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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 <attributes.h>
16 : : #include <memusage.h>
17 : : #include <random.h>
18 : : #include <span.h>
19 : : #include <util/feefrac.h>
20 : : #include <util/vecdeque.h>
21 : :
22 : : namespace cluster_linearize {
23 : :
24 : : /** Data type to represent transaction indices in DepGraphs and the clusters they represent. */
25 : : using DepGraphIndex = uint32_t;
26 : :
27 : : /** Data structure that holds a transaction graph's preprocessed data (fee, size, ancestors,
28 : : * descendants). */
29 : : template<typename SetType>
30 [ + - ][ + + : 365225 : class DepGraph
+ - + - ]
31 : : {
32 : : /** Information about a single transaction. */
33 : : struct Entry
34 : : {
35 : : /** Fee and size of transaction itself. */
36 : 32486 : FeeFrac feerate;
37 : : /** All ancestors of the transaction (including itself). */
38 : 32486 : SetType ancestors;
39 : : /** All descendants of the transaction (including itself). */
40 : 32486 : SetType descendants;
41 : :
42 : : /** Equality operator (primarily for testing purposes). */
43 [ + - + - : 64972 : friend bool operator==(const Entry&, const Entry&) noexcept = default;
- + ]
44 : :
45 : : /** Construct an empty entry. */
46 : 169690 : Entry() noexcept = default;
47 : : /** Construct an entry with a given feerate, ancestor set, descendant set. */
48 : 2620142 : Entry(const FeeFrac& f, const SetType& a, const SetType& d) noexcept : feerate(f), ancestors(a), descendants(d) {}
49 : : };
50 : :
51 : : /** Data for each transaction. */
52 : : std::vector<Entry> entries;
53 : :
54 : : /** Which positions are used. */
55 : : SetType m_used;
56 : :
57 : : public:
58 : : /** Equality operator (primarily for testing purposes). */
59 : 2008 : friend bool operator==(const DepGraph& a, const DepGraph& b) noexcept
60 : : {
61 [ + - ]: 2008 : if (a.m_used != b.m_used) return false;
62 : : // Only compare the used positions within the entries vector.
63 [ + + + + ]: 36400 : for (auto idx : a.m_used) {
64 [ + - ]: 32486 : if (a.entries[idx] != b.entries[idx]) return false;
65 : : }
66 : : return true;
67 : : }
68 : :
69 : : // Default constructors.
70 : 751749 : DepGraph() noexcept = default;
71 : 11817 : DepGraph(const DepGraph&) noexcept = default;
72 : 0 : DepGraph(DepGraph&&) noexcept = default;
73 : 308959 : DepGraph& operator=(const DepGraph&) noexcept = default;
74 : 364097 : DepGraph& operator=(DepGraph&&) noexcept = default;
75 : :
76 : : /** Construct a DepGraph object given another DepGraph and a mapping from old to new.
77 : : *
78 : : * @param depgraph The original DepGraph that is being remapped.
79 : : *
80 : : * @param mapping A span such that mapping[i] gives the position in the new DepGraph
81 : : * for position i in the old depgraph. Its size must be equal to
82 : : * depgraph.PositionRange(). The value of mapping[i] is ignored if
83 : : * position i is a hole in depgraph (i.e., if !depgraph.Positions()[i]).
84 : : *
85 : : * @param pos_range The PositionRange() for the new DepGraph. It must equal the largest
86 : : * value in mapping for any used position in depgraph plus 1, or 0 if
87 : : * depgraph.TxCount() == 0.
88 : : *
89 : : * Complexity: O(N^2) where N=depgraph.TxCount().
90 : : */
91 [ - + ]: 6295 : DepGraph(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> mapping, DepGraphIndex pos_range) noexcept : entries(pos_range)
92 : : {
93 [ - + ]: 6295 : Assume(mapping.size() == depgraph.PositionRange());
94 : 12590 : Assume((pos_range == 0) == (depgraph.TxCount() == 0));
95 [ + + ]: 123440 : for (DepGraphIndex i : depgraph.Positions()) {
96 [ - + ]: 117145 : auto new_idx = mapping[i];
97 [ - + ]: 117145 : Assume(new_idx < pos_range);
98 : : // Add transaction.
99 : 117145 : entries[new_idx].ancestors = SetType::Singleton(new_idx);
100 : 117145 : entries[new_idx].descendants = SetType::Singleton(new_idx);
101 : 117145 : m_used.Set(new_idx);
102 : : // Fill in fee and size.
103 : 117145 : entries[new_idx].feerate = depgraph.entries[i].feerate;
104 : : }
105 [ + + ]: 123440 : for (DepGraphIndex i : depgraph.Positions()) {
106 : : // Fill in dependencies by mapping direct parents.
107 : 117145 : SetType parents;
108 [ + + + + ]: 263998 : for (auto j : depgraph.GetReducedParents(i)) parents.Set(mapping[j]);
109 : 117145 : AddDependencies(parents, mapping[i]);
110 : : }
111 : : // Verify that the provided pos_range was correct (no unused positions at the end).
112 [ + + - + ]: 6295 : Assume(m_used.None() ? (pos_range == 0) : (pos_range == m_used.Last() + 1));
113 : 6295 : }
114 : :
115 : : /** Get the set of transactions positions in use. Complexity: O(1). */
116 [ + + + + : 9559238 : const SetType& Positions() const noexcept { return m_used; }
+ + + + +
+ + + + +
+ + + + +
- + + +
+ ]
117 : : /** Get the range of positions in this DepGraph. All entries in Positions() are in [0, PositionRange() - 1]. */
118 [ - + - + : 758744 : DepGraphIndex PositionRange() const noexcept { return entries.size(); }
- + + + -
+ - + - +
+ - - + +
- - + +
+ ][ - + +
- # # # #
# # # # #
# # # # #
# # # # #
# ][ - + -
+ - + - +
- + ]
119 : : /** Get the number of transactions in the graph. Complexity: O(1). */
120 [ - + + - : 511642 : auto TxCount() const noexcept { return m_used.Count(); }
+ + - + -
+ + + + +
+ - + + +
+ + - -
+ ][ - + #
# # # # #
# # # # #
# # # # #
# # # # #
# ]
121 : : /** Get the feerate of a given transaction i. Complexity: O(1). */
122 [ + - + + ]: 6496046 : const FeeFrac& FeeRate(DepGraphIndex i) const noexcept { return entries[i].feerate; }
123 : : /** Get the mutable feerate of a given transaction i. Complexity: O(1). */
124 [ - + - + : 12271855 : FeeFrac& FeeRate(DepGraphIndex i) noexcept { return entries[i].feerate; }
+ + + - #
# ][ + - -
+ - + + -
+ - ]
[ + + + - ]
125 : : /** Get the ancestors of a given transaction i. Complexity: O(1). */
126 [ + + + + : 177515907 : const SetType& Ancestors(DepGraphIndex i) const noexcept { return entries[i].ancestors; }
+ + + - -
+ + + + +
+ + + - -
+ + - + +
+ + - + -
+ + + -
+ ][ + - +
+ - + ]
127 : : /** Get the descendants of a given transaction i. Complexity: O(1). */
128 [ + + - + : 51651476 : const SetType& Descendants(DepGraphIndex i) const noexcept { return entries[i].descendants; }
+ - - + ]
[ + - ]
129 : :
130 : : /** Add a new unconnected transaction to this transaction graph (in the first available
131 : : * position), and return its DepGraphIndex.
132 : : *
133 : : * Complexity: O(1) (amortized, due to resizing of backing vector).
134 : : */
135 : 2666724 : DepGraphIndex AddTransaction(const FeeFrac& feefrac) noexcept
136 : : {
137 : : static constexpr auto ALL_POSITIONS = SetType::Fill(SetType::Size());
138 [ - + ]: 2666724 : auto available = ALL_POSITIONS - m_used;
139 [ - + ]: 2950867 : Assume(available.Any());
140 : 2666724 : DepGraphIndex new_idx = available.First();
141 [ - + + + ]: 2666724 : if (new_idx == entries.size()) {
142 : 2620142 : entries.emplace_back(feefrac, SetType::Singleton(new_idx), SetType::Singleton(new_idx));
143 : : } else {
144 : 46582 : entries[new_idx] = Entry(feefrac, SetType::Singleton(new_idx), SetType::Singleton(new_idx));
145 : : }
146 : 2666724 : m_used.Set(new_idx);
147 : 2666724 : return new_idx;
148 : : }
149 : :
150 : : /** Remove the specified positions from this DepGraph.
151 : : *
152 : : * The specified positions will no longer be part of Positions(), and dependencies with them are
153 : : * removed. Note that due to DepGraph only tracking ancestors/descendants (and not direct
154 : : * dependencies), if a parent is removed while a grandparent remains, the grandparent will
155 : : * remain an ancestor.
156 : : *
157 : : * Complexity: O(N) where N=TxCount().
158 : : */
159 : 445703 : void RemoveTransactions(const SetType& del) noexcept
160 : : {
161 : 445703 : m_used -= del;
162 : : // Remove now-unused trailing entries.
163 [ + + - + : 988345 : while (!entries.empty() && !m_used[entries.size() - 1]) {
+ + ]
164 : 542642 : entries.pop_back();
165 : : }
166 : : // Remove the deleted transactions from ancestors/descendants of other transactions. Note
167 : : // that the deleted positions will retain old feerate and dependency information. This does
168 : : // not matter as they will be overwritten by AddTransaction if they get used again.
169 [ + + ]: 10801236 : for (auto& entry : entries) {
170 [ + + ]: 27958271 : entry.ancestors &= m_used;
171 [ + + ]: 27958271 : entry.descendants &= m_used;
172 : : }
173 : 445703 : }
174 : :
175 : : /** Modify this transaction graph, adding multiple parents to a specified child.
176 : : *
177 : : * Complexity: O(N) where N=TxCount().
178 : : */
179 : 3621219 : void AddDependencies(const SetType& parents, DepGraphIndex child) noexcept
180 : : {
181 [ - + ]: 3621219 : Assume(m_used[child]);
182 [ - + ]: 4065054 : Assume(parents.IsSubsetOf(m_used));
183 : : // Compute the ancestors of parents that are not already ancestors of child.
184 [ + + ]: 3621219 : SetType par_anc;
185 [ + + + + ]: 7898062 : for (auto par : parents - Ancestors(child)) {
[ + + # # ]
186 : 3004451 : par_anc |= Ancestors(par);
187 : : }
188 [ + + ]: 3621219 : par_anc -= Ancestors(child);
189 : : // Bail out if there are no such ancestors.
190 [ + + ]: 3621219 : if (par_anc.None()) return;
191 : : // To each such ancestor, add as descendants the descendants of the child.
192 : 1855980 : const auto& chl_des = entries[child].descendants;
193 [ + + ]: 8376526 : for (auto anc_of_par : par_anc) {
194 : 7038812 : entries[anc_of_par].descendants |= chl_des;
195 : : }
196 : : // To each descendant of the child, add those ancestors.
197 [ + - + + ]: 5721091 : for (auto dec_of_chl : Descendants(child)) {
[ + + # # ]
198 : 2853694 : entries[dec_of_chl].ancestors |= par_anc;
199 : : }
200 : : }
201 : :
202 : : /** Compute the (reduced) set of parents of node i in this graph.
203 : : *
204 : : * This returns the minimal subset of the parents of i whose ancestors together equal all of
205 : : * i's ancestors (unless i is part of a cycle of dependencies). Note that DepGraph does not
206 : : * store the set of parents; this information is inferred from the ancestor sets.
207 : : *
208 : : * Complexity: O(N) where N=Ancestors(i).Count() (which is bounded by TxCount()).
209 : : */
210 : 8717711 : SetType GetReducedParents(DepGraphIndex i) const noexcept
211 : : {
212 : 8717711 : SetType parents = Ancestors(i);
213 : 8717711 : parents.Reset(i);
214 [ + + + + ]: 47974226 : for (auto parent : parents) {
[ + + # # ]
215 [ + + ]: 33282687 : if (parents[parent]) {
216 : 31739286 : parents -= Ancestors(parent);
217 : 31739286 : parents.Set(parent);
218 : : }
219 : : }
220 : 8717711 : return parents;
221 : : }
222 : :
223 : : /** Compute the (reduced) set of children of node i in this graph.
224 : : *
225 : : * This returns the minimal subset of the children of i whose descendants together equal all of
226 : : * i's descendants (unless i is part of a cycle of dependencies). Note that DepGraph does not
227 : : * store the set of children; this information is inferred from the descendant sets.
228 : : *
229 : : * Complexity: O(N) where N=Descendants(i).Count() (which is bounded by TxCount()).
230 : : */
231 : 236087 : SetType GetReducedChildren(DepGraphIndex i) const noexcept
232 : : {
233 : 236087 : SetType children = Descendants(i);
234 : 236087 : children.Reset(i);
235 [ + + + + ]: 1609741 : for (auto child : children) {
236 [ + + ]: 1213836 : if (children[child]) {
237 : 393253 : children -= Descendants(child);
238 : 393253 : children.Set(child);
239 : : }
240 : : }
241 : 236087 : return children;
242 : : }
243 : :
244 : : /** Compute the aggregate feerate of a set of nodes in this graph.
245 : : *
246 : : * Complexity: O(N) where N=elems.Count().
247 : : **/
248 : 34540845 : FeeFrac FeeRate(const SetType& elems) const noexcept
249 : : {
250 : 34540845 : FeeFrac ret;
251 [ + - + + ]: 671910787 : for (auto pos : elems) ret += entries[pos].feerate;
[ + + # # ]
252 : 34540845 : return ret;
253 : : }
254 : :
255 : : /** Get the connected component within the subset "todo" that contains tx (which must be in
256 : : * todo).
257 : : *
258 : : * Two transactions are considered connected if they are both in `todo`, and one is an ancestor
259 : : * of the other in the entire graph (so not just within `todo`), or transitively there is a
260 : : * path of transactions connecting them. This does mean that if `todo` contains a transaction
261 : : * and a grandparent, but misses the parent, they will still be part of the same component.
262 : : *
263 : : * Complexity: O(ret.Count()).
264 : : */
265 : 6726338 : SetType GetConnectedComponent(const SetType& todo, DepGraphIndex tx) const noexcept
266 : : {
267 [ - + ]: 6726338 : Assume(todo[tx]);
268 [ - + ]: 13003416 : Assume(todo.IsSubsetOf(m_used));
269 : 6726338 : auto to_add = SetType::Singleton(tx);
270 : 6726338 : SetType ret;
271 : : do {
272 : 14548784 : SetType old = ret;
273 [ + - + + ]: 41297774 : for (auto add : to_add) {
[ + + # # ]
274 : 48628193 : ret |= Descendants(add);
275 : 48628193 : ret |= Ancestors(add);
276 : : }
277 [ + + ]: 14548784 : ret &= todo;
278 : 14548784 : to_add = ret - old;
279 [ + + ]: 28009783 : } while (to_add.Any());
280 : 6726338 : return ret;
281 : : }
282 : :
283 : : /** Find some connected component within the subset "todo" of this graph.
284 : : *
285 : : * Specifically, this finds the connected component which contains the first transaction of
286 : : * todo (if any).
287 : : *
288 : : * Complexity: O(ret.Count()).
289 : : */
290 [ + + ]: 5563001 : SetType FindConnectedComponent(const SetType& todo) const noexcept
291 : : {
292 [ + + ]: 5563001 : if (todo.None()) return todo;
293 : 5555492 : return GetConnectedComponent(todo, todo.First());
294 : : }
295 : :
296 : : /** Determine if a subset is connected.
297 : : *
298 : : * Complexity: O(subset.Count()).
299 : : */
300 : 2100899 : bool IsConnected(const SetType& subset) const noexcept
301 : : {
302 [ + + ]: 2100899 : return FindConnectedComponent(subset) == subset;
303 : : }
304 : :
305 : : /** Determine if this entire graph is connected.
306 : : *
307 : : * Complexity: O(TxCount()).
308 : : */
309 : 432 : bool IsConnected() const noexcept { return IsConnected(m_used); }
310 : :
311 : : /** Append the entries of select to list in a topologically valid order.
312 : : *
313 : : * Complexity: O(select.Count() * log(select.Count())).
314 : : */
315 [ - + ]: 19847 : void AppendTopo(std::vector<DepGraphIndex>& list, const SetType& select) const noexcept
316 : : {
317 : 19847 : DepGraphIndex old_len = list.size();
318 [ + - + + ]: 80084 : for (auto i : select) list.push_back(i);
319 : 19847 : std::sort(list.begin() + old_len, list.end(), [&](DepGraphIndex a, DepGraphIndex b) noexcept {
320 [ + + ]: 99030 : const auto a_anc_count = entries[a].ancestors.Count();
321 : 99030 : const auto b_anc_count = entries[b].ancestors.Count();
322 [ + + ]: 99030 : if (a_anc_count != b_anc_count) return a_anc_count < b_anc_count;
323 : 29873 : return a < b;
324 : : });
325 : 19847 : }
326 : :
327 : : /** Check if this graph is acyclic. */
328 : 47661 : bool IsAcyclic() const noexcept
329 : : {
330 [ + + + + ]: 419890 : for (auto i : Positions()) {
331 [ + + ]: 324917 : if ((Ancestors(i) & Descendants(i)) != SetType::Singleton(i)) {
332 : : return false;
333 : : }
334 : : }
335 : : return true;
336 : : }
337 : :
338 : : unsigned CountDependencies() const noexcept
339 : : {
340 : : unsigned ret = 0;
341 : : for (auto i : Positions()) {
342 : : ret += GetReducedParents(i).Count();
343 : : }
344 : : return ret;
345 : : }
346 : :
347 : : /** Reduce memory usage if possible. No observable effect. */
348 : 972760 : void Compact() noexcept
349 : : {
350 [ - + ]: 972760 : entries.shrink_to_fit();
351 : : }
352 : :
353 : 2277189 : size_t DynamicMemoryUsage() const noexcept
354 : : {
355 [ - + - + : 2315479 : return memusage::DynamicUsage(entries);
- + ][ - + ]
356 : : }
357 : : };
358 : :
359 : : /** A set of transactions together with their aggregate feerate. */
360 : : template<typename SetType>
361 : : struct SetInfo
362 : : {
363 : : /** The transactions in the set. */
364 : 609 : SetType transactions;
365 : : /** Their combined fee and size. */
366 : 609 : FeeFrac feerate;
367 : :
368 : : /** Construct a SetInfo for the empty set. */
369 : 7262818 : SetInfo() noexcept = default;
370 : :
371 : : /** Construct a SetInfo for a specified set and feerate. */
372 : 1472 : SetInfo(const SetType& txn, const FeeFrac& fr) noexcept : transactions(txn), feerate(fr) {}
373 : :
374 : : /** Construct a SetInfo for a given transaction in a depgraph. */
375 : 17548661 : explicit SetInfo(const DepGraph<SetType>& depgraph, DepGraphIndex pos) noexcept :
376 : 17548661 : transactions(SetType::Singleton(pos)), feerate(depgraph.FeeRate(pos)) {}
377 : :
378 : : /** Construct a SetInfo for a set of transactions in a depgraph. */
379 : 34436419 : explicit SetInfo(const DepGraph<SetType>& depgraph, const SetType& txn) noexcept :
380 : 34436419 : transactions(txn), feerate(depgraph.FeeRate(txn)) {}
381 : :
382 : : /** Add a transaction to this SetInfo (which must not yet be in it). */
383 : 6737 : void Set(const DepGraph<SetType>& depgraph, DepGraphIndex pos) noexcept
384 : : {
385 [ - + ]: 6737 : Assume(!transactions[pos]);
386 : 6737 : transactions.Set(pos);
387 : 6737 : feerate += depgraph.FeeRate(pos);
388 : 6737 : }
389 : :
390 : : /** Add the transactions of other to this SetInfo (no overlap allowed). */
391 : 14499255 : SetInfo& operator|=(const SetInfo& other) noexcept
392 : : {
393 [ - + ]: 16122541 : Assume(!transactions.Overlaps(other.transactions));
394 : 14499255 : transactions |= other.transactions;
395 : 14499255 : feerate += other.feerate;
396 : 14499255 : return *this;
397 : : }
398 : :
399 : : /** Remove the transactions of other from this SetInfo (which must be a subset). */
400 : 1764578 : SetInfo& operator-=(const SetInfo& other) noexcept
401 : : {
402 [ - + ]: 1770425 : Assume(other.transactions.IsSubsetOf(transactions));
403 : 1764578 : transactions -= other.transactions;
404 : 1764578 : feerate -= other.feerate;
405 : 1764578 : return *this;
406 : : }
407 : :
408 : : /** Compute the difference between this and other SetInfo (which must be a subset). */
409 : : SetInfo operator-(const SetInfo& other) const noexcept
410 : : {
411 : : Assume(other.transactions.IsSubsetOf(transactions));
412 : : return {transactions - other.transactions, feerate - other.feerate};
413 : : }
414 : :
415 : : /** Swap two SetInfo objects. */
416 : : friend void swap(SetInfo& a, SetInfo& b) noexcept
417 : : {
418 : : swap(a.transactions, b.transactions);
419 : : swap(a.feerate, b.feerate);
420 : : }
421 : :
422 : : /** Permit equality testing. */
423 [ + - + - ]: 1218 : friend bool operator==(const SetInfo&, const SetInfo&) noexcept = default;
424 : : };
425 : :
426 : : /** Compute the chunks of linearization as SetInfos. */
427 : : template<typename SetType>
428 : 1207399 : std::vector<SetInfo<SetType>> ChunkLinearizationInfo(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> linearization) noexcept
429 : : {
430 : 1207399 : std::vector<SetInfo<SetType>> ret;
431 [ + + ]: 11493242 : for (DepGraphIndex i : linearization) {
432 : : /** The new chunk to be added, initially a singleton. */
433 : 10285843 : SetInfo<SetType> new_chunk(depgraph, i);
434 : : // As long as the new chunk has a higher feerate than the last chunk so far, absorb it.
435 [ + + + + ]: 14828386 : while (!ret.empty() && new_chunk.feerate >> ret.back().feerate) {
436 : 4542543 : new_chunk |= ret.back();
437 : 4542543 : ret.pop_back();
438 : : }
439 : : // Actually move that new chunk into the chunking.
440 : 10285843 : ret.emplace_back(std::move(new_chunk));
441 : : }
442 : 1207399 : return ret;
443 : : }
444 : :
445 : : /** Compute the feerates of the chunks of linearization. Identical to ChunkLinearizationInfo, but
446 : : * only returns the chunk feerates, not the corresponding transaction sets. */
447 : : template<typename SetType>
448 : 1431081 : std::vector<FeeFrac> ChunkLinearization(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> linearization) noexcept
449 : : {
450 : 1431081 : std::vector<FeeFrac> ret;
451 [ + + ]: 10939765 : for (DepGraphIndex i : linearization) {
452 : : /** The new chunk to be added, initially a singleton. */
453 : 9508684 : auto new_chunk = depgraph.FeeRate(i);
454 : : // As long as the new chunk has a higher feerate than the last chunk so far, absorb it.
455 [ + + + + ]: 14242965 : while (!ret.empty() && new_chunk >> ret.back()) {
456 : 4734281 : new_chunk += ret.back();
457 : 4734281 : ret.pop_back();
458 : : }
459 : : // Actually move that new chunk into the chunking.
460 : 9508684 : ret.push_back(std::move(new_chunk));
461 : : }
462 : 1431081 : return ret;
463 : : }
464 : :
465 : : /** Concept for function objects that return std::strong_ordering when invoked with two Args. */
466 : : template<typename F, typename Arg>
467 : : concept StrongComparator =
468 : : std::regular_invocable<F, Arg, Arg> &&
469 : : std::is_same_v<std::invoke_result_t<F, Arg, Arg>, std::strong_ordering>;
470 : :
471 : : /** Simple default transaction ordering function for SpanningForestState::GetLinearization() and
472 : : * Linearize(), which just sorts by DepGraphIndex. */
473 : : using IndexTxOrder = std::compare_three_way;
474 : :
475 : : /** Class to represent the internal state of the spanning-forest linearization (SFL) algorithm.
476 : : *
477 : : * At all times, each dependency is marked as either "active" or "inactive". The subset of active
478 : : * dependencies is the state of the SFL algorithm. The implementation maintains several other
479 : : * values to speed up operations, but everything is ultimately a function of what that subset of
480 : : * active dependencies is.
481 : : *
482 : : * Given such a subset, define a chunk as the set of transactions that are connected through active
483 : : * dependencies (ignoring their parent/child direction). Thus, every state implies a particular
484 : : * partitioning of the graph into chunks (including potential singletons). In the extreme, each
485 : : * transaction may be in its own chunk, or in the other extreme all transactions may form a single
486 : : * chunk. A chunk's feerate is its total fee divided by its total size.
487 : : *
488 : : * The algorithm consists of switching dependencies between active and inactive. The final
489 : : * linearization that is produced at the end consists of these chunks, sorted from high to low
490 : : * feerate, each individually sorted in an arbitrary but topological (= no child before parent)
491 : : * way.
492 : : *
493 : : * We define four quality properties the state can have:
494 : : *
495 : : * - acyclic: The state is acyclic whenever no cycle of active dependencies exists within the
496 : : * graph, ignoring the parent/child direction. This is equivalent to saying that within
497 : : * each chunk the set of active dependencies form a tree, and thus the overall set of
498 : : * active dependencies in the graph form a spanning forest, giving the algorithm its
499 : : * name. Being acyclic is also equivalent to every chunk of N transactions having
500 : : * exactly N-1 active dependencies.
501 : : *
502 : : * For example in a diamond graph, D->{B,C}->A, the 4 dependencies cannot be
503 : : * simultaneously active. If at least one is inactive, the state is acyclic.
504 : : *
505 : : * The algorithm maintains an acyclic state at *all* times as an invariant. This implies
506 : : * that activating a dependency always corresponds to merging two chunks, and that
507 : : * deactivating one always corresponds to splitting two chunks.
508 : : *
509 : : * - topological: We say the state is topological whenever it is acyclic and no inactive dependency
510 : : * exists between two distinct chunks such that the child chunk has higher or equal
511 : : * feerate than the parent chunk.
512 : : *
513 : : * The relevance is that whenever the state is topological, the produced output
514 : : * linearization will be topological too (i.e., not have children before parents).
515 : : * Note that the "or equal" part of the definition matters: if not, one can end up
516 : : * in a situation with mutually-dependent equal-feerate chunks that cannot be
517 : : * linearized. For example C->{A,B} and D->{A,B}, with C->A and D->B active. The AC
518 : : * chunk depends on DB through C->B, and the BD chunk depends on AC through D->A.
519 : : * Merging them into a single ABCD chunk fixes this.
520 : : *
521 : : * The algorithm attempts to keep the state topological as much as possible, so it
522 : : * can be interrupted to produce an output whenever, but will sometimes need to
523 : : * temporarily deviate from it when improving the state.
524 : : *
525 : : * - optimal: For every active dependency, define its top and bottom set as the set of transactions
526 : : * in the chunks that would result if the dependency were deactivated; the top being the
527 : : * one with the dependency's parent, and the bottom being the one with the child. Note
528 : : * that due to acyclicity, every deactivation splits a chunk exactly in two.
529 : : *
530 : : * We say the state is optimal whenever it is topological and it has no active
531 : : * dependency whose top feerate is strictly higher than its bottom feerate. The
532 : : * relevance is that it can be proven that whenever the state is optimal, the produced
533 : : * linearization will also be optimal (in the convexified feerate diagram sense). It can
534 : : * also be proven that for every graph at least one optimal state exists.
535 : : *
536 : : * Note that it is possible for the SFL state to not be optimal, but the produced
537 : : * linearization to still be optimal. This happens when the chunks of a state are
538 : : * identical to those of an optimal state, but the exact set of active dependencies
539 : : * within a chunk differ in such a way that the state optimality condition is not
540 : : * satisfied. Thus, the state being optimal is more a "the eventual output is *known*
541 : : * to be optimal".
542 : : *
543 : : * - minimal: We say the state is minimal when it is:
544 : : * - acyclic
545 : : * - topological, except that inactive dependencies between equal-feerate chunks are
546 : : * allowed as long as they do not form a loop.
547 : : * - like optimal, no active dependencies whose top feerate is strictly higher than
548 : : * the bottom feerate are allowed.
549 : : * - no chunk contains a proper non-empty subset which includes all its own in-chunk
550 : : * dependencies of the same feerate as the chunk itself.
551 : : *
552 : : * A minimal state effectively corresponds to an optimal state, where every chunk has
553 : : * been split into its minimal equal-feerate components.
554 : : *
555 : : * The algorithm terminates whenever a minimal state is reached.
556 : : *
557 : : *
558 : : * This leads to the following high-level algorithm:
559 : : * - Start with all dependencies inactive, and thus all transactions in their own chunk. This is
560 : : * definitely acyclic.
561 : : * - Activate dependencies (merging chunks) until the state is topological.
562 : : * - Loop until optimal (no dependencies with higher-feerate top than bottom), or time runs out:
563 : : * - Deactivate a violating dependency, potentially making the state non-topological.
564 : : * - Activate other dependencies to make the state topological again.
565 : : * - If there is time left and the state is optimal:
566 : : * - Attempt to split chunks into equal-feerate parts without mutual dependencies between them.
567 : : * When this succeeds, recurse into them.
568 : : * - If no such chunks can be found, the state is minimal.
569 : : * - Output the chunks from high to low feerate, each internally sorted topologically.
570 : : *
571 : : * When merging, we always either:
572 : : * - Merge upwards: merge a chunk with the lowest-feerate other chunk it depends on, among those
573 : : * with lower or equal feerate than itself.
574 : : * - Merge downwards: merge a chunk with the highest-feerate other chunk that depends on it, among
575 : : * those with higher or equal feerate than itself.
576 : : *
577 : : * Using these strategies in the improvement loop above guarantees that the output linearization
578 : : * after a deactivate + merge step is never worse or incomparable (in the convexified feerate
579 : : * diagram sense) than the output linearization that would be produced before the step. With that,
580 : : * we can refine the high-level algorithm to:
581 : : * - Start with all dependencies inactive.
582 : : * - Perform merges as described until none are possible anymore, making the state topological.
583 : : * - Loop until optimal or time runs out:
584 : : * - Pick a dependency D to deactivate among those with higher feerate top than bottom.
585 : : * - Deactivate D, causing the chunk it is in to split into top T and bottom B.
586 : : * - Do an upwards merge of T, if possible. If so, repeat the same with the merged result.
587 : : * - Do a downwards merge of B, if possible. If so, repeat the same with the merged result.
588 : : * - Split chunks further to obtain a minimal state, see below.
589 : : * - Output the chunks from high to low feerate, each internally sorted topologically.
590 : : *
591 : : * Instead of performing merges arbitrarily to make the initial state topological, it is possible
592 : : * to do so guided by an existing linearization. This has the advantage that the state's would-be
593 : : * output linearization is immediately as good as the existing linearization it was based on:
594 : : * - Start with all dependencies inactive.
595 : : * - For each transaction t in the existing linearization:
596 : : * - Find the chunk C that transaction is in (which will be singleton).
597 : : * - Do an upwards merge of C, if possible. If so, repeat the same with the merged result.
598 : : * No downwards merges are needed in this case.
599 : : *
600 : : * After reaching an optimal state, it can be transformed into a minimal state by attempting to
601 : : * split chunks further into equal-feerate parts. To do so, pick a specific transaction in each
602 : : * chunk (the pivot), and rerun the above split-then-merge procedure again:
603 : : * - first, while pretending the pivot transaction has an infinitesimally higher (or lower) fee
604 : : * than it really has. If a split exists with the pivot in the top part (or bottom part), this
605 : : * will find it.
606 : : * - if that fails to split, repeat while pretending the pivot transaction has an infinitesimally
607 : : * lower (or higher) fee. If a split exists with the pivot in the bottom part (or top part), this
608 : : * will find it.
609 : : * - if either succeeds, repeat the procedure for the newly found chunks to split them further.
610 : : * If not, the chunk is already minimal.
611 : : * If the chunk can be split into equal-feerate parts, then the pivot must exist in either the top
612 : : * or bottom part of that potential split. By trying both with the same pivot, if a split exists,
613 : : * it will be found.
614 : : *
615 : : * What remains to be specified are a number of heuristics:
616 : : *
617 : : * - How to decide which chunks to merge:
618 : : * - The merge upwards and downward rules specify that the lowest-feerate respectively
619 : : * highest-feerate candidate chunk is merged with, but if there are multiple equal-feerate
620 : : * candidates, a uniformly random one among them is picked.
621 : : *
622 : : * - How to decide what dependency to activate (when merging chunks):
623 : : * - After picking two chunks to be merged (see above), a uniformly random dependency between the
624 : : * two chunks is activated.
625 : : *
626 : : * - How to decide which chunk to find a dependency to split in:
627 : : * - A round-robin queue of chunks to improve is maintained. The initial ordering of this queue
628 : : * is uniformly randomly permuted.
629 : : *
630 : : * - How to decide what dependency to deactivate (when splitting chunks):
631 : : * - Inside the selected chunk (see above), among the dependencies whose top feerate is strictly
632 : : * higher than its bottom feerate in the selected chunk, if any, a uniformly random dependency
633 : : * is deactivated.
634 : : * - After every split, it is possible that the top and the bottom chunk merge with each other
635 : : * again in the merge sequence (through a top->bottom dependency, not through the deactivated
636 : : * one, which was bottom->top). Call this a self-merge. If a self-merge does not occur after
637 : : * a split, the resulting linearization is strictly improved (the area under the convexified
638 : : * feerate diagram increases by at least gain/2), while self-merges do not change it.
639 : : *
640 : : * - How to decide the exact output linearization:
641 : : * - When there are multiple equal-feerate chunks with no dependencies between them, output a
642 : : * uniformly random one among the ones with no missing dependent chunks first.
643 : : * - Within chunks, repeatedly pick a uniformly random transaction among those with no missing
644 : : * dependencies.
645 : : */
646 : : template<typename SetType>
647 : : class SpanningForestState
648 : : {
649 : : private:
650 : : /** Internal RNG. */
651 : : InsecureRandomContext m_rng;
652 : :
653 : : /** Data type to represent indexing into m_tx_data. */
654 : : using TxIdx = DepGraphIndex;
655 : : /** Data type to represent indexing into m_set_info. Use the smallest type possible to improve
656 : : * cache locality. */
657 : : using SetIdx = std::conditional_t<(SetType::Size() <= 0xff),
658 : : uint8_t,
659 : : std::conditional_t<(SetType::Size() <= 0xffff),
660 : : uint16_t,
661 : : uint32_t>>;
662 : : /** An invalid SetIdx. */
663 : : static constexpr SetIdx INVALID_SET_IDX = SetIdx(-1);
664 : :
665 : : /** Structure with information about a single transaction. */
666 : 7285377 : struct TxData {
667 : : /** The top set for every active child dependency this transaction has, indexed by child
668 : : * TxIdx. Only defined for indexes in active_children. */
669 : : std::array<SetIdx, SetType::Size()> dep_top_idx;
670 : : /** The set of parent transactions of this transaction. Immutable after construction. */
671 : : SetType parents;
672 : : /** The set of child transactions of this transaction. Immutable after construction. */
673 : : SetType children;
674 : : /** The set of child transactions reachable through an active dependency. */
675 : : SetType active_children;
676 : : /** Which chunk this transaction belongs to. */
677 : : SetIdx chunk_idx;
678 : : };
679 : :
680 : : /** The set of all TxIdx's of transactions in the cluster indexing into m_tx_data. */
681 : : SetType m_transaction_idxs;
682 : : /** The set of all chunk SetIdx's. This excludes the SetIdxs that refer to active
683 : : * dependencies' tops. */
684 : : SetType m_chunk_idxs;
685 : : /** The set of all SetIdx's that appear in m_suboptimal_chunks. Note that they do not need to
686 : : * be chunks: some of these sets may have been converted to a dependency's top set since being
687 : : * added to m_suboptimal_chunks. */
688 : : SetType m_suboptimal_idxs;
689 : : /** Information about each transaction (and chunks). Keeps the "holes" from DepGraph during
690 : : * construction. Indexed by TxIdx. */
691 : : std::vector<TxData> m_tx_data;
692 : : /** Information about each set (chunk, or active dependency top set). Indexed by SetIdx. */
693 : : std::vector<SetInfo<SetType>> m_set_info;
694 : : /** For each chunk, indexed by SetIdx, the set of out-of-chunk reachable transactions, in the
695 : : * upwards (.first) and downwards (.second) direction. */
696 : : std::vector<std::pair<SetType, SetType>> m_reachable;
697 : : /** A FIFO of chunk SetIdxs for chunks that may be improved still. */
698 : : VecDeque<SetIdx> m_suboptimal_chunks;
699 : : /** A FIFO of chunk indexes with a pivot transaction in them, and a flag to indicate their
700 : : * status:
701 : : * - bit 1: currently attempting to move the pivot down, rather than up.
702 : : * - bit 2: this is the second stage, so we have already tried moving the pivot in the other
703 : : * direction.
704 : : */
705 : : VecDeque<std::tuple<SetIdx, TxIdx, unsigned>> m_nonminimal_chunks;
706 : :
707 : : /** The number of updated transactions in activations/deactivations. */
708 : : uint64_t m_cost{0};
709 : :
710 : : /** The DepGraph we are trying to linearize. */
711 : : const DepGraph<SetType>& m_depgraph;
712 : :
713 : : /** Pick a random transaction within a set (which must be non-empty). */
714 : 3997445 : TxIdx PickRandomTx(const SetType& tx_idxs) noexcept
715 : : {
716 [ - + ]: 4021090 : Assume(tx_idxs.Any());
717 : 3997445 : unsigned pos = m_rng.randrange<unsigned>(tx_idxs.Count());
718 [ + - + - ]: 9731019 : for (auto tx_idx : tx_idxs) {
[ + - # # ]
719 [ + + ]: 5757219 : if (pos == 0) return tx_idx;
720 : 1759774 : --pos;
721 : : }
722 : 0 : Assume(false);
723 : 0 : return TxIdx(-1);
724 : : }
725 : :
726 : : /** Find the set of out-of-chunk transactions reachable from tx_idxs, both in upwards and
727 : : * downwards direction. Only used by SanityCheck to verify the precomputed reachable sets in
728 : : * m_reachable that are maintained by Activate/Deactivate. */
729 : 46513 : std::pair<SetType, SetType> GetReachable(const SetType& tx_idxs) const noexcept
730 : : {
731 : 46513 : SetType parents, children;
732 [ + - + + ]: 189552 : for (auto tx_idx : tx_idxs) {
733 : 96526 : const auto& tx_data = m_tx_data[tx_idx];
734 : 96526 : parents |= tx_data.parents;
735 : 96526 : children |= tx_data.children;
736 : : }
737 : 46513 : return {parents - tx_idxs, children - tx_idxs};
738 : : }
739 : :
740 : : /** Make the inactive dependency from child to parent, which must not be in the same chunk
741 : : * already, active. Returns the merged chunk idx. */
742 : 3624626 : SetIdx Activate(TxIdx parent_idx, TxIdx child_idx) noexcept
743 : : {
744 : : // Gather and check information about the parent and child transactions.
745 : 3624626 : auto& parent_data = m_tx_data[parent_idx];
746 : 3624626 : auto& child_data = m_tx_data[child_idx];
747 [ - + ]: 3624626 : Assume(parent_data.children[child_idx]);
748 [ - + ]: 3624626 : Assume(!parent_data.active_children[child_idx]);
749 : : // Get the set index of the chunks the parent and child are currently in. The parent chunk
750 : : // will become the top set of the newly activated dependency, while the child chunk will be
751 : : // grown to become the merged chunk.
752 : 3624626 : auto parent_chunk_idx = parent_data.chunk_idx;
753 : 3624626 : auto child_chunk_idx = child_data.chunk_idx;
754 [ - + ]: 3624626 : Assume(parent_chunk_idx != child_chunk_idx);
755 [ - + ]: 3624626 : Assume(m_chunk_idxs[parent_chunk_idx]);
756 [ - + ]: 3624626 : Assume(m_chunk_idxs[child_chunk_idx]);
757 [ + - ]: 3624626 : auto& top_info = m_set_info[parent_chunk_idx];
758 : 3624626 : auto& bottom_info = m_set_info[child_chunk_idx];
759 : :
760 : : // Consider the following example:
761 : : //
762 : : // A A There are two chunks, ABC and DEF, and the inactive E->C dependency
763 : : // / \ / \ is activated, resulting in a single chunk ABCDEF.
764 : : // B C B C
765 : : // : ==> | Dependency | top set before | top set after | change
766 : : // D E D E B->A | AC | ACDEF | +DEF
767 : : // \ / \ / C->A | AB | AB |
768 : : // F F F->D | D | D |
769 : : // F->E | E | ABCE | +ABC
770 : : //
771 : : // The common pattern here is that any dependency which has the parent or child of the
772 : : // dependency being activated (E->C here) in its top set, will have the opposite part added
773 : : // to it. This is true for B->A and F->E, but not for C->A and F->D.
774 : : //
775 : : // Traverse the old parent chunk top_info (ABC in example), and add bottom_info (DEF) to
776 : : // every dependency's top set which has the parent (C) in it. At the same time, change the
777 : : // chunk_idx for each to be child_chunk_idx, which becomes the set for the merged chunk.
778 [ + - + + ]: 23057442 : for (auto tx_idx : top_info.transactions) {
[ + + # # ]
779 [ + + ]: 15818486 : auto& tx_data = m_tx_data[tx_idx];
780 : 15818486 : tx_data.chunk_idx = child_chunk_idx;
781 [ + + + + ]: 37568009 : for (auto dep_child_idx : tx_data.active_children) {
[ + + # # ]
782 : 12193860 : auto& dep_top_info = m_set_info[tx_data.dep_top_idx[dep_child_idx]];
783 [ + + ]: 12193860 : if (dep_top_info.transactions[parent_idx]) dep_top_info |= bottom_info;
784 : : }
785 : : }
786 : : // Traverse the old child chunk bottom_info (DEF in example), and add top_info (ABC) to
787 : : // every dependency's top set which has the child (E) in it.
788 [ + - + + ]: 13963169 : for (auto tx_idx : bottom_info.transactions) {
[ + + # # ]
789 [ + + ]: 6724213 : auto& tx_data = m_tx_data[tx_idx];
790 [ + + + + ]: 12509238 : for (auto dep_child_idx : tx_data.active_children) {
[ + + # # ]
791 : 3099587 : auto& dep_top_info = m_set_info[tx_data.dep_top_idx[dep_child_idx]];
792 [ + + ]: 3099587 : if (dep_top_info.transactions[child_idx]) dep_top_info |= top_info;
793 : : }
794 : : }
795 : : // Merge top_info into bottom_info, which becomes the merged chunk.
796 : 3624626 : bottom_info |= top_info;
797 : 3624626 : m_cost += bottom_info.transactions.Count();
798 : : // Compute merged sets of reachable transactions from the new chunk, based on the input
799 : : // chunks' reachable sets.
800 : 3624626 : m_reachable[child_chunk_idx].first |= m_reachable[parent_chunk_idx].first;
801 : 3624626 : m_reachable[child_chunk_idx].second |= m_reachable[parent_chunk_idx].second;
802 : 3624626 : m_reachable[child_chunk_idx].first -= bottom_info.transactions;
803 : 3624626 : m_reachable[child_chunk_idx].second -= bottom_info.transactions;
804 : : // Make parent chunk the set for the new active dependency.
805 : 3624626 : parent_data.dep_top_idx[child_idx] = parent_chunk_idx;
806 : 3624626 : parent_data.active_children.Set(child_idx);
807 : 3624626 : m_chunk_idxs.Reset(parent_chunk_idx);
808 : : // Return the newly merged chunk.
809 : 3624626 : return child_chunk_idx;
810 : : }
811 : :
812 : : /** Make a specified active dependency inactive. Returns the created parent and child chunk
813 : : * indexes. */
814 : 420082 : std::pair<SetIdx, SetIdx> Deactivate(TxIdx parent_idx, TxIdx child_idx) noexcept
815 : : {
816 : : // Gather and check information about the parent transactions.
817 : 420082 : auto& parent_data = m_tx_data[parent_idx];
818 [ - + ]: 420082 : Assume(parent_data.children[child_idx]);
819 [ - + ]: 420082 : Assume(parent_data.active_children[child_idx]);
820 : : // Get the top set of the active dependency (which will become the parent chunk) and the
821 : : // chunk set the transactions are currently in (which will become the bottom chunk).
822 [ - + ]: 420082 : auto parent_chunk_idx = parent_data.dep_top_idx[child_idx];
823 : 420082 : auto child_chunk_idx = parent_data.chunk_idx;
824 [ - + ]: 420082 : Assume(parent_chunk_idx != child_chunk_idx);
825 [ - + ]: 420082 : Assume(m_chunk_idxs[child_chunk_idx]);
826 [ - + ]: 420082 : Assume(!m_chunk_idxs[parent_chunk_idx]); // top set, not a chunk
827 : 420082 : auto& top_info = m_set_info[parent_chunk_idx];
828 : 420082 : auto& bottom_info = m_set_info[child_chunk_idx];
829 : :
830 : : // Remove the active dependency.
831 : 420082 : parent_data.active_children.Reset(child_idx);
832 : 420082 : m_chunk_idxs.Set(parent_chunk_idx);
833 : 420082 : m_cost += bottom_info.transactions.Count();
834 : : // Subtract the top_info from the bottom_info, as it will become the child chunk.
835 : 420082 : bottom_info -= top_info;
836 : : // See the comment above in Activate(). We perform the opposite operations here, removing
837 : : // instead of adding. Simultaneously, aggregate the top/bottom's union of parents/children.
838 : 420082 : SetType top_parents, top_children;
839 [ + - + + ]: 2833735 : for (auto tx_idx : top_info.transactions) {
[ + + # # ]
840 [ + + ]: 1996195 : auto& tx_data = m_tx_data[tx_idx];
841 : 1996195 : tx_data.chunk_idx = parent_chunk_idx;
842 [ + + ]: 2016073 : top_parents |= tx_data.parents;
843 : 1996195 : top_children |= tx_data.children;
844 [ + + + + ]: 4771614 : for (auto dep_child_idx : tx_data.active_children) {
[ + + # # ]
845 : 1576113 : auto& dep_top_info = m_set_info[tx_data.dep_top_idx[dep_child_idx]];
846 [ + + ]: 1576113 : if (dep_top_info.transactions[parent_idx]) dep_top_info -= bottom_info;
847 : : }
848 : : }
849 : 420082 : SetType bottom_parents, bottom_children;
850 [ + - + + ]: 1915671 : for (auto tx_idx : bottom_info.transactions) {
[ + + # # ]
851 [ + + ]: 1078131 : auto& tx_data = m_tx_data[tx_idx];
852 [ + + ]: 1093488 : bottom_parents |= tx_data.parents;
853 : 1078131 : bottom_children |= tx_data.children;
854 [ + + + + ]: 2225935 : for (auto dep_child_idx : tx_data.active_children) {
[ + + # # ]
855 : 658049 : auto& dep_top_info = m_set_info[tx_data.dep_top_idx[dep_child_idx]];
856 [ + + ]: 658049 : if (dep_top_info.transactions[child_idx]) dep_top_info -= top_info;
857 : : }
858 : : }
859 : : // Compute the new sets of reachable transactions for each new chunk, based on the
860 : : // top/bottom parents and children computed above.
861 : 420082 : m_reachable[parent_chunk_idx].first = top_parents - top_info.transactions;
862 : 420082 : m_reachable[parent_chunk_idx].second = top_children - top_info.transactions;
863 : 420082 : m_reachable[child_chunk_idx].first = bottom_parents - bottom_info.transactions;
864 : 420082 : m_reachable[child_chunk_idx].second = bottom_children - bottom_info.transactions;
865 : : // Return the two new set idxs.
866 : 420082 : return {parent_chunk_idx, child_chunk_idx};
867 : : }
868 : :
869 : : /** Activate a dependency from the bottom set to the top set, which must exist. Return the
870 : : * index of the merged chunk. */
871 : 3624626 : SetIdx MergeChunks(SetIdx top_idx, SetIdx bottom_idx) noexcept
872 : : {
873 [ - + ]: 3624626 : Assume(m_chunk_idxs[top_idx]);
874 [ - + ]: 3624626 : Assume(m_chunk_idxs[bottom_idx]);
875 [ + - ]: 3624626 : auto& top_chunk_info = m_set_info[top_idx];
876 : 3624626 : auto& bottom_chunk_info = m_set_info[bottom_idx];
877 : : // Count the number of dependencies between bottom_chunk and top_chunk.
878 : 3624626 : unsigned num_deps{0};
879 [ + - + + ]: 23057442 : for (auto tx_idx : top_chunk_info.transactions) {
[ + + # # ]
880 : 15818486 : auto& tx_data = m_tx_data[tx_idx];
881 : 15818486 : num_deps += (tx_data.children & bottom_chunk_info.transactions).Count();
882 : : }
883 [ - + ]: 3624626 : Assume(num_deps > 0);
884 : : // Uniformly randomly pick one of them and activate it.
885 : 3624626 : unsigned pick = m_rng.randrange(num_deps);
886 [ + - + - ]: 16334350 : for (auto tx_idx : top_chunk_info.transactions) {
[ + - # # ]
887 [ + + ]: 12720020 : auto& tx_data = m_tx_data[tx_idx];
888 [ + + ]: 12720020 : auto intersect = tx_data.children & bottom_chunk_info.transactions;
889 : 12720020 : auto count = intersect.Count();
890 [ + + ]: 12720020 : if (pick < count) {
891 [ + - + - ]: 7249115 : for (auto child_idx : intersect) {
[ + - # # ]
892 [ + + ]: 3634785 : if (pick == 0) return Activate(tx_idx, child_idx);
893 : 10159 : --pick;
894 : : }
895 : 0 : Assume(false);
896 : : break;
897 : : }
898 : 9095394 : pick -= count;
899 : : }
900 : 0 : Assume(false);
901 : 0 : return INVALID_SET_IDX;
902 : : }
903 : :
904 : : /** Activate a dependency from chunk_idx to merge_chunk_idx (if !DownWard), or a dependency
905 : : * from merge_chunk_idx to chunk_idx (if DownWard). Return the index of the merged chunk. */
906 : : template<bool DownWard>
907 : 3577053 : SetIdx MergeChunksDirected(SetIdx chunk_idx, SetIdx merge_chunk_idx) noexcept
908 : : {
909 : : if constexpr (DownWard) {
910 : 16327 : return MergeChunks(chunk_idx, merge_chunk_idx);
911 : : } else {
912 : 3560726 : return MergeChunks(merge_chunk_idx, chunk_idx);
913 : : }
914 : : }
915 : :
916 : : /** Determine which chunk to merge chunk_idx with, or INVALID_SET_IDX if none. */
917 : : template<bool DownWard>
918 : 13168759 : SetIdx PickMergeCandidate(SetIdx chunk_idx) noexcept
919 : : {
920 : : /** Information about the chunk. */
921 [ - + ]: 13168759 : Assume(m_chunk_idxs[chunk_idx]);
922 : 13168759 : auto& chunk_info = m_set_info[chunk_idx];
923 : : // Iterate over all chunks reachable from this one. For those depended-on chunks,
924 : : // remember the highest-feerate (if DownWard) or lowest-feerate (if !DownWard) one.
925 : : // If multiple equal-feerate candidate chunks to merge with exist, pick a random one
926 : : // among them.
927 : :
928 : : /** The minimum feerate (if downward) or maximum feerate (if upward) to consider when
929 : : * looking for candidate chunks to merge with. Initially, this is the original chunk's
930 : : * feerate, but is updated to be the current best candidate whenever one is found. */
931 : 13168759 : FeeFrac best_other_chunk_feerate = chunk_info.feerate;
932 : : /** The chunk index for the best candidate chunk to merge with. INVALID_SET_IDX if none. */
933 : 13168759 : SetIdx best_other_chunk_idx = INVALID_SET_IDX;
934 : : /** We generate random tiebreak values to pick between equal-feerate candidate chunks.
935 : : * This variable stores the tiebreak of the current best candidate. */
936 : 13168759 : uint64_t best_other_chunk_tiebreak{0};
937 : :
938 : : /** Which parent/child transactions we still need to process the chunks for. */
939 : 13168759 : auto todo = DownWard ? m_reachable[chunk_idx].second : m_reachable[chunk_idx].first;
940 : 13168759 : unsigned steps = 0;
941 [ + + ]: 27226318 : while (todo.Any()) {
942 : 13977660 : ++steps;
943 : : // Find a chunk for a transaction in todo, and remove all its transactions from todo.
944 [ + + ]: 13977660 : auto reached_chunk_idx = m_tx_data[todo.First()].chunk_idx;
945 : 13977660 : auto& reached_chunk_info = m_set_info[reached_chunk_idx];
946 [ + + ]: 13977660 : todo -= reached_chunk_info.transactions;
947 : : // See if it has an acceptable feerate.
948 [ + + ]: 941044 : auto cmp = DownWard ? FeeRateCompare(best_other_chunk_feerate, reached_chunk_info.feerate)
949 [ + + ]: 13036616 : : FeeRateCompare(reached_chunk_info.feerate, best_other_chunk_feerate);
950 [ + + ]: 13977660 : if (cmp > 0) continue;
951 [ + + ]: 4374253 : uint64_t tiebreak = m_rng.rand64();
952 [ + + + + ]: 4374253 : if (cmp < 0 || tiebreak >= best_other_chunk_tiebreak) {
953 : 4178173 : best_other_chunk_feerate = reached_chunk_info.feerate;
954 : 4178173 : best_other_chunk_idx = reached_chunk_idx;
955 : 4178173 : best_other_chunk_tiebreak = tiebreak;
956 : : }
957 : : }
958 [ - + - + ]: 13168759 : Assume(steps <= m_set_info.size());
959 : :
960 : 13168759 : return best_other_chunk_idx;
961 : : }
962 : :
963 : : /** Perform an upward or downward merge step, on the specified chunk. Returns the merged chunk,
964 : : * or INVALID_SET_IDX if no merge took place. */
965 : : template<bool DownWard>
966 : 13168759 : SetIdx MergeStep(SetIdx chunk_idx) noexcept
967 : : {
968 : 13168759 : auto merge_chunk_idx = PickMergeCandidate<DownWard>(chunk_idx);
969 [ + + ]: 13168759 : if (merge_chunk_idx == INVALID_SET_IDX) return INVALID_SET_IDX;
970 : 3577053 : chunk_idx = MergeChunksDirected<DownWard>(chunk_idx, merge_chunk_idx);
971 [ - + ]: 3577053 : Assume(chunk_idx != INVALID_SET_IDX);
972 : : return chunk_idx;
973 : : }
974 : :
975 : : /** Perform an upward or downward merge sequence on the specified chunk. */
976 : : template<bool DownWard>
977 : 66328 : void MergeSequence(SetIdx chunk_idx) noexcept
978 : : {
979 [ - + ]: 66328 : Assume(m_chunk_idxs[chunk_idx]);
980 : 11617 : while (true) {
981 : 77945 : auto merged_chunk_idx = MergeStep<DownWard>(chunk_idx);
982 [ + + ]: 77945 : if (merged_chunk_idx == INVALID_SET_IDX) break;
983 : 11617 : chunk_idx = merged_chunk_idx;
984 : : }
985 : : // Add the chunk to the queue of improvable chunks, if it wasn't already there.
986 [ + + ]: 66328 : if (!m_suboptimal_idxs[chunk_idx]) {
987 : 62999 : m_suboptimal_idxs.Set(chunk_idx);
988 : 62999 : m_suboptimal_chunks.push_back(chunk_idx);
989 : : }
990 : 66328 : }
991 : :
992 : : /** Split a chunk, and then merge the resulting two chunks to make the graph topological
993 : : * again. */
994 : 69452 : void Improve(TxIdx parent_idx, TxIdx child_idx) noexcept
995 : : {
996 : : // Deactivate the specified dependency, splitting it into two new chunks: a top containing
997 : : // the parent, and a bottom containing the child. The top should have a higher feerate.
998 [ + + ]: 69452 : auto [parent_chunk_idx, child_chunk_idx] = Deactivate(parent_idx, child_idx);
999 : :
1000 : : // At this point we have exactly two chunks which may violate topology constraints (the
1001 : : // parent chunk and child chunk that were produced by deactivation). We can fix
1002 : : // these using just merge sequences, one upwards and one downwards, avoiding the need for a
1003 : : // full MakeTopological.
1004 [ + + ]: 69452 : const auto& parent_reachable = m_reachable[parent_chunk_idx].first;
1005 [ + + ]: 69452 : const auto& child_chunk_txn = m_set_info[child_chunk_idx].transactions;
1006 [ + + ]: 69452 : if (parent_reachable.Overlaps(child_chunk_txn)) {
1007 : : // The parent chunk has a dependency on a transaction in the child chunk. In this case,
1008 : : // the parent needs to merge back with the child chunk (a self-merge), and no other
1009 : : // merges are needed. Special-case this, so the overhead of PickMergeCandidate and
1010 : : // MergeSequence can be avoided.
1011 : :
1012 : : // In the self-merge, the roles reverse: the parent chunk (from the split) depends
1013 : : // on the child chunk, so child_chunk_idx is the "top" and parent_chunk_idx is the
1014 : : // "bottom" for MergeChunks.
1015 : 36288 : auto merged_chunk_idx = MergeChunks(child_chunk_idx, parent_chunk_idx);
1016 [ + - ]: 36288 : if (!m_suboptimal_idxs[merged_chunk_idx]) {
1017 : 36288 : m_suboptimal_idxs.Set(merged_chunk_idx);
1018 : 36288 : m_suboptimal_chunks.push_back(merged_chunk_idx);
1019 : : }
1020 : : } else {
1021 : : // Merge the top chunk with lower-feerate chunks it depends on.
1022 : 33164 : MergeSequence<false>(parent_chunk_idx);
1023 : : // Merge the bottom chunk with higher-feerate chunks that depend on it.
1024 : 33164 : MergeSequence<true>(child_chunk_idx);
1025 : : }
1026 : 69452 : }
1027 : :
1028 : : /** Determine the next chunk to optimize, or INVALID_SET_IDX if none. */
1029 : 3736718 : SetIdx PickChunkToOptimize() noexcept
1030 : : {
1031 [ + + ]: 3738104 : while (!m_suboptimal_chunks.empty()) {
1032 : : // Pop an entry from the potentially-suboptimal chunk queue.
1033 : 3738019 : SetIdx chunk_idx = m_suboptimal_chunks.front();
1034 [ - + ]: 3738019 : Assume(m_suboptimal_idxs[chunk_idx]);
1035 : 3738019 : m_suboptimal_idxs.Reset(chunk_idx);
1036 : 3738019 : m_suboptimal_chunks.pop_front();
1037 [ + + ]: 3738019 : if (m_chunk_idxs[chunk_idx]) return chunk_idx;
1038 : : // If what was popped is not currently a chunk, continue. This may
1039 : : // happen when a split chunk merges in Improve() with one or more existing chunks that
1040 : : // are themselves on the suboptimal queue already.
1041 : : }
1042 : : return INVALID_SET_IDX;
1043 : : }
1044 : :
1045 : : /** Find a (parent, child) dependency to deactivate in chunk_idx, or (-1, -1) if none. */
1046 : 3736633 : std::pair<TxIdx, TxIdx> PickDependencyToSplit(SetIdx chunk_idx) noexcept
1047 : : {
1048 [ - + ]: 3736633 : Assume(m_chunk_idxs[chunk_idx]);
1049 [ + - ]: 3736633 : auto& chunk_info = m_set_info[chunk_idx];
1050 : :
1051 : : // Remember the best dependency {par, chl} seen so far.
1052 : 3736633 : std::pair<TxIdx, TxIdx> candidate_dep = {TxIdx(-1), TxIdx(-1)};
1053 : 3736633 : uint64_t candidate_tiebreak = 0;
1054 : : // Iterate over all transactions.
1055 [ + - + + ]: 15914819 : for (auto tx_idx : chunk_info.transactions) {
[ + + # # ]
1056 [ + + ]: 8462850 : const auto& tx_data = m_tx_data[tx_idx];
1057 : : // Iterate over all active child dependencies of the transaction.
1058 [ + + + + ]: 17113478 : for (auto child_idx : tx_data.active_children) {
[ + + # # ]
1059 [ + + ]: 4726217 : auto& dep_top_info = m_set_info[tx_data.dep_top_idx[child_idx]];
1060 : : // Skip if this dependency is ineligible (the top chunk that would be created
1061 : : // does not have higher feerate than the chunk it is currently part of).
1062 [ + + ]: 4726217 : auto cmp = FeeRateCompare(dep_top_info.feerate, chunk_info.feerate);
1063 [ + + ]: 4726217 : if (cmp <= 0) continue;
1064 : : // Generate a random tiebreak for this dependency, and reject it if its tiebreak
1065 : : // is worse than the best so far. This means that among all eligible
1066 : : // dependencies, a uniformly random one will be chosen.
1067 : 215737 : uint64_t tiebreak = m_rng.rand64();
1068 [ + + ]: 215737 : if (tiebreak < candidate_tiebreak) continue;
1069 : : // Remember this as our (new) candidate dependency.
1070 : 110128 : candidate_dep = {tx_idx, child_idx};
1071 : 110128 : candidate_tiebreak = tiebreak;
1072 : : }
1073 : : }
1074 : 3736633 : return candidate_dep;
1075 : : }
1076 : :
1077 : : public:
1078 : : /** Construct a spanning forest for the given DepGraph, with every transaction in its own chunk
1079 : : * (not topological). */
1080 : 959333 : explicit SpanningForestState(const DepGraph<SetType>& depgraph LIFETIMEBOUND, uint64_t rng_seed) noexcept :
1081 [ - + ]: 959333 : m_rng(rng_seed), m_depgraph(depgraph)
1082 : : {
1083 : 959333 : m_transaction_idxs = depgraph.Positions();
1084 [ - + ]: 959333 : auto num_transactions = m_transaction_idxs.Count();
1085 [ - + ]: 959333 : m_tx_data.resize(depgraph.PositionRange());
1086 : 959333 : m_set_info.resize(num_transactions);
1087 : 959333 : m_reachable.resize(num_transactions);
1088 : 959333 : size_t num_chunks = 0;
1089 [ + + + + ]: 9180792 : for (auto tx_idx : m_transaction_idxs) {
[ + + # # ]
1090 : : // Fill in transaction data.
1091 : 7262818 : auto& tx_data = m_tx_data[tx_idx];
1092 : 7262818 : tx_data.parents = depgraph.GetReducedParents(tx_idx);
1093 [ + + + + ]: 19096946 : for (auto parent_idx : tx_data.parents) {
[ + + # # ]
1094 : 6736364 : m_tx_data[parent_idx].children.Set(tx_idx);
1095 : : }
1096 : : // Create a singleton chunk for it.
1097 : 7262818 : tx_data.chunk_idx = num_chunks;
1098 : 7262818 : m_set_info[num_chunks++] = SetInfo(depgraph, tx_idx);
1099 : : }
1100 : : // Set the reachable transactions for each chunk to the transactions' parents and children.
1101 [ + + ]: 8222151 : for (SetIdx chunk_idx = 0; chunk_idx < num_transactions; ++chunk_idx) {
1102 : 7262818 : auto& tx_data = m_tx_data[m_set_info[chunk_idx].transactions.First()];
1103 : 7262818 : m_reachable[chunk_idx].first = tx_data.parents;
1104 : 7262818 : m_reachable[chunk_idx].second = tx_data.children;
1105 : : }
1106 [ - + ]: 959333 : Assume(num_chunks == num_transactions);
1107 : : // Mark all chunk sets as chunks.
1108 : 959333 : m_chunk_idxs = SetType::Fill(num_chunks);
1109 : 959333 : }
1110 : :
1111 : : /** Load an existing linearization. Must be called immediately after constructor. The result is
1112 : : * topological if the linearization is valid. Otherwise, MakeTopological still needs to be
1113 : : * called. */
1114 : 958066 : void LoadLinearization(std::span<const DepGraphIndex> old_linearization) noexcept
1115 : : {
1116 : : // Add transactions one by one, in order of existing linearization.
1117 [ + + ]: 8192295 : for (DepGraphIndex tx_idx : old_linearization) {
1118 : 7234229 : auto chunk_idx = m_tx_data[tx_idx].chunk_idx;
1119 : : // Merge the chunk upwards, as long as merging succeeds.
1120 : : while (true) {
1121 : 10779706 : chunk_idx = MergeStep<false>(chunk_idx);
1122 [ + + ]: 10779706 : if (chunk_idx == INVALID_SET_IDX) break;
1123 : : }
1124 : : }
1125 : 958066 : }
1126 : :
1127 : : /** Make state topological. Can be called after constructing, or after LoadLinearization. */
1128 : 569800 : void MakeTopological() noexcept
1129 : : {
1130 [ - + ]: 569800 : Assume(m_suboptimal_chunks.empty());
1131 : : /** What direction to initially merge chunks in; one of the two directions is enough. This
1132 : : * is sufficient because if a non-topological inactive dependency exists between two
1133 : : * chunks, at least one of the two chunks will eventually be processed in a direction that
1134 : : * discovers it - either the lower chunk tries upward, or the upper chunk tries downward.
1135 : : * Chunks that are the result of the merging are always tried in both directions. */
1136 : 569800 : unsigned init_dir = m_rng.randbool();
1137 : : /** Which chunks are the result of merging, and thus need merge attempts in both
1138 : : * directions. */
1139 : 569800 : SetType merged_chunks;
1140 : : // Mark chunks as suboptimal.
1141 : 569800 : m_suboptimal_idxs = m_chunk_idxs;
1142 [ + + + + ]: 3437644 : for (auto chunk_idx : m_chunk_idxs) {
[ - + # # ]
1143 : 2298135 : m_suboptimal_chunks.emplace_back(chunk_idx);
1144 : : // Randomize the initial order of suboptimal chunks in the queue.
1145 : 2298135 : SetIdx j = m_rng.randrange<SetIdx>(m_suboptimal_chunks.size());
1146 [ + + ]: 2298135 : if (j != m_suboptimal_chunks.size() - 1) {
1147 : 1405266 : std::swap(m_suboptimal_chunks.back(), m_suboptimal_chunks[j]);
1148 : : }
1149 : : }
1150 [ + + ]: 2882062 : while (!m_suboptimal_chunks.empty()) {
1151 : : // Pop an entry from the potentially-suboptimal chunk queue.
1152 : 2312262 : SetIdx chunk_idx = m_suboptimal_chunks.front();
1153 : 2312262 : m_suboptimal_chunks.pop_front();
1154 [ - + ]: 2312262 : Assume(m_suboptimal_idxs[chunk_idx]);
1155 : 2312262 : m_suboptimal_idxs.Reset(chunk_idx);
1156 : : // If what was popped is not currently a chunk, continue. This may
1157 : : // happen when it was merged with something else since being added.
1158 [ + + ]: 2312262 : if (!m_chunk_idxs[chunk_idx]) continue;
1159 : : /** What direction(s) to attempt merging in. 1=up, 2=down, 3=both. */
1160 [ + + ]: 2303898 : unsigned direction = merged_chunks[chunk_idx] ? 3 : init_dir + 1;
1161 : 2303898 : int flip = m_rng.randbool();
1162 [ + + ]: 6880779 : for (int i = 0; i < 2; ++i) {
1163 [ + + ]: 4596840 : if (i ^ flip) {
1164 [ + + ]: 2299626 : if (!(direction & 1)) continue;
1165 : : // Attempt to merge the chunk upwards.
1166 : 1169628 : auto result_up = MergeStep<false>(chunk_idx);
1167 [ + + ]: 1169628 : if (result_up != INVALID_SET_IDX) {
1168 [ + - ]: 12078 : if (!m_suboptimal_idxs[result_up]) {
1169 : 12078 : m_suboptimal_idxs.Set(result_up);
1170 : 12078 : m_suboptimal_chunks.push_back(result_up);
1171 : : }
1172 : 12078 : merged_chunks.Set(result_up);
1173 : 12078 : break;
1174 : : }
1175 : : } else {
1176 [ + + ]: 2297214 : if (!(direction & 2)) continue;
1177 : : // Attempt to merge the chunk downwards.
1178 : 1141480 : auto result_down = MergeStep<true>(chunk_idx);
1179 [ + + ]: 1141480 : if (result_down != INVALID_SET_IDX) {
1180 [ + + ]: 7881 : if (!m_suboptimal_idxs[result_down]) {
1181 : 2049 : m_suboptimal_idxs.Set(result_down);
1182 : 2049 : m_suboptimal_chunks.push_back(result_down);
1183 : : }
1184 : 7881 : merged_chunks.Set(result_down);
1185 : 7881 : break;
1186 : : }
1187 : : }
1188 : : }
1189 : : }
1190 : 569800 : }
1191 : :
1192 : : /** Initialize the data structure for optimization. It must be topological already. */
1193 : 945959 : void StartOptimizing() noexcept
1194 : : {
1195 [ - + ]: 945959 : Assume(m_suboptimal_chunks.empty());
1196 : : // Mark chunks suboptimal.
1197 : 945959 : m_suboptimal_idxs = m_chunk_idxs;
1198 [ + + + + ]: 5531105 : for (auto chunk_idx : m_chunk_idxs) {
[ + + # # ]
1199 : 3639873 : m_suboptimal_chunks.push_back(chunk_idx);
1200 : : // Randomize the initial order of suboptimal chunks in the queue.
1201 : 3639873 : SetIdx j = m_rng.randrange<SetIdx>(m_suboptimal_chunks.size());
1202 [ + + ]: 3639873 : if (j != m_suboptimal_chunks.size() - 1) {
1203 : 2148728 : std::swap(m_suboptimal_chunks.back(), m_suboptimal_chunks[j]);
1204 : : }
1205 : : }
1206 : 945959 : }
1207 : :
1208 : : /** Try to improve the forest. Returns false if it is optimal, true otherwise. */
1209 : 3736718 : bool OptimizeStep() noexcept
1210 : : {
1211 : 3736718 : auto chunk_idx = PickChunkToOptimize();
1212 [ + + ]: 3736718 : if (chunk_idx == INVALID_SET_IDX) {
1213 : : // No improvable chunk was found, we are done.
1214 : : return false;
1215 : : }
1216 [ + + ]: 3736633 : auto [parent_idx, child_idx] = PickDependencyToSplit(chunk_idx);
1217 [ + + ]: 3736633 : if (parent_idx == TxIdx(-1)) {
1218 : : // Nothing to improve in chunk_idx. Need to continue with other chunks, if any.
1219 : 3667181 : return !m_suboptimal_chunks.empty();
1220 : : }
1221 : : // Deactivate the found dependency and then make the state topological again with a
1222 : : // sequence of merges.
1223 : 69452 : Improve(parent_idx, child_idx);
1224 : 69452 : return true;
1225 : : }
1226 : :
1227 : : /** Initialize data structure for minimizing the chunks. Can only be called if state is known
1228 : : * to be optimal. OptimizeStep() cannot be called anymore afterwards. */
1229 : 945428 : void StartMinimizing() noexcept
1230 : : {
1231 : 945428 : m_nonminimal_chunks.clear();
1232 [ + + ]: 945428 : m_nonminimal_chunks.reserve(m_transaction_idxs.Count());
1233 : : // Gather all chunks, and for each, add it with a random pivot in it, and a random initial
1234 : : // direction, to m_nonminimal_chunks.
1235 [ + + + + ]: 5548270 : for (auto chunk_idx : m_chunk_idxs) {
[ + + # # ]
1236 : 3658100 : TxIdx pivot_idx = PickRandomTx(m_set_info[chunk_idx].transactions);
1237 : 3658100 : m_nonminimal_chunks.emplace_back(chunk_idx, pivot_idx, m_rng.randbits<1>());
1238 : : // Randomize the initial order of nonminimal chunks in the queue.
1239 : 3658100 : SetIdx j = m_rng.randrange<SetIdx>(m_nonminimal_chunks.size());
1240 [ + + ]: 3658100 : if (j != m_nonminimal_chunks.size() - 1) {
1241 : 2168039 : std::swap(m_nonminimal_chunks.back(), m_nonminimal_chunks[j]);
1242 : : }
1243 : : }
1244 : 945428 : }
1245 : :
1246 : : /** Try to reduce a chunk's size. Returns false if all chunks are minimal, true otherwise. */
1247 : 5421466 : bool MinimizeStep() noexcept
1248 : : {
1249 : : // If the queue of potentially-non-minimal chunks is empty, we are done.
1250 [ + + ]: 5421466 : if (m_nonminimal_chunks.empty()) return false;
1251 : : // Pop an entry from the potentially-non-minimal chunk queue.
1252 : 4476582 : auto [chunk_idx, pivot_idx, flags] = m_nonminimal_chunks.front();
1253 : 4476582 : m_nonminimal_chunks.pop_front();
1254 [ + - ]: 4476582 : auto& chunk_info = m_set_info[chunk_idx];
1255 : : /** Whether to move the pivot down rather than up. */
1256 : 4476582 : bool move_pivot_down = flags & 1;
1257 : : /** Whether this is already the second stage. */
1258 : 4476582 : bool second_stage = flags & 2;
1259 : :
1260 : : // Find a random dependency whose top and bottom set feerates are equal, and which has
1261 : : // pivot in bottom set (if move_pivot_down) or in top set (if !move_pivot_down).
1262 : 4476582 : std::pair<TxIdx, TxIdx> candidate_dep;
1263 : 4476582 : uint64_t candidate_tiebreak{0};
1264 : 4476582 : bool have_any = false;
1265 : : // Iterate over all transactions.
1266 [ + - + + ]: 17909007 : for (auto tx_idx : chunk_info.transactions) {
[ + + # # ]
1267 [ + + ]: 8982780 : const auto& tx_data = m_tx_data[tx_idx];
1268 : : // Iterate over all active child dependencies of the transaction.
1269 [ + + + + ]: 17242655 : for (auto child_idx : tx_data.active_children) {
[ + + # # ]
1270 [ + + ]: 4506198 : const auto& dep_top_info = m_set_info[tx_data.dep_top_idx[child_idx]];
1271 : : // Skip if this dependency does not have equal top and bottom set feerates. Note
1272 : : // that the top cannot have higher feerate than the bottom, or OptimizeSteps would
1273 : : // have dealt with it.
1274 [ + + ]: 4506198 : if (dep_top_info.feerate << chunk_info.feerate) continue;
1275 : 1440958 : have_any = true;
1276 : : // Skip if this dependency does not have pivot in the right place.
1277 [ + + ]: 1440958 : if (move_pivot_down == dep_top_info.transactions[pivot_idx]) continue;
1278 : : // Remember this as our chosen dependency if it has a better tiebreak.
1279 : 811418 : uint64_t tiebreak = m_rng.rand64() | 1;
1280 [ + + ]: 811418 : if (tiebreak > candidate_tiebreak) {
1281 : 460411 : candidate_tiebreak = tiebreak;
1282 : 460411 : candidate_dep = {tx_idx, child_idx};
1283 : : }
1284 : : }
1285 : : }
1286 : : // If no dependencies have equal top and bottom set feerate, this chunk is minimal.
1287 [ + + ]: 4476582 : if (!have_any) return true;
1288 : : // If all found dependencies have the pivot in the wrong place, try moving it in the other
1289 : : // direction. If this was the second stage already, we are done.
1290 [ + + ]: 482438 : if (candidate_tiebreak == 0) {
1291 : : // Switch to other direction, and to second phase.
1292 : 131808 : flags ^= 3;
1293 [ + + ]: 131808 : if (!second_stage) m_nonminimal_chunks.emplace_back(chunk_idx, pivot_idx, flags);
1294 : 131808 : return true;
1295 : : }
1296 : :
1297 : : // Otherwise, deactivate the dependency that was found.
1298 [ + + ]: 350630 : auto [parent_chunk_idx, child_chunk_idx] = Deactivate(candidate_dep.first, candidate_dep.second);
1299 : : // Determine if there is a dependency from the new bottom to the new top (opposite from the
1300 : : // dependency that was just deactivated).
1301 [ + + ]: 350630 : auto& parent_reachable = m_reachable[parent_chunk_idx].first;
1302 [ + + ]: 350630 : auto& child_chunk_txn = m_set_info[child_chunk_idx].transactions;
1303 [ + + ]: 350630 : if (parent_reachable.Overlaps(child_chunk_txn)) {
1304 : : // A self-merge is needed. Note that the child_chunk_idx is the top, and
1305 : : // parent_chunk_idx is the bottom, because we activate a dependency in the reverse
1306 : : // direction compared to the deactivation above.
1307 : 11285 : auto merged_chunk_idx = MergeChunks(child_chunk_idx, parent_chunk_idx);
1308 : : // Re-insert the chunk into the queue, in the same direction. Note that the chunk_idx
1309 : : // will have changed.
1310 : 11285 : m_nonminimal_chunks.emplace_back(merged_chunk_idx, pivot_idx, flags);
1311 : : } else {
1312 : : // No self-merge happens, and thus we have found a way to split the chunk. Create two
1313 : : // smaller chunks, and add them to the queue. The one that contains the current pivot
1314 : : // gets to continue with it in the same direction, to minimize the number of times we
1315 : : // alternate direction. If we were in the second phase already, the newly created chunk
1316 : : // inherits that too, because we know no split with the pivot on the other side is
1317 : : // possible already. The new chunk without the current pivot gets a new randomly-chosen
1318 : : // one.
1319 [ + + ]: 339345 : if (move_pivot_down) {
1320 : 164141 : auto parent_pivot_idx = PickRandomTx(m_set_info[parent_chunk_idx].transactions);
1321 : 164141 : m_nonminimal_chunks.emplace_back(parent_chunk_idx, parent_pivot_idx, m_rng.randbits<1>());
1322 : 164141 : m_nonminimal_chunks.emplace_back(child_chunk_idx, pivot_idx, flags);
1323 : : } else {
1324 : 175204 : auto child_pivot_idx = PickRandomTx(m_set_info[child_chunk_idx].transactions);
1325 : 175204 : m_nonminimal_chunks.emplace_back(parent_chunk_idx, pivot_idx, flags);
1326 : 175204 : m_nonminimal_chunks.emplace_back(child_chunk_idx, child_pivot_idx, m_rng.randbits<1>());
1327 : : }
1328 [ + + ]: 339345 : if (m_rng.randbool()) {
1329 : 169091 : std::swap(m_nonminimal_chunks.back(), m_nonminimal_chunks[m_nonminimal_chunks.size() - 2]);
1330 : : }
1331 : : }
1332 : : return true;
1333 : : }
1334 : :
1335 : : /** Construct a topologically-valid linearization from the current forest state. Must be
1336 : : * topological. fallback_order is a comparator that defines a strong order for DepGraphIndexes
1337 : : * in this cluster, used to order equal-feerate transactions and chunks.
1338 : : *
1339 : : * Specifically, the resulting order consists of:
1340 : : * - The chunks of the current SFL state, sorted by (in decreasing order of priority):
1341 : : * - topology (parents before children)
1342 : : * - highest chunk feerate first
1343 : : * - smallest chunk size first
1344 : : * - the chunk with the lowest maximum transaction, by fallback_order, first
1345 : : * - The transactions within a chunk, sorted by (in decreasing order of priority):
1346 : : * - topology (parents before children)
1347 : : * - highest tx feerate first
1348 : : * - smallest tx size first
1349 : : * - the lowest transaction, by fallback_order, first
1350 : : */
1351 : 961472 : std::vector<DepGraphIndex> GetLinearization(const StrongComparator<DepGraphIndex> auto& fallback_order) const noexcept
1352 : : {
1353 : : /** The output linearization. */
1354 : 961472 : std::vector<DepGraphIndex> ret;
1355 [ - + ]: 961472 : ret.reserve(m_set_info.size());
1356 : : /** A heap with all chunks (by set index) that can currently be included, sorted by
1357 : : * chunk feerate (high to low), chunk size (small to large), and by least maximum element
1358 : : * according to the fallback order (which is the second pair element). */
1359 : 961472 : std::vector<std::pair<SetIdx, TxIdx>> ready_chunks;
1360 : : /** For every chunk, indexed by SetIdx, the number of unmet dependencies the chunk has on
1361 : : * other chunks (not including dependencies within the chunk itself). */
1362 [ - + - + ]: 961472 : std::vector<TxIdx> chunk_deps(m_set_info.size(), 0);
1363 : : /** For every transaction, indexed by TxIdx, the number of unmet dependencies the
1364 : : * transaction has. */
1365 [ - + + + ]: 961472 : std::vector<TxIdx> tx_deps(m_tx_data.size(), 0);
[ - + # # ]
1366 : : /** A heap with all transactions within the current chunk that can be included, sorted by
1367 : : * tx feerate (high to low), tx size (small to large), and fallback order. */
1368 : 961472 : std::vector<TxIdx> ready_tx;
1369 : : // Populate chunk_deps and tx_deps.
1370 [ + + + + ]: 9248049 : for (TxIdx chl_idx : m_transaction_idxs) {
[ + + # # ]
1371 : 7325797 : const auto& chl_data = m_tx_data[chl_idx];
1372 : 7325797 : tx_deps[chl_idx] = chl_data.parents.Count();
1373 : 7325797 : auto chl_chunk_idx = chl_data.chunk_idx;
1374 : 7325797 : auto& chl_chunk_info = m_set_info[chl_chunk_idx];
1375 : 7325797 : chunk_deps[chl_chunk_idx] += (chl_data.parents - chl_chunk_info.transactions).Count();
1376 : : }
1377 : : /** Function to compute the highest element of a chunk, by fallback_order. */
1378 : 5053117 : auto max_fallback_fn = [&](SetIdx chunk_idx) noexcept {
1379 [ + - ]: 4091645 : auto& chunk = m_set_info[chunk_idx].transactions;
1380 : 4091645 : auto it = chunk.begin();
1381 : 4091645 : DepGraphIndex ret = *it;
1382 : 4091645 : ++it;
1383 [ + + ]: 7325797 : while (it != chunk.end()) {
1384 [ + - + - ]: 3298777 : if (fallback_order(*it, ret) > 0) ret = *it;
[ + + # # ]
1385 : 3234152 : ++it;
1386 : : }
1387 : 4091645 : return ret;
1388 : : };
1389 : : /** Comparison function for the transaction heap. Note that it is a max-heap, so
1390 : : * tx_cmp_fn(a, b) == true means "a appears after b in the linearization". */
1391 : 3218202 : auto tx_cmp_fn = [&](const auto& a, const auto& b) noexcept {
1392 : : // Bail out for identical transactions.
1393 [ + - ]: 2256730 : if (a == b) return false;
1394 : : // First sort by increasing transaction feerate.
1395 [ + + ]: 2256730 : auto& a_feerate = m_depgraph.FeeRate(a);
1396 : 2256730 : auto& b_feerate = m_depgraph.FeeRate(b);
1397 [ + + ]: 2256730 : auto feerate_cmp = FeeRateCompare(a_feerate, b_feerate);
1398 [ + + ]: 2256730 : if (feerate_cmp != 0) return feerate_cmp < 0;
1399 : : // Then by decreasing transaction size.
1400 [ + + ]: 833559 : if (a_feerate.size != b_feerate.size) {
1401 : 62521 : return a_feerate.size > b_feerate.size;
1402 : : }
1403 : : // Tie-break by decreasing fallback_order.
1404 [ + + + - ]: 810335 : auto fallback_cmp = fallback_order(a, b);
1405 [ + - ]: 771038 : if (fallback_cmp != 0) return fallback_cmp > 0;
1406 : : // This should not be hit, because fallback_order defines a strong ordering.
1407 : 0 : Assume(false);
1408 : 0 : return a < b;
1409 : : };
1410 : : // Construct a heap with all chunks that have no out-of-chunk dependencies.
1411 : : /** Comparison function for the chunk heap. Note that it is a max-heap, so
1412 : : * chunk_cmp_fn(a, b) == true means "a appears after b in the linearization". */
1413 : 10406867 : auto chunk_cmp_fn = [&](const auto& a, const auto& b) noexcept {
1414 : : // Bail out for identical chunks.
1415 [ + - ]: 9445395 : if (a.first == b.first) return false;
1416 : : // First sort by increasing chunk feerate.
1417 [ + + ]: 9445395 : auto& chunk_feerate_a = m_set_info[a.first].feerate;
1418 : 9445395 : auto& chunk_feerate_b = m_set_info[b.first].feerate;
1419 [ + + ]: 9445395 : auto feerate_cmp = FeeRateCompare(chunk_feerate_a, chunk_feerate_b);
1420 [ + + ]: 9445395 : if (feerate_cmp != 0) return feerate_cmp < 0;
1421 : : // Then by decreasing chunk size.
1422 [ + + ]: 3126062 : if (chunk_feerate_a.size != chunk_feerate_b.size) {
1423 : 182557 : return chunk_feerate_a.size > chunk_feerate_b.size;
1424 : : }
1425 : : // Tie-break by decreasing fallback_order.
1426 [ + - + - ]: 3030716 : auto fallback_cmp = fallback_order(a.second, b.second);
1427 [ + - ]: 2943505 : if (fallback_cmp != 0) return fallback_cmp > 0;
1428 : : // This should not be hit, because fallback_order defines a strong ordering.
1429 : 0 : Assume(false);
1430 : 0 : return a.second < b.second;
1431 : : };
1432 : : // Construct a heap with all chunks that have no out-of-chunk dependencies.
1433 [ + + + + ]: 6013897 : for (SetIdx chunk_idx : m_chunk_idxs) {
[ + + # # ]
1434 [ + + ]: 4091645 : if (chunk_deps[chunk_idx] == 0) {
1435 : 1684776 : ready_chunks.emplace_back(chunk_idx, max_fallback_fn(chunk_idx));
1436 : : }
1437 : : }
1438 : 961472 : std::make_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
1439 : : // Pop chunks off the heap.
1440 [ + + ]: 5053117 : while (!ready_chunks.empty()) {
1441 : 4091645 : auto [chunk_idx, _rnd] = ready_chunks.front();
1442 [ - + ]: 4091645 : std::pop_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
1443 : 4091645 : ready_chunks.pop_back();
1444 [ - + ]: 4091645 : Assume(chunk_deps[chunk_idx] == 0);
1445 [ - + ]: 4091645 : const auto& chunk_txn = m_set_info[chunk_idx].transactions;
1446 : : // Build heap of all includable transactions in chunk.
1447 [ - + ]: 4091645 : Assume(ready_tx.empty());
1448 [ + - + + ]: 15485442 : for (TxIdx tx_idx : chunk_txn) {
[ + + # # ]
1449 [ + + ]: 7325797 : if (tx_deps[tx_idx] == 0) ready_tx.push_back(tx_idx);
1450 : : }
1451 [ - + ]: 4091645 : Assume(!ready_tx.empty());
1452 : 4091645 : std::make_heap(ready_tx.begin(), ready_tx.end(), tx_cmp_fn);
1453 : : // Pick transactions from the ready heap, append them to linearization, and decrement
1454 : : // dependency counts.
1455 [ + + ]: 11417442 : while (!ready_tx.empty()) {
1456 : : // Pop an element from the tx_ready heap.
1457 : 7325797 : auto tx_idx = ready_tx.front();
1458 : 7325797 : std::pop_heap(ready_tx.begin(), ready_tx.end(), tx_cmp_fn);
1459 : 7325797 : ready_tx.pop_back();
1460 : : // Append to linearization.
1461 : 7325797 : ret.push_back(tx_idx);
1462 : : // Decrement dependency counts.
1463 [ + + ]: 7325797 : auto& tx_data = m_tx_data[tx_idx];
1464 [ + + + + ]: 18915811 : for (TxIdx chl_idx : tx_data.children) {
[ + + # # ]
1465 [ - + ]: 6811442 : auto& chl_data = m_tx_data[chl_idx];
1466 : : // Decrement tx dependency count.
1467 [ - + ]: 6811442 : Assume(tx_deps[chl_idx] > 0);
1468 [ + + + + ]: 6811442 : if (--tx_deps[chl_idx] == 0 && chunk_txn[chl_idx]) {
1469 : : // Child tx has no dependencies left, and is in this chunk. Add it to the tx heap.
1470 : 2873901 : ready_tx.push_back(chl_idx);
1471 : 2873901 : std::push_heap(ready_tx.begin(), ready_tx.end(), tx_cmp_fn);
1472 : : }
1473 : : // Decrement chunk dependency count if this is out-of-chunk dependency.
1474 [ + + ]: 6811442 : if (chl_data.chunk_idx != chunk_idx) {
1475 [ - + ]: 3399802 : Assume(chunk_deps[chl_data.chunk_idx] > 0);
1476 [ + + ]: 3399802 : if (--chunk_deps[chl_data.chunk_idx] == 0) {
1477 : : // Child chunk has no dependencies left. Add it to the chunk heap.
1478 : 2406869 : ready_chunks.emplace_back(chl_data.chunk_idx, max_fallback_fn(chl_data.chunk_idx));
1479 : 2406869 : std::push_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
1480 : : }
1481 : : }
1482 : : }
1483 : : }
1484 : : }
1485 [ - + - + : 961472 : Assume(ret.size() == m_set_info.size());
- + ]
1486 : 961472 : return ret;
1487 : 961472 : }
1488 : :
1489 : : /** Get the diagram for the current state, which must be topological. Test-only.
1490 : : *
1491 : : * The linearization produced by GetLinearization() is always at least as good (in the
1492 : : * CompareChunks() sense) as this diagram, but may be better.
1493 : : *
1494 : : * After an OptimizeStep(), the diagram will always be at least as good as before. Once
1495 : : * OptimizeStep() returns false, the diagram will be equivalent to that produced by
1496 : : * GetLinearization(), and optimal.
1497 : : *
1498 : : * After a MinimizeStep(), the diagram cannot change anymore (in the CompareChunks() sense),
1499 : : * but its number of segments can increase still. Once MinimizeStep() returns false, the number
1500 : : * of chunks of the produced linearization will match the number of segments in the diagram.
1501 : : */
1502 : 32939 : std::vector<FeeFrac> GetDiagram() const noexcept
1503 : : {
1504 : 32939 : std::vector<FeeFrac> ret;
1505 [ + - + + ]: 576857 : for (auto chunk_idx : m_chunk_idxs) {
1506 : 510979 : ret.push_back(m_set_info[chunk_idx].feerate);
1507 : : }
1508 : 32939 : std::sort(ret.begin(), ret.end(), std::greater{});
1509 : 32939 : return ret;
1510 : : }
1511 : :
1512 : : /** Determine how much work was performed so far. */
1513 : 10067885 : uint64_t GetCost() const noexcept { return m_cost; }
1514 : :
1515 : : /** Verify internal consistency of the data structure. */
1516 : 3455 : void SanityCheck() const
1517 : : {
1518 : : //
1519 : : // Verify dependency parent/child information, and build list of (active) dependencies.
1520 : : //
1521 : 3455 : std::vector<std::pair<TxIdx, TxIdx>> expected_dependencies;
1522 : 3455 : std::vector<std::pair<TxIdx, TxIdx>> all_dependencies;
1523 : 3455 : std::vector<std::pair<TxIdx, TxIdx>> active_dependencies;
1524 [ + - + + ]: 103436 : for (auto parent_idx : m_depgraph.Positions()) {
1525 [ + + + + ]: 285419 : for (auto child_idx : m_depgraph.GetReducedChildren(parent_idx)) {
1526 [ + - ]: 122661 : expected_dependencies.emplace_back(parent_idx, child_idx);
1527 : : }
1528 : : }
1529 [ + - + + ]: 103436 : for (auto tx_idx : m_transaction_idxs) {
1530 [ + + + + ]: 285419 : for (auto child_idx : m_tx_data[tx_idx].children) {
1531 [ + - ]: 122661 : all_dependencies.emplace_back(tx_idx, child_idx);
1532 [ + + ]: 122661 : if (m_tx_data[tx_idx].active_children[child_idx]) {
1533 [ + - ]: 50013 : active_dependencies.emplace_back(tx_idx, child_idx);
1534 : : }
1535 : : }
1536 : : }
1537 : 3455 : std::sort(expected_dependencies.begin(), expected_dependencies.end());
1538 : 3455 : std::sort(all_dependencies.begin(), all_dependencies.end());
1539 [ - + ]: 3455 : assert(expected_dependencies == all_dependencies);
1540 : :
1541 : : //
1542 : : // Verify the chunks against the list of active dependencies
1543 : : //
1544 : 3455 : SetType chunk_cover;
1545 [ + - + + ]: 53423 : for (auto chunk_idx : m_chunk_idxs) {
1546 [ + - ]: 46513 : const auto& chunk_info = m_set_info[chunk_idx];
1547 : : // Verify that transactions in the chunk point back to it. This guarantees
1548 : : // that chunks are non-overlapping.
1549 [ + - + + ]: 189552 : for (auto tx_idx : chunk_info.transactions) {
1550 [ - + ]: 96526 : assert(m_tx_data[tx_idx].chunk_idx == chunk_idx);
1551 : : }
1552 [ - + ]: 46513 : assert(!chunk_cover.Overlaps(chunk_info.transactions));
1553 [ - + ]: 46513 : chunk_cover |= chunk_info.transactions;
1554 : : // Verify the chunk's transaction set: start from an arbitrary chunk transaction,
1555 : : // and for every active dependency, if it contains the parent or child, add the
1556 : : // other. It must have exactly N-1 active dependencies in it, guaranteeing it is
1557 : : // acyclic.
1558 [ - + ]: 46513 : assert(chunk_info.transactions.Any());
1559 : 46513 : SetType expected_chunk = SetType::Singleton(chunk_info.transactions.First());
1560 : : while (true) {
1561 : 64012 : auto old = expected_chunk;
1562 : 64012 : size_t active_dep_count{0};
1563 [ + + ]: 844610 : for (const auto& [par, chl] : active_dependencies) {
1564 [ + + + + ]: 780598 : if (expected_chunk[par] || expected_chunk[chl]) {
1565 : 164327 : expected_chunk.Set(par);
1566 : 164327 : expected_chunk.Set(chl);
1567 : 164327 : ++active_dep_count;
1568 : : }
1569 : : }
1570 [ + + ]: 64012 : if (old == expected_chunk) {
1571 [ - + ]: 46513 : assert(expected_chunk.Count() == active_dep_count + 1);
1572 : : break;
1573 : : }
1574 : : }
1575 [ - + ]: 46513 : assert(chunk_info.transactions == expected_chunk);
1576 : : // Verify the chunk's feerate.
1577 [ + - ]: 46513 : assert(chunk_info.feerate == m_depgraph.FeeRate(chunk_info.transactions));
1578 : : // Verify the chunk's reachable transactions.
1579 [ + - ]: 46513 : assert(m_reachable[chunk_idx] == GetReachable(expected_chunk));
1580 : : // Verify that the chunk's reachable transactions don't include its own transactions.
1581 [ - + ]: 46513 : assert(!m_reachable[chunk_idx].first.Overlaps(chunk_info.transactions));
1582 [ - + ]: 46513 : assert(!m_reachable[chunk_idx].second.Overlaps(chunk_info.transactions));
1583 : : }
1584 : : // Verify that together, the chunks cover all transactions.
1585 [ - + ]: 3455 : assert(chunk_cover == m_depgraph.Positions());
1586 : :
1587 : : //
1588 : : // Verify transaction data.
1589 : : //
1590 [ - + ]: 3455 : assert(m_transaction_idxs == m_depgraph.Positions());
1591 [ + - + + ]: 103436 : for (auto tx_idx : m_transaction_idxs) {
1592 : 96526 : const auto& tx_data = m_tx_data[tx_idx];
1593 : : // Verify it has a valid chunk index, and that chunk includes this transaction.
1594 [ - + ]: 96526 : assert(m_chunk_idxs[tx_data.chunk_idx]);
1595 [ - + ]: 96526 : assert(m_set_info[tx_data.chunk_idx].transactions[tx_idx]);
1596 : : // Verify parents/children.
1597 [ - + ]: 96526 : assert(tx_data.parents == m_depgraph.GetReducedParents(tx_idx));
1598 [ - + ]: 96526 : assert(tx_data.children == m_depgraph.GetReducedChildren(tx_idx));
1599 : : // Verify active_children is a subset of children.
1600 [ - + ]: 96526 : assert(tx_data.active_children.IsSubsetOf(tx_data.children));
1601 : : // Verify each active child's dep_top_idx points to a valid non-chunk set.
1602 [ + + + + ]: 187099 : for (auto child_idx : tx_data.active_children) {
1603 [ - + - + ]: 50013 : assert(tx_data.dep_top_idx[child_idx] < m_set_info.size());
1604 [ - + ]: 50013 : assert(!m_chunk_idxs[tx_data.dep_top_idx[child_idx]]);
1605 : : }
1606 : : }
1607 : :
1608 : : //
1609 : : // Verify active dependencies' top sets.
1610 : : //
1611 [ + + ]: 53468 : for (const auto& [par_idx, chl_idx] : active_dependencies) {
1612 : : // Verify the top set's transactions: it must contain the parent, and for every
1613 : : // active dependency, except the chl_idx->par_idx dependency itself, if it contains the
1614 : : // parent or child, it must contain both. It must have exactly N-1 active dependencies
1615 : : // in it, guaranteeing it is acyclic.
1616 : 50013 : SetType expected_top = SetType::Singleton(par_idx);
1617 : : while (true) {
1618 : 153082 : auto old = expected_top;
1619 : 153082 : size_t active_dep_count{0};
1620 [ + + + + ]: 3713636 : for (const auto& [par2_idx, chl2_idx] : active_dependencies) {
1621 [ + + + + ]: 3560554 : if (par_idx == par2_idx && chl_idx == chl2_idx) continue;
1622 [ + + + + ]: 3407472 : if (expected_top[par2_idx] || expected_top[chl2_idx]) {
1623 : 1173769 : expected_top.Set(par2_idx);
1624 : 1173769 : expected_top.Set(chl2_idx);
1625 : 1173769 : ++active_dep_count;
1626 : : }
1627 : : }
1628 [ + + ]: 153082 : if (old == expected_top) {
1629 [ - + ]: 50013 : assert(expected_top.Count() == active_dep_count + 1);
1630 : : break;
1631 : : }
1632 : : }
1633 [ - + ]: 50013 : assert(!expected_top[chl_idx]);
1634 [ - + ]: 50013 : auto& dep_top_info = m_set_info[m_tx_data[par_idx].dep_top_idx[chl_idx]];
1635 [ - + ]: 50013 : assert(dep_top_info.transactions == expected_top);
1636 : : // Verify the top set's feerate.
1637 [ + - ]: 100026 : assert(dep_top_info.feerate == m_depgraph.FeeRate(dep_top_info.transactions));
1638 : : }
1639 : :
1640 : : //
1641 : : // Verify m_suboptimal_chunks.
1642 : : //
1643 : 3455 : SetType suboptimal_idxs;
1644 [ + + ]: 13449 : for (size_t i = 0; i < m_suboptimal_chunks.size(); ++i) {
1645 : 9994 : auto chunk_idx = m_suboptimal_chunks[i];
1646 [ - + ]: 9994 : assert(!suboptimal_idxs[chunk_idx]);
1647 : 9994 : suboptimal_idxs.Set(chunk_idx);
1648 : : }
1649 [ - + ]: 3455 : assert(m_suboptimal_idxs == suboptimal_idxs);
1650 : :
1651 : : //
1652 : : // Verify m_nonminimal_chunks.
1653 : : //
1654 : 3455 : SetType nonminimal_idxs;
1655 [ + + ]: 12968 : for (size_t i = 0; i < m_nonminimal_chunks.size(); ++i) {
1656 [ - + ]: 9513 : auto [chunk_idx, pivot, flags] = m_nonminimal_chunks[i];
1657 [ - + ]: 9513 : assert(m_tx_data[pivot].chunk_idx == chunk_idx);
1658 [ - + ]: 9513 : assert(!nonminimal_idxs[chunk_idx]);
1659 : 9513 : nonminimal_idxs.Set(chunk_idx);
1660 : : }
1661 [ - + ]: 3455 : assert(nonminimal_idxs.IsSubsetOf(m_chunk_idxs));
1662 : 3455 : }
1663 : : };
1664 : :
1665 : : /** Find or improve a linearization for a cluster.
1666 : : *
1667 : : * @param[in] depgraph Dependency graph of the cluster to be linearized.
1668 : : * @param[in] max_iterations Upper bound on the amount of work that will be done.
1669 : : * @param[in] rng_seed A random number seed to control search order. This prevents peers
1670 : : * from predicting exactly which clusters would be hard for us to
1671 : : * linearize.
1672 : : * @param[in] fallback_order A comparator to order transactions, used to sort equal-feerate
1673 : : * chunks and transactions. See SpanningForestState::GetLinearization
1674 : : * for details.
1675 : : * @param[in] old_linearization An existing linearization for the cluster, or empty.
1676 : : * @param[in] is_topological (Only relevant if old_linearization is not empty) Whether
1677 : : * old_linearization is topologically valid.
1678 : : * @return A tuple of:
1679 : : * - The resulting linearization. It is guaranteed to be at least as
1680 : : * good (in the feerate diagram sense) as old_linearization.
1681 : : * - A boolean indicating whether the result is guaranteed to be
1682 : : * optimal with minimal chunks.
1683 : : * - How many optimization steps were actually performed.
1684 : : */
1685 : : template<typename SetType>
1686 : 958469 : std::tuple<std::vector<DepGraphIndex>, bool, uint64_t> Linearize(
1687 : : const DepGraph<SetType>& depgraph,
1688 : : uint64_t max_iterations,
1689 : : uint64_t rng_seed,
1690 : : const StrongComparator<DepGraphIndex> auto& fallback_order,
1691 : : std::span<const DepGraphIndex> old_linearization = {},
1692 : : bool is_topological = true) noexcept
1693 : : {
1694 : : /** Initialize a spanning forest data structure for this cluster. */
1695 [ + + ]: 958469 : SpanningForestState forest(depgraph, rng_seed);
1696 [ + + ]: 958469 : if (!old_linearization.empty()) {
1697 : 957744 : forest.LoadLinearization(old_linearization);
1698 [ + + ]: 957744 : if (!is_topological) forest.MakeTopological();
1699 : : } else {
1700 : 725 : forest.MakeTopological();
1701 : : }
1702 : : // Make improvement steps to it until we hit the max_iterations limit, or an optimal result
1703 : : // is found.
1704 [ + + ]: 958469 : if (forest.GetCost() < max_iterations) {
1705 : 945095 : forest.StartOptimizing();
1706 : : do {
1707 [ + + ]: 3722260 : if (!forest.OptimizeStep()) break;
1708 [ + + ]: 2777696 : } while (forest.GetCost() < max_iterations);
1709 : : }
1710 : : // Make chunk minimization steps until we hit the max_iterations limit, or all chunks are
1711 : : // minimal.
1712 : 958469 : bool optimal = false;
1713 [ + + ]: 958469 : if (forest.GetCost() < max_iterations) {
1714 : 944564 : forest.StartMinimizing();
1715 : : do {
1716 [ + + ]: 5405577 : if (!forest.MinimizeStep()) {
1717 : : optimal = true;
1718 : : break;
1719 : : }
1720 [ + + ]: 4461557 : } while (forest.GetCost() < max_iterations);
1721 : : }
1722 : 958469 : return {forest.GetLinearization(fallback_order), optimal, forest.GetCost()};
1723 : 958469 : }
1724 : :
1725 : : /** Improve a given linearization.
1726 : : *
1727 : : * @param[in] depgraph Dependency graph of the cluster being linearized.
1728 : : * @param[in,out] linearization On input, an existing linearization for depgraph. On output, a
1729 : : * potentially better linearization for the same graph.
1730 : : *
1731 : : * Postlinearization guarantees:
1732 : : * - The resulting chunks are connected.
1733 : : * - If the input has a tree shape (either all transactions have at most one child, or all
1734 : : * transactions have at most one parent), the result is optimal.
1735 : : * - Given a linearization L1 and a leaf transaction T in it. Let L2 be L1 with T moved to the end,
1736 : : * optionally with its fee increased. Let L3 be the postlinearization of L2. L3 will be at least
1737 : : * as good as L1. This means that replacing transactions with same-size higher-fee transactions
1738 : : * will not worsen linearizations through a "drop conflicts, append new transactions,
1739 : : * postlinearize" process.
1740 : : */
1741 : : template<typename SetType>
1742 [ - + ]: 958191 : void PostLinearize(const DepGraph<SetType>& depgraph, std::span<DepGraphIndex> linearization)
1743 : : {
1744 : : // This algorithm performs a number of passes (currently 2); the even ones operate from back to
1745 : : // front, the odd ones from front to back. Each results in an equal-or-better linearization
1746 : : // than the one started from.
1747 : : // - One pass in either direction guarantees that the resulting chunks are connected.
1748 : : // - Each direction corresponds to one shape of tree being linearized optimally (forward passes
1749 : : // guarantee this for graphs where each transaction has at most one child; backward passes
1750 : : // guarantee this for graphs where each transaction has at most one parent).
1751 : : // - Starting with a backward pass guarantees the moved-tree property.
1752 : : //
1753 : : // During an odd (forward) pass, the high-level operation is:
1754 : : // - Start with an empty list of groups L=[].
1755 : : // - For every transaction i in the old linearization, from front to back:
1756 : : // - Append a new group C=[i], containing just i, to the back of L.
1757 : : // - While L has at least one group before C, and the group immediately before C has feerate
1758 : : // lower than C:
1759 : : // - If C depends on P:
1760 : : // - Merge P into C, making C the concatenation of P+C, continuing with the combined C.
1761 : : // - Otherwise:
1762 : : // - Swap P with C, continuing with the now-moved C.
1763 : : // - The output linearization is the concatenation of the groups in L.
1764 : : //
1765 : : // During even (backward) passes, i iterates from the back to the front of the existing
1766 : : // linearization, and new groups are prepended instead of appended to the list L. To enable
1767 : : // more code reuse, both passes append groups, but during even passes the meanings of
1768 : : // parent/child, and of high/low feerate are reversed, and the final concatenation is reversed
1769 : : // on output.
1770 : : //
1771 : : // In the implementation below, the groups are represented by singly-linked lists (pointing
1772 : : // from the back to the front), which are themselves organized in a singly-linked circular
1773 : : // list (each group pointing to its predecessor, with a special sentinel group at the front
1774 : : // that points back to the last group).
1775 : : //
1776 : : // Information about transaction t is stored in entries[t + 1], while the sentinel is in
1777 : : // entries[0].
1778 : :
1779 : : /** Index of the sentinel in the entries array below. */
1780 : : static constexpr DepGraphIndex SENTINEL{0};
1781 : : /** Indicator that a group has no previous transaction. */
1782 : : static constexpr DepGraphIndex NO_PREV_TX{0};
1783 : :
1784 : :
1785 : : /** Data structure per transaction entry. */
1786 : 8206304 : struct TxEntry
1787 : : {
1788 : : /** The index of the previous transaction in this group; NO_PREV_TX if this is the first
1789 : : * entry of a group. */
1790 : : DepGraphIndex prev_tx;
1791 : :
1792 : : // The fields below are only used for transactions that are the last one in a group
1793 : : // (referred to as tail transactions below).
1794 : :
1795 : : /** Index of the first transaction in this group, possibly itself. */
1796 : : DepGraphIndex first_tx;
1797 : : /** Index of the last transaction in the previous group. The first group (the sentinel)
1798 : : * points back to the last group here, making it a singly-linked circular list. */
1799 : : DepGraphIndex prev_group;
1800 : : /** All transactions in the group. Empty for the sentinel. */
1801 : : SetType group;
1802 : : /** All dependencies of the group (descendants in even passes; ancestors in odd ones). */
1803 : : SetType deps;
1804 : : /** The combined fee/size of transactions in the group. Fee is negated in even passes. */
1805 : : FeeFrac feerate;
1806 : : };
1807 : :
1808 : : // As an example, consider the state corresponding to the linearization [1,0,3,2], with
1809 : : // groups [1,0,3] and [2], in an odd pass. The linked lists would be:
1810 : : //
1811 : : // +-----+
1812 : : // 0<-P-- | 0 S | ---\ Legend:
1813 : : // +-----+ |
1814 : : // ^ | - digit in box: entries index
1815 : : // /--------------F---------+ G | (note: one more than tx value)
1816 : : // v \ | | - S: sentinel group
1817 : : // +-----+ +-----+ +-----+ | (empty feerate)
1818 : : // 0<-P-- | 2 | <--P-- | 1 | <--P-- | 4 T | | - T: tail transaction, contains
1819 : : // +-----+ +-----+ +-----+ | fields beyond prev_tv.
1820 : : // ^ | - P: prev_tx reference
1821 : : // G G - F: first_tx reference
1822 : : // | | - G: prev_group reference
1823 : : // +-----+ |
1824 : : // 0<-P-- | 3 T | <--/
1825 : : // +-----+
1826 : : // ^ |
1827 : : // \-F-/
1828 : : //
1829 : : // During an even pass, the diagram above would correspond to linearization [2,3,0,1], with
1830 : : // groups [2] and [3,0,1].
1831 : :
1832 : 958191 : std::vector<TxEntry> entries(depgraph.PositionRange() + 1);
1833 : :
1834 : : // Perform two passes over the linearization.
1835 [ + + ]: 2874573 : for (int pass = 0; pass < 2; ++pass) {
1836 [ - + ]: 1916382 : int rev = !(pass & 1);
1837 : : // Construct a sentinel group, identifying the start of the list.
1838 : 1916382 : entries[SENTINEL].prev_group = SENTINEL;
1839 [ - + ]: 1916382 : Assume(entries[SENTINEL].feerate.IsEmpty());
1840 : :
1841 : : // Iterate over all elements in the existing linearization.
1842 [ + + ]: 16375558 : for (DepGraphIndex i = 0; i < linearization.size(); ++i) {
1843 : : // Even passes are from back to front; odd passes from front to back.
1844 [ + + ]: 14459176 : DepGraphIndex idx = linearization[rev ? linearization.size() - 1 - i : i];
1845 : : // Construct a new group containing just idx. In even passes, the meaning of
1846 : : // parent/child and high/low feerate are swapped.
1847 : 14459176 : DepGraphIndex cur_group = idx + 1;
1848 [ + + ]: 14459176 : entries[cur_group].group = SetType::Singleton(idx);
1849 [ + + + + ]: 14459176 : entries[cur_group].deps = rev ? depgraph.Descendants(idx): depgraph.Ancestors(idx);
1850 : 14459176 : entries[cur_group].feerate = depgraph.FeeRate(idx);
1851 [ + + ]: 14459176 : if (rev) entries[cur_group].feerate.fee = -entries[cur_group].feerate.fee;
1852 : 14459176 : entries[cur_group].prev_tx = NO_PREV_TX; // No previous transaction in group.
1853 : 14459176 : entries[cur_group].first_tx = cur_group; // Transaction itself is first of group.
1854 : : // Insert the new group at the back of the groups linked list.
1855 : 14459176 : entries[cur_group].prev_group = entries[SENTINEL].prev_group;
1856 : 14459176 : entries[SENTINEL].prev_group = cur_group;
1857 : :
1858 : : // Start merge/swap cycle.
1859 : 14459176 : DepGraphIndex next_group = SENTINEL; // We inserted at the end, so next group is sentinel.
1860 : 14459176 : DepGraphIndex prev_group = entries[cur_group].prev_group;
1861 : : // Continue as long as the current group has higher feerate than the previous one.
1862 [ + + ]: 21018059 : while (entries[cur_group].feerate >> entries[prev_group].feerate) {
1863 : : // prev_group/cur_group/next_group refer to (the last transactions of) 3
1864 : : // consecutive entries in groups list.
1865 [ - + ]: 6558883 : Assume(cur_group == entries[next_group].prev_group);
1866 [ - + ]: 6558883 : Assume(prev_group == entries[cur_group].prev_group);
1867 : : // The sentinel has empty feerate, which is neither higher or lower than other
1868 : : // feerates. Thus, the while loop we are in here guarantees that cur_group and
1869 : : // prev_group are not the sentinel.
1870 [ - + ]: 6558883 : Assume(cur_group != SENTINEL);
1871 [ - + ]: 6558883 : Assume(prev_group != SENTINEL);
1872 [ + + ]: 6575578 : if (entries[cur_group].deps.Overlaps(entries[prev_group].group)) {
1873 : : // There is a dependency between cur_group and prev_group; merge prev_group
1874 : : // into cur_group. The group/deps/feerate fields of prev_group remain unchanged
1875 : : // but become unused.
1876 [ + + ]: 6240998 : entries[cur_group].group |= entries[prev_group].group;
1877 [ + + ]: 6240998 : entries[cur_group].deps |= entries[prev_group].deps;
1878 : 6210310 : entries[cur_group].feerate += entries[prev_group].feerate;
1879 : : // Make the first of the current group point to the tail of the previous group.
1880 : 6210310 : entries[entries[cur_group].first_tx].prev_tx = prev_group;
1881 : : // The first of the previous group becomes the first of the newly-merged group.
1882 : 6210310 : entries[cur_group].first_tx = entries[prev_group].first_tx;
1883 : : // The previous group becomes whatever group was before the former one.
1884 : 6210310 : prev_group = entries[prev_group].prev_group;
1885 : 6210310 : entries[cur_group].prev_group = prev_group;
1886 : : } else {
1887 : : // There is no dependency between cur_group and prev_group; swap them.
1888 : 348573 : DepGraphIndex preprev_group = entries[prev_group].prev_group;
1889 : : // If PP, P, C, N were the old preprev, prev, cur, next groups, then the new
1890 : : // layout becomes [PP, C, P, N]. Update prev_groups to reflect that order.
1891 : 348573 : entries[next_group].prev_group = prev_group;
1892 : 348573 : entries[prev_group].prev_group = cur_group;
1893 : 348573 : entries[cur_group].prev_group = preprev_group;
1894 : : // The current group remains the same, but the groups before/after it have
1895 : : // changed.
1896 : 348573 : next_group = prev_group;
1897 : 348573 : prev_group = preprev_group;
1898 : : }
1899 : : }
1900 : : }
1901 : :
1902 : : // Convert the entries back to linearization (overwriting the existing one).
1903 : 1916382 : DepGraphIndex cur_group = entries[0].prev_group;
1904 : 1916382 : DepGraphIndex done = 0;
1905 [ + + ]: 10165248 : while (cur_group != SENTINEL) {
1906 : 8248866 : DepGraphIndex cur_tx = cur_group;
1907 : : // Traverse the transactions of cur_group (from back to front), and write them in the
1908 : : // same order during odd passes, and reversed (front to back) in even passes.
1909 [ + + ]: 8248866 : if (rev) {
1910 : : do {
1911 [ + + ]: 7229588 : *(linearization.begin() + (done++)) = cur_tx - 1;
1912 [ + + ]: 7229588 : cur_tx = entries[cur_tx].prev_tx;
1913 [ + + ]: 7229588 : } while (cur_tx != NO_PREV_TX);
1914 : : } else {
1915 : : do {
1916 [ + + ]: 7229588 : *(linearization.end() - (++done)) = cur_tx - 1;
1917 [ + + ]: 7229588 : cur_tx = entries[cur_tx].prev_tx;
1918 [ + + ]: 7229588 : } while (cur_tx != NO_PREV_TX);
1919 : : }
1920 : 8248866 : cur_group = entries[cur_group].prev_group;
1921 : : }
1922 [ - + ]: 1916382 : Assume(done == linearization.size());
1923 : : }
1924 : 958191 : }
1925 : :
1926 : : } // namespace cluster_linearize
1927 : :
1928 : : #endif // BITCOIN_CLUSTER_LINEARIZE_H
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