunk_rep=*/top_rep, /*dep_change=*/bottom_part);
765 : : // Let UpdateChunk traverse the old child chunk bottom_part, and remove top_part from every
766 : : // dependency's top_set which has the child in it. At the same time, change the
767 : : // representative of each of these transactions to be bottom_rep.
768 : 1034734 : UpdateChunk<true>(/*chunk=*/bottom_part.transactions, /*query=*/dep_data.child,
769 : : /*chunk_rep=*/bottom_rep, /*dep_change=*/top_part);
770 : 1034734 : }
771 : :
772 : : /** Activate a dependency from the chunk represented by bottom_rep to the chunk represented by
773 : : * top_rep, which must exist. Return the representative of the merged chunk. */
774 : 4566369 : TxIdx MergeChunks(TxIdx top_rep, TxIdx bottom_rep) noexcept
775 : : {
776 [ + - ]: 4566369 : auto& top_chunk = m_tx_data[top_rep];
777 [ + - ]: 4566369 : Assume(top_chunk.chunk_rep == top_rep);
778 : 4566369 : auto& bottom_chunk = m_tx_data[bottom_rep];
779 : 4566369 : Assume(bottom_chunk.chunk_rep == bottom_rep);
780 : : // Count the number of dependencies between bottom_chunk and top_chunk.
781 : 4566369 : TxIdx num_deps{0};
782 [ + + + + ]: 43389606 : for (auto tx : top_chunk.chunk_setinfo.transactions) {
783 : 37158648 : auto& tx_data = m_tx_data[tx];
784 : 37158648 : num_deps += (tx_data.children & bottom_chunk.chunk_setinfo.transactions).Count();
785 : : }
786 : 4566369 : Assume(num_deps > 0);
787 : : // Uniformly randomly pick one of them and activate it.
788 : 4566369 : TxIdx pick = m_rng.randrange(num_deps);
789 [ + - + - ]: 16960778 : for (auto tx : top_chunk.chunk_setinfo.transactions) {
790 [ + + ]: 15296189 : auto& tx_data = m_tx_data[tx];
791 [ + + ]: 15296189 : auto intersect = tx_data.children & bottom_chunk.chunk_setinfo.transactions;
792 : 15296189 : auto count = intersect.Count();
793 [ + + ]: 15296189 : if (pick < count) {
794 [ + - ]: 30554337 : for (auto dep : tx_data.child_deps) {
795 [ + + ]: 30554337 : auto& dep_data = m_dep_data[dep];
796 [ + + ]: 30554337 : if (bottom_chunk.chunk_setinfo.transactions[dep_data.child]) {
797 [ + + ]: 5990514 : if (pick == 0) return Activate(dep);
798 : 1424145 : --pick;
799 : : }
800 : : }
801 : : break;
802 : : }
803 : 10729820 : pick -= count;
804 : : }
805 : 0 : Assume(false);
806 : 0 : return TxIdx(-1);
807 : : }
808 : :
809 : : /** Perform an upward or downward merge step, on the specified chunk representative. Returns
810 : : * the representative of the merged chunk, or TxIdx(-1) if no merge took place. */
811 : : template<bool DownWard>
812 : 12199923 : TxIdx MergeStep(TxIdx chunk_rep) noexcept
813 : : {
814 : : /** Information about the chunk that tx_idx is currently in. */
815 [ + - ]: 12199923 : auto& chunk_data = m_tx_data[chunk_rep];
816 : 12199923 : SetType chunk_txn = chunk_data.chunk_setinfo.transactions;
817 : : // Iterate over all transactions in the chunk, figuring out which other chunk each
818 : : // depends on, but only testing each other chunk once. For those depended-on chunks,
819 : : // remember the highest-feerate (if DownWard) or lowest-feerate (if !DownWard) one.
820 : : // If multiple equal-feerate candidate chunks to merge with exist, pick a random one
821 : : // among them.
822 : :
823 : : /** Which transactions have been reached from this chunk already. Initialize with the
824 : : * chunk itself, so internal dependencies within the chunk are ignored. */
825 : 12199923 : SetType explored = chunk_txn;
826 : : /** The minimum feerate (if downward) or maximum feerate (if upward) to consider when
827 : : * looking for candidate chunks to merge with. Initially, this is the original chunk's
828 : : * feerate, but is updated to be the current best candidate whenever one is found. */
829 : 12199923 : FeeFrac best_other_chunk_feerate = chunk_data.chunk_setinfo.feerate;
830 : : /** The representative for the best candidate chunk to merge with. -1 if none. */
831 : 12199923 : TxIdx best_other_chunk_rep = TxIdx(-1);
832 : : /** We generate random tiebreak values to pick between equal-feerate candidate chunks.
833 : : * This variable stores the tiebreak of the current best candidate. */
834 : 12199923 : uint64_t best_other_chunk_tiebreak{0};
835 [ + + + + ]: 130069842 : for (auto tx : chunk_txn) {
836 : 113442626 : auto& tx_data = m_tx_data[tx];
837 : : /** The transactions reached by following dependencies from tx that have not been
838 : : * explored before. */
839 : 113442626 : auto newly_reached = (DownWard ? tx_data.children : tx_data.parents) - explored;
840 : 140345382 : explored |= newly_reached;
841 [ + + ]: 254882191 : while (newly_reached.Any()) {
842 : : // Find a chunk inside newly_reached, and remove it from newly_reached.
843 [ + + ]: 41156802 : auto reached_chunk_rep = m_tx_data[newly_reached.First()].chunk_rep;
844 : 41156802 : auto& reached_chunk = m_tx_data[reached_chunk_rep].chunk_setinfo;
845 [ + + ]: 41156802 : newly_reached -= reached_chunk.transactions;
846 : : // See if it has an acceptable feerate.
847 [ + + ]: 10745711 : auto cmp = DownWard ? FeeRateCompare(best_other_chunk_feerate, reached_chunk.feerate)
848 [ + + ]: 30411091 : : FeeRateCompare(reached_chunk.feerate, best_other_chunk_feerate);
849 [ + + ]: 41156802 : if (cmp > 0) continue;
850 [ + + ]: 7114142 : uint64_t tiebreak = m_rng.rand64();
851 [ + + + + ]: 7114142 : if (cmp < 0 || tiebreak >= best_other_chunk_tiebreak) {
852 : 6195361 : best_other_chunk_feerate = reached_chunk.feerate;
853 : 6195361 : best_other_chunk_rep = reached_chunk_rep;
854 : 6195361 : best_other_chunk_tiebreak = tiebreak;
855 : : }
856 : : }
857 : : }
858 : : // Stop if there are no candidate chunks to merge with.
859 [ + + ]: 12199923 : if (best_other_chunk_rep == TxIdx(-1)) return TxIdx(-1);
860 : : if constexpr (DownWard) {
861 : 554539 : chunk_rep = MergeChunks(chunk_rep, best_other_chunk_rep);
862 : : } else {
863 : 4011830 : chunk_rep = MergeChunks(best_other_chunk_rep, chunk_rep);
864 : : }
865 : 4566369 : Assume(chunk_rep != TxIdx(-1));
866 : 4566369 : return chunk_rep;
867 : : }
868 : :
869 : :
870 : : /** Perform an upward or downward merge sequence on the specified transaction. */
871 : : template<bool DownWard>
872 : 2069468 : void MergeSequence(TxIdx tx_idx) noexcept
873 : : {
874 : 2069468 : auto chunk_rep = m_tx_data[tx_idx].chunk_rep;
875 : 845899 : while (true) {
876 : 2915367 : auto merged_rep = MergeStep<DownWard>(chunk_rep);
877 [ + + ]: 2915367 : if (merged_rep == TxIdx(-1)) break;
878 : 845899 : chunk_rep = merged_rep;
879 : : }
880 : : // Add the chunk to the queue of improvable chunks.
881 : 2069468 : m_suboptimal_chunks.push_back(chunk_rep);
882 : 2069468 : }
883 : :
884 : : /** Split a chunk, and then merge the resulting two chunks to make the graph topological
885 : : * again. */
886 : 1034734 : void Improve(DepIdx dep_idx) noexcept
887 : : {
888 : 1034734 : auto& dep_data = m_dep_data[dep_idx];
889 : 1034734 : Assume(dep_data.active);
890 : : // Deactivate the specified dependency, splitting it into two new chunks: a top containing
891 : : // the parent, and a bottom containing the child. The top should have a higher feerate.
892 : 1034734 : Deactivate(dep_idx);
893 : :
894 : : // At this point we have exactly two chunks which may violate topology constraints (the
895 : : // parent chunk and child chunk that were produced by deactivating dep_idx). We can fix
896 : : // these using just merge sequences, one upwards and one downwards, avoiding the need for a
897 : : // full MakeTopological.
898 : :
899 : : // Merge the top chunk with lower-feerate chunks it depends on (which may be the bottom it
900 : : // was just split from, or other pre-existing chunks).
901 : 1034734 : MergeSequence<false>(dep_data.parent);
902 : : // Merge the bottom chunk with higher-feerate chunks that depend on it.
903 : 1034734 : MergeSequence<true>(dep_data.child);
904 : 1034734 : }
905 : :
906 : : public:
907 : : /** Construct a spanning forest for the given DepGraph, with every transaction in its own chunk
908 : : * (not topological). */
909 [ - + ]: 188100 : explicit SpanningForestState(const DepGraph<SetType>& depgraph, uint64_t rng_seed) noexcept : m_rng(rng_seed)
910 : : {
911 : 188100 : m_transaction_idxs = depgraph.Positions();
912 [ - + ]: 188100 : auto num_transactions = m_transaction_idxs.Count();
913 [ - + ]: 188100 : m_tx_data.resize(depgraph.PositionRange());
914 : : // Reserve the maximum number of (reserved) dependencies the cluster can have, so
915 : : // m_dep_data won't need any reallocations during construction. For a cluster with N
916 : : // transactions, the worst case consists of two sets of transactions, the parents and the
917 : : // children, where each child depends on each parent and nothing else. For even N, both
918 : : // sets can be sized N/2, which means N^2/4 dependencies. For odd N, one can be (N + 1)/2
919 : : // and the other can be (N - 1)/2, meaning (N^2 - 1)/4 dependencies. Because N^2 is odd in
920 : : // this case, N^2/4 (with rounding-down division) is the correct value in both cases.
921 : 188100 : m_dep_data.reserve((num_transactions * num_transactions) / 4);
922 [ + + + + ]: 5291867 : for (auto tx : m_transaction_idxs) {
923 : : // Fill in transaction data.
924 : 5031467 : auto& tx_data = m_tx_data[tx];
925 : 5031467 : tx_data.chunk_rep = tx;
926 : 5031467 : tx_data.chunk_setinfo.transactions = SetType::Singleton(tx);
927 : 5031467 : tx_data.chunk_setinfo.feerate = depgraph.FeeRate(tx);
928 : : // Add its dependencies.
929 : 5031467 : SetType parents = depgraph.GetReducedParents(tx);
930 [ + + + + ]: 21477101 : for (auto par : parents) {
931 [ - + ]: 14996170 : auto& par_tx_data = m_tx_data[par];
932 [ - + ]: 14996170 : auto dep_idx = m_dep_data.size();
933 : : // Construct new dependency.
934 : 14996170 : auto& dep = m_dep_data.emplace_back();
935 : 14996170 : dep.active = false;
936 : 14996170 : dep.parent = par;
937 : 14996170 : dep.child = tx;
938 : : // Add it as parent of the child.
939 : 14996170 : tx_data.parents.Set(par);
940 : : // Add it as child of the parent.
941 : 14996170 : par_tx_data.child_deps.push_back(dep_idx);
942 : 14996170 : par_tx_data.children.Set(tx);
943 : : }
944 : : }
945 : 188100 : }
946 : :
947 : : /** Load an existing linearization. Must be called immediately after constructor. The result is
948 : : * topological if the linearization is valid. Otherwise, MakeTopological still needs to be
949 : : * called. */
950 : 125570 : void LoadLinearization(std::span<const DepGraphIndex> old_linearization) noexcept
951 : : {
952 : : // Add transactions one by one, in order of existing linearization.
953 [ + + ]: 3477034 : for (DepGraphIndex tx : old_linearization) {
954 : 3351464 : auto chunk_rep = m_tx_data[tx].chunk_rep;
955 : : // Merge the chunk upwards, as long as merging succeeds.
956 : : while (true) {
957 : 5779287 : chunk_rep = MergeStep<false>(chunk_rep);
958 [ + + ]: 5779287 : if (chunk_rep == TxIdx(-1)) break;
959 : : }
960 : : }
961 : 125570 : }
962 : :
963 : : /** Make state topological. Can be called after constructing, or after LoadLinearization. */
964 : 62530 : void MakeTopological() noexcept
965 : : {
966 [ + + + + ]: 1766122 : for (auto tx : m_transaction_idxs) {
967 [ + - ]: 1680003 : auto& tx_data = m_tx_data[tx];
968 [ + - ]: 1680003 : if (tx_data.chunk_rep == tx) {
969 : 1680003 : m_suboptimal_chunks.emplace_back(tx);
970 : : // Randomize the initial order of suboptimal chunks in the queue.
971 : 1680003 : TxIdx j = m_rng.randrange<TxIdx>(m_suboptimal_chunks.size());
972 [ + + ]: 1680003 : if (j != m_suboptimal_chunks.size() - 1) {
973 : 1450952 : std::swap(m_suboptimal_chunks.back(), m_suboptimal_chunks[j]);
974 : : }
975 : : }
976 : : }
977 [ + + ]: 3035180 : while (!m_suboptimal_chunks.empty()) {
978 : : // Pop an entry from the potentially-suboptimal chunk queue.
979 : 2972650 : TxIdx chunk = m_suboptimal_chunks.front();
980 : 2972650 : m_suboptimal_chunks.pop_front();
981 [ + + ]: 2972650 : auto& chunk_data = m_tx_data[chunk];
982 : : // If what was popped is not currently a chunk representative, continue. This may
983 : : // happen when it was merged with something else since being added.
984 [ + + ]: 2972650 : if (chunk_data.chunk_rep != chunk) continue;
985 : 2135412 : int flip = m_rng.randbool();
986 [ + + ]: 4348034 : for (int i = 0; i < 2; ++i) {
987 [ + + ]: 3505269 : if (i ^ flip) {
988 : : // Attempt to merge the chunk upwards.
989 : 1810798 : auto result_up = MergeStep<false>(chunk);
990 [ + + ]: 1810798 : if (result_up != TxIdx(-1)) {
991 : 763225 : m_suboptimal_chunks.push_back(result_up);
992 : : break;
993 : : }
994 : : } else {
995 : : // Attempt to merge the chunk downwards.
996 : 1694471 : auto result_down = MergeStep<true>(chunk);
997 [ + + ]: 1694471 : if (result_down != TxIdx(-1)) {
998 : 529422 : m_suboptimal_chunks.push_back(result_down);
999 : : break;
1000 : : }
1001 : : }
1002 : : }
1003 : : }
1004 : 62530 : }
1005 : :
1006 : : /** Initialize the data structure for optimization. It must be topological already. */
1007 : 188094 : void StartOptimizing() noexcept
1008 : : {
1009 : : // Mark chunks suboptimal.
1010 [ + + + + ]: 5291492 : for (auto tx : m_transaction_idxs) {
1011 [ + + ]: 5031104 : auto& tx_data = m_tx_data[tx];
1012 [ + + ]: 5031104 : if (tx_data.chunk_rep == tx) {
1013 : 1310991 : m_suboptimal_chunks.push_back(tx);
1014 : : // Randomize the initial order of suboptimal chunks in the queue.
1015 : 1310991 : TxIdx j = m_rng.randrange<TxIdx>(m_suboptimal_chunks.size());
1016 [ + + ]: 1310991 : if (j != m_suboptimal_chunks.size() - 1) {
1017 : 930861 : std::swap(m_suboptimal_chunks.back(), m_suboptimal_chunks[j]);
1018 : : }
1019 : : }
1020 : : }
1021 : 188094 : }
1022 : :
1023 : : /** Try to improve the forest. Returns false if it is optimal, true otherwise. */
1024 : 2670561 : bool OptimizeStep() noexcept
1025 : : {
1026 [ + - ]: 3380459 : while (!m_suboptimal_chunks.empty()) {
1027 : : // Pop an entry from the potentially-suboptimal chunk queue.
1028 : 3380459 : TxIdx chunk = m_suboptimal_chunks.front();
1029 : 3380459 : m_suboptimal_chunks.pop_front();
1030 [ + + ]: 3380459 : auto& chunk_data = m_tx_data[chunk];
1031 : : // If what was popped is not currently a chunk representative, continue. This may
1032 : : // happen when a split chunk merges in Improve() with one or more existing chunks that
1033 : : // are themselves on the suboptimal queue already.
1034 [ + + ]: 3380459 : if (chunk_data.chunk_rep != chunk) continue;
1035 : : // Remember the best dependency seen so far.
1036 : 2670561 : DepIdx candidate_dep = DepIdx(-1);
1037 : 2670561 : uint64_t candidate_tiebreak = 0;
1038 : : // Iterate over all transactions.
1039 [ + + + + ]: 35546543 : for (auto tx : chunk_data.chunk_setinfo.transactions) {
1040 [ - + ]: 31919175 : const auto& tx_data = m_tx_data[tx];
1041 : : // Iterate over all active child dependencies of the transaction.
1042 [ - + ]: 31919175 : const auto children = std::span{tx_data.child_deps};
1043 [ + + ]: 246905127 : for (DepIdx dep_idx : children) {
1044 [ + + ]: 214985952 : const auto& dep_data = m_dep_data[dep_idx];
1045 [ + + ]: 214985952 : if (!dep_data.active) continue;
1046 : : // Skip if this dependency is ineligible (the top chunk that would be created
1047 : : // does not have higher feerate than the chunk it is currently part of).
1048 [ + + ]: 29248614 : auto cmp = FeeRateCompare(dep_data.top_setinfo.feerate, chunk_data.chunk_setinfo.feerate);
1049 [ + + ]: 29248614 : if (cmp <= 0) continue;
1050 : : // Generate a random tiebreak for this dependency, and reject it if its tiebreak
1051 : : // is worse than the best so far. This means that among all eligible
1052 : : // dependencies, a uniformly random one will be chosen.
1053 : 4647898 : uint64_t tiebreak = m_rng.rand64();
1054 [ + + ]: 4647898 : if (tiebreak < candidate_tiebreak) continue;
1055 : : // Remember this as our (new) candidate dependency.
1056 : : candidate_dep = dep_idx;
1057 : : candidate_tiebreak = tiebreak;
1058 : : }
1059 : : }
1060 : : // If a candidate with positive gain was found, deactivate it and then make the state
1061 : : // topological again with a sequence of merges.
1062 [ + + ]: 2670561 : if (candidate_dep != DepIdx(-1)) Improve(candidate_dep);
1063 : : // Stop processing for now, even if nothing was activated, as the loop above may have
1064 : : // had a nontrivial cost.
1065 : 2670561 : return !m_suboptimal_chunks.empty();
1066 : : }
1067 : : // No improvable chunk was found, we are done.
1068 : : return false;
1069 : : }
1070 : :
1071 : : /** Construct a topologically-valid linearization from the current forest state. Must be
1072 : : * topological. */
1073 : 188100 : std::vector<DepGraphIndex> GetLinearization() noexcept
1074 : : {
1075 : : /** The output linearization. */
1076 : 188100 : std::vector<DepGraphIndex> ret;
1077 : 188100 : ret.reserve(m_transaction_idxs.Count());
1078 : : /** A heap with all chunks (by representative) that can currently be included, sorted by
1079 : : * chunk feerate and a random tie-breaker. */
1080 : 188100 : std::vector<std::pair<TxIdx, uint64_t>> ready_chunks;
1081 : : /** Information about chunks:
1082 : : * - The first value is only used for chunk representatives, and counts the number of
1083 : : * unmet dependencies this chunk has on other chunks (not including dependencies within
1084 : : * the chunk itself).
1085 : : * - The second value is the number of unmet dependencies overall.
1086 : : */
1087 [ - + + - ]: 188100 : std::vector<std::pair<TxIdx, TxIdx>> chunk_deps(m_tx_data.size(), {0, 0});
1088 : : /** The set of all chunk representatives. */
1089 : 188100 : SetType chunk_reps;
1090 : : /** A list with all transactions within the current chunk that can be included. */
1091 : 188100 : std::vector<TxIdx> ready_tx;
1092 : : // Populate chunk_deps[c] with the number of {out-of-chunk dependencies, dependencies} the
1093 : : // child has.
1094 [ + + + + ]: 5291867 : for (TxIdx chl_idx : m_transaction_idxs) {
1095 [ + + ]: 5031467 : const auto& chl_data = m_tx_data[chl_idx];
1096 [ + + ]: 5031467 : chunk_deps[chl_idx].second = chl_data.parents.Count();
1097 [ + + ]: 5031467 : auto chl_chunk_rep = chl_data.chunk_rep;
1098 : 5031467 : chunk_reps.Set(chl_chunk_rep);
1099 [ + + + + ]: 21477101 : for (auto par_idx : chl_data.parents) {
1100 : 14996170 : auto par_chunk_rep = m_tx_data[par_idx].chunk_rep;
1101 : 14996170 : chunk_deps[chl_chunk_rep].first += (par_chunk_rep != chl_chunk_rep);
1102 : : }
1103 : : }
1104 : : // Construct a heap with all chunks that have no out-of-chunk dependencies.
1105 : : /** Comparison function for the heap. */
1106 : 4868409 : auto chunk_cmp_fn = [&](const std::pair<TxIdx, uint64_t>& a, const std::pair<TxIdx, uint64_t>& b) noexcept {
1107 [ # # ][ + + : 4680309 : auto& chunk_a = m_tx_data[a.first];
+ + + + +
+ + + ]
1108 : 4680309 : auto& chunk_b = m_tx_data[b.first];
1109 [ # # ][ + + : 4680309 : Assume(chunk_a.chunk_rep == a.first);
+ + + + +
+ + + ]
1110 : 4680309 : Assume(chunk_b.chunk_rep == b.first);
1111 : : // First sort by chunk feerate.
1112 [ # # ][ + + : 4680309 : if (chunk_a.chunk_setinfo.feerate != chunk_b.chunk_setinfo.feerate) {
+ + + + +
+ + + ]
1113 : 3392073 : return chunk_a.chunk_setinfo.feerate < chunk_b.chunk_setinfo.feerate;
1114 : : }
1115 : : // Tie-break randomly.
1116 [ # # ][ + - : 1288236 : if (a.second != b.second) return a.second < b.second;
+ - + - +
- + - ]
1117 : : // Lastly, tie-break by chunk representative.
1118 : 0 : return a.first < b.first;
1119 : : };
1120 [ + + + + ]: 1760232 : for (TxIdx chunk_rep : chunk_reps) {
1121 [ + + ]: 1499832 : if (chunk_deps[chunk_rep].first == 0) ready_chunks.emplace_back(chunk_rep, m_rng.rand64());
1122 : : }
1123 : 188100 : std::make_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
1124 : : // Pop chunks off the heap, highest-feerate ones first.
1125 [ + + ]: 1687932 : while (!ready_chunks.empty()) {
1126 : 1499832 : auto [chunk_rep, _rnd] = ready_chunks.front();
1127 [ + - ]: 1499832 : std::pop_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
1128 : 1499832 : ready_chunks.pop_back();
1129 [ + - ]: 1499832 : Assume(m_tx_data[chunk_rep].chunk_rep == chunk_rep);
1130 : 1499832 : Assume(chunk_deps[chunk_rep].first == 0);
1131 [ + - ]: 1499832 : const auto& chunk_txn = m_tx_data[chunk_rep].chunk_setinfo.transactions;
1132 : : // Build heap of all includable transactions in chunk.
1133 [ + + + + ]: 7070331 : for (TxIdx tx_idx : chunk_txn) {
1134 [ + + ]: 5031467 : if (chunk_deps[tx_idx].second == 0) {
1135 : 2113838 : ready_tx.push_back(tx_idx);
1136 : : }
1137 : : }
1138 : 1499832 : Assume(!ready_tx.empty());
1139 : : // Pick transactions from the ready queue, append them to linearization, and decrement
1140 : : // dependency counts.
1141 [ + + ]: 6531299 : while (!ready_tx.empty()) {
1142 : : // Move a random queue element to the back.
1143 [ - + - + ]: 5031467 : auto pos = m_rng.randrange(ready_tx.size());
1144 [ + + ]: 5031467 : if (pos != ready_tx.size() - 1) std::swap(ready_tx.back(), ready_tx[pos]);
1145 : : // Pop from the back.
1146 : 5031467 : auto tx_idx = ready_tx.back();
1147 : 5031467 : Assume(chunk_txn[tx_idx]);
1148 : 5031467 : ready_tx.pop_back();
1149 : : // Append to linearization.
1150 : 5031467 : ret.push_back(tx_idx);
1151 : : // Decrement dependency counts.
1152 [ + + ]: 5031467 : auto& tx_data = m_tx_data[tx_idx];
1153 [ + + + + ]: 20972925 : for (TxIdx chl_idx : tx_data.children) {
1154 [ + + ]: 14996170 : auto& chl_data = m_tx_data[chl_idx];
1155 : : // Decrement tx dependency count.
1156 : 14996170 : Assume(chunk_deps[chl_idx].second > 0);
1157 [ + + + + ]: 14996170 : if (--chunk_deps[chl_idx].second == 0 && chunk_txn[chl_idx]) {
1158 : : // Child tx has no dependencies left, and is in this chunk. Add it to the tx queue.
1159 : 2917629 : ready_tx.push_back(chl_idx);
1160 : : }
1161 : : // Decrement chunk dependency count if this is out-of-chunk dependency.
1162 [ + + ]: 14996170 : if (chl_data.chunk_rep != chunk_rep) {
1163 [ + + ]: 7859535 : Assume(chunk_deps[chl_data.chunk_rep].first > 0);
1164 [ + + ]: 7859535 : if (--chunk_deps[chl_data.chunk_rep].first == 0) {
1165 : : // Child chunk has no dependencies left. Add it to the chunk heap.
1166 : 1043834 : ready_chunks.emplace_back(chl_data.chunk_rep, m_rng.rand64());
1167 : 1043834 : std::push_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
1168 : : }
1169 : : }
1170 : : }
1171 : : }
1172 : : }
1173 [ - + ]: 188100 : Assume(ret.size() == m_transaction_idxs.Count());
1174 : 188100 : return ret;
1175 : 188100 : }
1176 : :
1177 : : /** Get the diagram for the current state, which must be topological. Test-only.
1178 : : *
1179 : : * The linearization produced by GetLinearization() is always at least as good (in the
1180 : : * CompareChunks() sense) as this diagram, but may be better.
1181 : : *
1182 : : * After an OptimizeStep(), the diagram will always be at least as good as before. Once
1183 : : * OptimizeStep() returns false, the diagram will be equivalent to that produced by
1184 : : * GetLinearization(), and optimal.
1185 : : */
1186 : : std::vector<FeeFrac> GetDiagram() const noexcept
1187 : : {
1188 : : std::vector<FeeFrac> ret;
1189 : : for (auto tx : m_transaction_idxs) {
1190 : : if (m_tx_data[tx].chunk_rep == tx) {
1191 : : ret.push_back(m_tx_data[tx].chunk_setinfo.feerate);
1192 : : }
1193 : : }
1194 : : std::sort(ret.begin(), ret.end(), std::greater{});
1195 : : return ret;
1196 : : }
1197 : :
1198 : : /** Determine how much work was performed so far. */
1199 : 2858667 : uint64_t GetCost() const noexcept { return m_cost; }
1200 : :
1201 : : /** Verify internal consistency of the data structure. */
1202 : : void SanityCheck(const DepGraph<SetType>& depgraph) const
1203 : : {
1204 : : //
1205 : : // Verify dependency parent/child information, and build list of (active) dependencies.
1206 : : //
1207 : : std::vector<std::pair<TxIdx, TxIdx>> expected_dependencies;
1208 : : std::vector<std::tuple<TxIdx, TxIdx, DepIdx>> all_dependencies;
1209 : : std::vector<std::tuple<TxIdx, TxIdx, DepIdx>> active_dependencies;
1210 : : for (auto parent_idx : depgraph.Positions()) {
1211 : : for (auto child_idx : depgraph.GetReducedChildren(parent_idx)) {
1212 : : expected_dependencies.emplace_back(parent_idx, child_idx);
1213 : : }
1214 : : }
1215 : : for (DepIdx dep_idx = 0; dep_idx < m_dep_data.size(); ++dep_idx) {
1216 : : const auto& dep_data = m_dep_data[dep_idx];
1217 : : all_dependencies.emplace_back(dep_data.parent, dep_data.child, dep_idx);
1218 : : // Also add to active_dependencies if it is active.
1219 : : if (m_dep_data[dep_idx].active) {
1220 : : active_dependencies.emplace_back(dep_data.parent, dep_data.child, dep_idx);
1221 : : }
1222 : : }
1223 : : std::sort(expected_dependencies.begin(), expected_dependencies.end());
1224 : : std::sort(all_dependencies.begin(), all_dependencies.end());
1225 : : assert(expected_dependencies.size() == all_dependencies.size());
1226 : : for (size_t i = 0; i < expected_dependencies.size(); ++i) {
1227 : : assert(expected_dependencies[i] ==
1228 : : std::make_pair(std::get<0>(all_dependencies[i]),
1229 : : std::get<1>(all_dependencies[i])));
1230 : : }
1231 : :
1232 : : //
1233 : : // Verify the chunks against the list of active dependencies
1234 : : //
1235 : : for (auto tx_idx: depgraph.Positions()) {
1236 : : // Only process chunks for now.
1237 : : if (m_tx_data[tx_idx].chunk_rep == tx_idx) {
1238 : : const auto& chunk_data = m_tx_data[tx_idx];
1239 : : // Verify that transactions in the chunk point back to it. This guarantees
1240 : : // that chunks are non-overlapping.
1241 : : for (auto chunk_tx : chunk_data.chunk_setinfo.transactions) {
1242 : : assert(m_tx_data[chunk_tx].chunk_rep == tx_idx);
1243 : : }
1244 : : // Verify the chunk's transaction set: it must contain the representative, and for
1245 : : // every active dependency, if it contains the parent or child, it must contain
1246 : : // both. It must have exactly N-1 active dependencies in it, guaranteeing it is
1247 : : // acyclic.
1248 : : SetType expected_chunk = SetType::Singleton(tx_idx);
1249 : : while (true) {
1250 : : auto old = expected_chunk;
1251 : : size_t active_dep_count{0};
1252 : : for (const auto& [par, chl, _dep] : active_dependencies) {
1253 : : if (expected_chunk[par] || expected_chunk[chl]) {
1254 : : expected_chunk.Set(par);
1255 : : expected_chunk.Set(chl);
1256 : : ++active_dep_count;
1257 : : }
1258 : : }
1259 : : if (old == expected_chunk) {
1260 : : assert(expected_chunk.Count() == active_dep_count + 1);
1261 : : break;
1262 : : }
1263 : : }
1264 : : assert(chunk_data.chunk_setinfo.transactions == expected_chunk);
1265 : : // Verify the chunk's feerate.
1266 : : assert(chunk_data.chunk_setinfo.feerate ==
1267 : : depgraph.FeeRate(chunk_data.chunk_setinfo.transactions));
1268 : : }
1269 : : }
1270 : :
1271 : : //
1272 : : // Verify other transaction data.
1273 : : //
1274 : : assert(m_transaction_idxs == depgraph.Positions());
1275 : : for (auto tx_idx : m_transaction_idxs) {
1276 : : const auto& tx_data = m_tx_data[tx_idx];
1277 : : // Verify it has a valid chunk representative, and that chunk includes this
1278 : : // transaction.
1279 : : assert(m_tx_data[tx_data.chunk_rep].chunk_rep == tx_data.chunk_rep);
1280 : : assert(m_tx_data[tx_data.chunk_rep].chunk_setinfo.transactions[tx_idx]);
1281 : : // Verify parents/children.
1282 : : assert(tx_data.parents == depgraph.GetReducedParents(tx_idx));
1283 : : assert(tx_data.children == depgraph.GetReducedChildren(tx_idx));
1284 : : // Verify list of child dependencies.
1285 : : std::vector<DepIdx> expected_child_deps;
1286 : : for (const auto& [par_idx, chl_idx, dep_idx] : all_dependencies) {
1287 : : if (tx_idx == par_idx) {
1288 : : assert(tx_data.children[chl_idx]);
1289 : : expected_child_deps.push_back(dep_idx);
1290 : : }
1291 : : }
1292 : : std::sort(expected_child_deps.begin(), expected_child_deps.end());
1293 : : auto child_deps_copy = tx_data.child_deps;
1294 : : std::sort(child_deps_copy.begin(), child_deps_copy.end());
1295 : : assert(expected_child_deps == child_deps_copy);
1296 : : }
1297 : :
1298 : : //
1299 : : // Verify active dependencies' top_setinfo.
1300 : : //
1301 : : for (const auto& [par_idx, chl_idx, dep_idx] : active_dependencies) {
1302 : : const auto& dep_data = m_dep_data[dep_idx];
1303 : : // Verify the top_info's transactions: it must contain the parent, and for every
1304 : : // active dependency, except dep_idx itself, if it contains the parent or child, it
1305 : : // must contain both.
1306 : : SetType expected_top = SetType::Singleton(par_idx);
1307 : : while (true) {
1308 : : auto old = expected_top;
1309 : : for (const auto& [par2_idx, chl2_idx, dep2_idx] : active_dependencies) {
1310 : : if (dep2_idx != dep_idx && (expected_top[par2_idx] || expected_top[chl2_idx])) {
1311 : : expected_top.Set(par2_idx);
1312 : : expected_top.Set(chl2_idx);
1313 : : }
1314 : : }
1315 : : if (old == expected_top) break;
1316 : : }
1317 : : assert(!expected_top[chl_idx]);
1318 : : assert(dep_data.top_setinfo.transactions == expected_top);
1319 : : // Verify the top_info's feerate.
1320 : : assert(dep_data.top_setinfo.feerate ==
1321 : : depgraph.FeeRate(dep_data.top_setinfo.transactions));
1322 : : }
1323 : :
1324 : : //
1325 : : // Verify m_suboptimal_chunks.
1326 : : //
1327 : : for (size_t i = 0; i < m_suboptimal_chunks.size(); ++i) {
1328 : : auto tx_idx = m_suboptimal_chunks[i];
1329 : : assert(m_transaction_idxs[tx_idx]);
1330 : : }
1331 : : }
1332 : : };
1333 : :
1334 : : /** Find or improve a linearization for a cluster.
1335 : : *
1336 : : * @param[in] depgraph Dependency graph of the cluster to be linearized.
1337 : : * @param[in] max_iterations Upper bound on the amount of work that will be done.
1338 : : * @param[in] rng_seed A random number seed to control search order. This prevents peers
1339 : : * from predicting exactly which clusters would be hard for us to
1340 : : * linearize.
1341 : : * @param[in] old_linearization An existing linearization for the cluster (which must be
1342 : : * topologically valid), or empty.
1343 : : * @return A tuple of:
1344 : : * - The resulting linearization. It is guaranteed to be at least as
1345 : : * good (in the feerate diagram sense) as old_linearization.
1346 : : * - A boolean indicating whether the result is guaranteed to be
1347 : : * optimal.
1348 : : * - How many optimization steps were actually performed.
1349 : : */
1350 : : template<typename SetType>
1351 : 188100 : std::tuple<std::vector<DepGraphIndex>, bool, uint64_t> Linearize(const DepGraph<SetType>& depgraph, uint64_t max_iterations, uint64_t rng_seed, std::span<const DepGraphIndex> old_linearization = {}) noexcept
1352 : : {
1353 : : /** Initialize a spanning forest data structure for this cluster. */
1354 [ + + ]: 188100 : SpanningForestState forest(depgraph, rng_seed);
1355 [ + + ]: 188100 : if (!old_linearization.empty()) {
1356 : 125570 : forest.LoadLinearization(old_linearization);
1357 : : } else {
1358 : 62530 : forest.MakeTopological();
1359 : : }
1360 : : // Make improvement steps to it until we hit the max_iterations limit, or an optimal result
1361 : : // is found.
1362 : 188100 : bool optimal = false;
1363 [ + + ]: 188100 : if (forest.GetCost() < max_iterations) {
1364 : 188094 : forest.StartOptimizing();
1365 : : do {
1366 [ + + ]: 2670561 : if (!forest.OptimizeStep()) {
1367 : : optimal = true;
1368 : : break;
1369 : : }
1370 [ + - ]: 2482467 : } while (forest.GetCost() < max_iterations);
1371 : : }
1372 : 188100 : return {forest.GetLinearization(), optimal, forest.GetCost()};
1373 : 188100 : }
1374 : :
1375 : : /** Improve a given linearization.
1376 : : *
1377 : : * @param[in] depgraph Dependency graph of the cluster being linearized.
1378 : : * @param[in,out] linearization On input, an existing linearization for depgraph. On output, a
1379 : : * potentially better linearization for the same graph.
1380 : : *
1381 : : * Postlinearization guarantees:
1382 : : * - The resulting chunks are connected.
1383 : : * - If the input has a tree shape (either all transactions have at most one child, or all
1384 : : * transactions have at most one parent), the result is optimal.
1385 : : * - Given a linearization L1 and a leaf transaction T in it. Let L2 be L1 with T moved to the end,
1386 : : * optionally with its fee increased. Let L3 be the postlinearization of L2. L3 will be at least
1387 : : * as good as L1. This means that replacing transactions with same-size higher-fee transactions
1388 : : * will not worsen linearizations through a "drop conflicts, append new transactions,
1389 : : * postlinearize" process.
1390 : : */
1391 : : template<typename SetType>
1392 [ - + ]: 5695 : void PostLinearize(const DepGraph<SetType>& depgraph, std::span<DepGraphIndex> linearization)
1393 : : {
1394 : : // This algorithm performs a number of passes (currently 2); the even ones operate from back to
1395 : : // front, the odd ones from front to back. Each results in an equal-or-better linearization
1396 : : // than the one started from.
1397 : : // - One pass in either direction guarantees that the resulting chunks are connected.
1398 : : // - Each direction corresponds to one shape of tree being linearized optimally (forward passes
1399 : : // guarantee this for graphs where each transaction has at most one child; backward passes
1400 : : // guarantee this for graphs where each transaction has at most one parent).
1401 : : // - Starting with a backward pass guarantees the moved-tree property.
1402 : : //
1403 : : // During an odd (forward) pass, the high-level operation is:
1404 : : // - Start with an empty list of groups L=[].
1405 : : // - For every transaction i in the old linearization, from front to back:
1406 : : // - Append a new group C=[i], containing just i, to the back of L.
1407 : : // - While L has at least one group before C, and the group immediately before C has feerate
1408 : : // lower than C:
1409 : : // - If C depends on P:
1410 : : // - Merge P into C, making C the concatenation of P+C, continuing with the combined C.
1411 : : // - Otherwise:
1412 : : // - Swap P with C, continuing with the now-moved C.
1413 : : // - The output linearization is the concatenation of the groups in L.
1414 : : //
1415 : : // During even (backward) passes, i iterates from the back to the front of the existing
1416 : : // linearization, and new groups are prepended instead of appended to the list L. To enable
1417 : : // more code reuse, both passes append groups, but during even passes the meanings of
1418 : : // parent/child, and of high/low feerate are reversed, and the final concatenation is reversed
1419 : : // on output.
1420 : : //
1421 : : // In the implementation below, the groups are represented by singly-linked lists (pointing
1422 : : // from the back to the front), which are themselves organized in a singly-linked circular
1423 : : // list (each group pointing to its predecessor, with a special sentinel group at the front
1424 : : // that points back to the last group).
1425 : : //
1426 : : // Information about transaction t is stored in entries[t + 1], while the sentinel is in
1427 : : // entries[0].
1428 : :
1429 : : /** Index of the sentinel in the entries array below. */
1430 : : static constexpr DepGraphIndex SENTINEL{0};
1431 : : /** Indicator that a group has no previous transaction. */
1432 : : static constexpr DepGraphIndex NO_PREV_TX{0};
1433 : :
1434 : :
1435 : : /** Data structure per transaction entry. */
1436 : 90357 : struct TxEntry
1437 : : {
1438 : : /** The index of the previous transaction in this group; NO_PREV_TX if this is the first
1439 : : * entry of a group. */
1440 : : DepGraphIndex prev_tx;
1441 : :
1442 : : // The fields below are only used for transactions that are the last one in a group
1443 : : // (referred to as tail transactions below).
1444 : :
1445 : : /** Index of the first transaction in this group, possibly itself. */
1446 : : DepGraphIndex first_tx;
1447 : : /** Index of the last transaction in the previous group. The first group (the sentinel)
1448 : : * points back to the last group here, making it a singly-linked circular list. */
1449 : : DepGraphIndex prev_group;
1450 : : /** All transactions in the group. Empty for the sentinel. */
1451 : : SetType group;
1452 : : /** All dependencies of the group (descendants in even passes; ancestors in odd ones). */
1453 : : SetType deps;
1454 : : /** The combined fee/size of transactions in the group. Fee is negated in even passes. */
1455 : : FeeFrac feerate;
1456 : : };
1457 : :
1458 : : // As an example, consider the state corresponding to the linearization [1,0,3,2], with
1459 : : // groups [1,0,3] and [2], in an odd pass. The linked lists would be:
1460 : : //
1461 : : // +-----+
1462 : : // 0<-P-- | 0 S | ---\ Legend:
1463 : : // +-----+ |
1464 : : // ^ | - digit in box: entries index
1465 : : // /--------------F---------+ G | (note: one more than tx value)
1466 : : // v \ | | - S: sentinel group
1467 : : // +-----+ +-----+ +-----+ | (empty feerate)
1468 : : // 0<-P-- | 2 | <--P-- | 1 | <--P-- | 4 T | | - T: tail transaction, contains
1469 : : // +-----+ +-----+ +-----+ | fields beyond prev_tv.
1470 : : // ^ | - P: prev_tx reference
1471 : : // G G - F: first_tx reference
1472 : : // | | - G: prev_group reference
1473 : : // +-----+ |
1474 : : // 0<-P-- | 3 T | <--/
1475 : : // +-----+
1476 : : // ^ |
1477 : : // \-F-/
1478 : : //
1479 : : // During an even pass, the diagram above would correspond to linearization [2,3,0,1], with
1480 : : // groups [2] and [3,0,1].
1481 : :
1482 : 5695 : std::vector<TxEntry> entries(depgraph.PositionRange() + 1);
1483 : :
1484 : : // Perform two passes over the linearization.
1485 [ + + ]: 17085 : for (int pass = 0; pass < 2; ++pass) {
1486 : 11390 : int rev = !(pass & 1);
1487 : : // Construct a sentinel group, identifying the start of the list.
1488 : 11390 : entries[SENTINEL].prev_group = SENTINEL;
1489 : 11390 : Assume(entries[SENTINEL].feerate.IsEmpty());
1490 : :
1491 : : // Iterate over all elements in the existing linearization.
1492 [ + + ]: 180714 : for (DepGraphIndex i = 0; i < linearization.size(); ++i) {
1493 : : // Even passes are from back to front; odd passes from front to back.
1494 [ + + ]: 169324 : DepGraphIndex idx = linearization[rev ? linearization.size() - 1 - i : i];
1495 : : // Construct a new group containing just idx. In even passes, the meaning of
1496 : : // parent/child and high/low feerate are swapped.
1497 [ + + ]: 169324 : DepGraphIndex cur_group = idx + 1;
1498 [ + + ]: 169324 : entries[cur_group].group = SetType::Singleton(idx);
1499 [ + + + + ]: 169324 : entries[cur_group].deps = rev ? depgraph.Descendants(idx): depgraph.Ancestors(idx);
1500 : 169324 : entries[cur_group].feerate = depgraph.FeeRate(idx);
1501 [ + + ]: 169324 : if (rev) entries[cur_group].feerate.fee = -entries[cur_group].feerate.fee;
1502 : 169324 : entries[cur_group].prev_tx = NO_PREV_TX; // No previous transaction in group.
1503 : 169324 : entries[cur_group].first_tx = cur_group; // Transaction itself is first of group.
1504 : : // Insert the new group at the back of the groups linked list.
1505 : 169324 : entries[cur_group].prev_group = entries[SENTINEL].prev_group;
1506 : 169324 : entries[SENTINEL].prev_group = cur_group;
1507 : :
1508 : : // Start merge/swap cycle.
1509 : 169324 : DepGraphIndex next_group = SENTINEL; // We inserted at the end, so next group is sentinel.
1510 : 169324 : DepGraphIndex prev_group = entries[cur_group].prev_group;
1511 : : // Continue as long as the current group has higher feerate than the previous one.
1512 [ + + ]: 193487 : while (entries[cur_group].feerate >> entries[prev_group].feerate) {
1513 : : // prev_group/cur_group/next_group refer to (the last transactions of) 3
1514 : : // consecutive entries in groups list.
1515 [ + + ]: 24163 : Assume(cur_group == entries[next_group].prev_group);
1516 : 24163 : Assume(prev_group == entries[cur_group].prev_group);
1517 : : // The sentinel has empty feerate, which is neither higher or lower than other
1518 : : // feerates. Thus, the while loop we are in here guarantees that cur_group and
1519 : : // prev_group are not the sentinel.
1520 : 24163 : Assume(cur_group != SENTINEL);
1521 : 24163 : Assume(prev_group != SENTINEL);
1522 [ + + ]: 24163 : if (entries[cur_group].deps.Overlaps(entries[prev_group].group)) {
1523 : : // There is a dependency between cur_group and prev_group; merge prev_group
1524 : : // into cur_group. The group/deps/feerate fields of prev_group remain unchanged
1525 : : // but become unused.
1526 : 23488 : entries[cur_group].group |= entries[prev_group].group;
1527 : 23488 : entries[cur_group].deps |= entries[prev_group].deps;
1528 : 23488 : entries[cur_group].feerate += entries[prev_group].feerate;
1529 : : // Make the first of the current group point to the tail of the previous group.
1530 : 23488 : entries[entries[cur_group].first_tx].prev_tx = prev_group;
1531 : : // The first of the previous group becomes the first of the newly-merged group.
1532 : 23488 : entries[cur_group].first_tx = entries[prev_group].first_tx;
1533 : : // The previous group becomes whatever group was before the former one.
1534 : 23488 : prev_group = entries[prev_group].prev_group;
1535 : 23488 : entries[cur_group].prev_group = prev_group;
1536 : : } else {
1537 : : // There is no dependency between cur_group and prev_group; swap them.
1538 : 675 : DepGraphIndex preprev_group = entries[prev_group].prev_group;
1539 : : // If PP, P, C, N were the old preprev, prev, cur, next groups, then the new
1540 : : // layout becomes [PP, C, P, N]. Update prev_groups to reflect that order.
1541 : 675 : entries[next_group].prev_group = prev_group;
1542 : 675 : entries[prev_group].prev_group = cur_group;
1543 : 675 : entries[cur_group].prev_group = preprev_group;
1544 : : // The current group remains the same, but the groups before/after it have
1545 : : // changed.
1546 : 675 : next_group = prev_group;
1547 : 675 : prev_group = preprev_group;
1548 : : }
1549 : : }
1550 : : }
1551 : :
1552 : : // Convert the entries back to linearization (overwriting the existing one).
1553 : 11390 : DepGraphIndex cur_group = entries[0].prev_group;
1554 : 11390 : DepGraphIndex done = 0;
1555 [ + + ]: 157226 : while (cur_group != SENTINEL) {
1556 : 145836 : DepGraphIndex cur_tx = cur_group;
1557 : : // Traverse the transactions of cur_group (from back to front), and write them in the
1558 : : // same order during odd passes, and reversed (front to back) in even passes.
1559 [ + + ]: 145836 : if (rev) {
1560 : : do {
1561 [ + + ]: 84662 : *(linearization.begin() + (done++)) = cur_tx - 1;
1562 [ + + ]: 84662 : cur_tx = entries[cur_tx].prev_tx;
1563 [ + + ]: 84662 : } while (cur_tx != NO_PREV_TX);
1564 : : } else {
1565 : : do {
1566 [ + + ]: 84662 : *(linearization.end() - (++done)) = cur_tx - 1;
1567 [ + + ]: 84662 : cur_tx = entries[cur_tx].prev_tx;
1568 [ + + ]: 84662 : } while (cur_tx != NO_PREV_TX);
1569 : : }
1570 : 145836 : cur_group = entries[cur_group].prev_group;
1571 : : }
1572 : 11390 : Assume(done == linearization.size());
1573 : : }
1574 : 5695 : }
1575 : :
1576 : : /** Make linearization topological, retaining its ordering where possible. */
1577 : : template<typename SetType>
1578 : 64060 : void FixLinearization(const DepGraph<SetType>& depgraph, std::span<DepGraphIndex> linearization) noexcept
1579 : : {
1580 : : // This algorithm can be summarized as moving every element in the linearization backwards
1581 : : // until it is placed after all its ancestors.
1582 : 64060 : SetType done;
1583 : 64060 : const auto len = linearization.size();
1584 : : // Iterate over the elements of linearization from back to front (i is distance from back).
1585 [ + + ]: 1754022 : for (DepGraphIndex i = 0; i < len; ++i) {
1586 : : /** The element at that position. */
1587 : 1689962 : DepGraphIndex elem = linearization[len - 1 - i];
1588 : : /** j represents how far from the back of the linearization elem should be placed. */
1589 : 1689962 : DepGraphIndex j = i;
1590 : : // Figure out which elements need to be moved before elem.
1591 : 1689962 : SetType place_before = done & depgraph.Ancestors(elem);
1592 : : // Find which position to place elem in (updating j), continuously moving the elements
1593 : : // in between forward.
1594 [ + + ]: 15512475 : while (place_before.Any()) {
1595 : : // j cannot be 0 here; if it was, then there was necessarily nothing earlier which
1596 : : // elem needs to be placed before anymore, and place_before would be empty.
1597 : 7708602 : Assume(j > 0);
1598 : 7708602 : auto to_swap = linearization[len - 1 - (j - 1)];
1599 : 7708602 : place_before.Reset(to_swap);
1600 : 7708602 : linearization[len - 1 - (j--)] = to_swap;
1601 : : }
1602 : : // Put elem in its final position and mark it as done.
1603 : 1689962 : linearization[len - 1 - j] = elem;
1604 : 1689962 : done.Set(elem);
1605 : : }
1606 : 64060 : }
1607 : :
1608 : : } // namespace cluster_linearize
1609 : :
1610 : : #endif // BITCOIN_CLUSTER_LINEARIZE_H
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