1 //===-- HeuristicSolver.h - Heuristic PBQP Solver --------------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // Heuristic PBQP solver. This solver is able to perform optimal reductions for
11 // nodes of degree 0, 1 or 2. For nodes of degree >2 a plugable heuristic is
12 // used to select a node for reduction.
14 //===----------------------------------------------------------------------===//
16 #ifndef LLVM_CODEGEN_PBQP_HEURISTICSOLVER_H
17 #define LLVM_CODEGEN_PBQP_HEURISTICSOLVER_H
26 /// \brief Heuristic PBQP solver implementation.
28 /// This class should usually be created (and destroyed) indirectly via a call
29 /// to HeuristicSolver<HImpl>::solve(Graph&).
30 /// See the comments for HeuristicSolver.
32 /// HeuristicSolverImpl provides the R0, R1 and R2 reduction rules,
33 /// backpropagation phase, and maintains the internal copy of the graph on
34 /// which the reduction is carried out (the original being kept to facilitate
36 template <typename HImpl>
37 class HeuristicSolverImpl {
40 typedef typename HImpl::NodeData HeuristicNodeData;
41 typedef typename HImpl::EdgeData HeuristicEdgeData;
43 typedef std::list<Graph::EdgeItr> SolverEdges;
47 /// \brief Iterator type for edges in the solver graph.
48 typedef SolverEdges::iterator SolverEdgeItr;
54 NodeData() : solverDegree(0) {}
56 HeuristicNodeData& getHeuristicData() { return hData; }
58 SolverEdgeItr addSolverEdge(Graph::EdgeItr eItr) {
60 return solverEdges.insert(solverEdges.end(), eItr);
63 void removeSolverEdge(SolverEdgeItr seItr) {
65 solverEdges.erase(seItr);
68 SolverEdgeItr solverEdgesBegin() { return solverEdges.begin(); }
69 SolverEdgeItr solverEdgesEnd() { return solverEdges.end(); }
70 unsigned getSolverDegree() const { return solverDegree; }
71 void clearSolverEdges() {
77 HeuristicNodeData hData;
78 unsigned solverDegree;
79 SolverEdges solverEdges;
84 HeuristicEdgeData& getHeuristicData() { return hData; }
86 void setN1SolverEdgeItr(SolverEdgeItr n1SolverEdgeItr) {
87 this->n1SolverEdgeItr = n1SolverEdgeItr;
90 SolverEdgeItr getN1SolverEdgeItr() { return n1SolverEdgeItr; }
92 void setN2SolverEdgeItr(SolverEdgeItr n2SolverEdgeItr){
93 this->n2SolverEdgeItr = n2SolverEdgeItr;
96 SolverEdgeItr getN2SolverEdgeItr() { return n2SolverEdgeItr; }
100 HeuristicEdgeData hData;
101 SolverEdgeItr n1SolverEdgeItr, n2SolverEdgeItr;
107 std::vector<Graph::NodeItr> stack;
109 typedef std::list<NodeData> NodeDataList;
110 NodeDataList nodeDataList;
112 typedef std::list<EdgeData> EdgeDataList;
113 EdgeDataList edgeDataList;
117 /// \brief Construct a heuristic solver implementation to solve the given
119 /// @param g The graph representing the problem instance to be solved.
120 HeuristicSolverImpl(Graph &g) : g(g), h(*this) {}
122 /// \brief Get the graph being solved by this solver.
123 /// @return The graph representing the problem instance being solved by this
125 Graph& getGraph() { return g; }
127 /// \brief Get the heuristic data attached to the given node.
128 /// @param nItr Node iterator.
129 /// @return The heuristic data attached to the given node.
130 HeuristicNodeData& getHeuristicNodeData(Graph::NodeItr nItr) {
131 return getSolverNodeData(nItr).getHeuristicData();
134 /// \brief Get the heuristic data attached to the given edge.
135 /// @param eItr Edge iterator.
136 /// @return The heuristic data attached to the given node.
137 HeuristicEdgeData& getHeuristicEdgeData(Graph::EdgeItr eItr) {
138 return getSolverEdgeData(eItr).getHeuristicData();
141 /// \brief Begin iterator for the set of edges adjacent to the given node in
142 /// the solver graph.
143 /// @param nItr Node iterator.
144 /// @return Begin iterator for the set of edges adjacent to the given node
145 /// in the solver graph.
146 SolverEdgeItr solverEdgesBegin(Graph::NodeItr nItr) {
147 return getSolverNodeData(nItr).solverEdgesBegin();
150 /// \brief End iterator for the set of edges adjacent to the given node in
151 /// the solver graph.
152 /// @param nItr Node iterator.
153 /// @return End iterator for the set of edges adjacent to the given node in
154 /// the solver graph.
155 SolverEdgeItr solverEdgesEnd(Graph::NodeItr nItr) {
156 return getSolverNodeData(nItr).solverEdgesEnd();
159 /// \brief Remove a node from the solver graph.
160 /// @param eItr Edge iterator for edge to be removed.
162 /// Does <i>not</i> notify the heuristic of the removal. That should be
163 /// done manually if necessary.
164 void removeSolverEdge(Graph::EdgeItr eItr) {
165 EdgeData &eData = getSolverEdgeData(eItr);
166 NodeData &n1Data = getSolverNodeData(g.getEdgeNode1(eItr)),
167 &n2Data = getSolverNodeData(g.getEdgeNode2(eItr));
169 n1Data.removeSolverEdge(eData.getN1SolverEdgeItr());
170 n2Data.removeSolverEdge(eData.getN2SolverEdgeItr());
173 /// \brief Compute a solution to the PBQP problem instance with which this
174 /// heuristic solver was constructed.
175 /// @return A solution to the PBQP problem.
177 /// Performs the full PBQP heuristic solver algorithm, including setup,
178 /// calls to the heuristic (which will call back to the reduction rules in
179 /// this class), and cleanup.
180 Solution computeSolution() {
190 /// \brief Add to the end of the stack.
191 /// @param nItr Node iterator to add to the reduction stack.
192 void pushToStack(Graph::NodeItr nItr) {
193 getSolverNodeData(nItr).clearSolverEdges();
194 stack.push_back(nItr);
197 /// \brief Returns the solver degree of the given node.
198 /// @param nItr Node iterator for which degree is requested.
199 /// @return Node degree in the <i>solver</i> graph (not the original graph).
200 unsigned getSolverDegree(Graph::NodeItr nItr) {
201 return getSolverNodeData(nItr).getSolverDegree();
204 /// \brief Set the solution of the given node.
205 /// @param nItr Node iterator to set solution for.
206 /// @param selection Selection for node.
207 void setSolution(const Graph::NodeItr &nItr, unsigned selection) {
208 s.setSelection(nItr, selection);
210 for (Graph::AdjEdgeItr aeItr = g.adjEdgesBegin(nItr),
211 aeEnd = g.adjEdgesEnd(nItr);
212 aeItr != aeEnd; ++aeItr) {
213 Graph::EdgeItr eItr(*aeItr);
214 Graph::NodeItr anItr(g.getEdgeOtherNode(eItr, nItr));
215 getSolverNodeData(anItr).addSolverEdge(eItr);
219 /// \brief Apply rule R0.
220 /// @param nItr Node iterator for node to apply R0 to.
222 /// Node will be automatically pushed to the solver stack.
223 void applyR0(Graph::NodeItr nItr) {
224 assert(getSolverNodeData(nItr).getSolverDegree() == 0 &&
225 "R0 applied to node with degree != 0.");
227 // Nothing to do. Just push the node onto the reduction stack.
231 /// \brief Apply rule R1.
232 /// @param xnItr Node iterator for node to apply R1 to.
234 /// Node will be automatically pushed to the solver stack.
235 void applyR1(Graph::NodeItr xnItr) {
236 NodeData &nd = getSolverNodeData(xnItr);
237 assert(nd.getSolverDegree() == 1 &&
238 "R1 applied to node with degree != 1.");
240 Graph::EdgeItr eItr = *nd.solverEdgesBegin();
242 const Matrix &eCosts = g.getEdgeCosts(eItr);
243 const Vector &xCosts = g.getNodeCosts(xnItr);
245 // Duplicate a little to avoid transposing matrices.
246 if (xnItr == g.getEdgeNode1(eItr)) {
247 Graph::NodeItr ynItr = g.getEdgeNode2(eItr);
248 Vector &yCosts = g.getNodeCosts(ynItr);
249 for (unsigned j = 0; j < yCosts.getLength(); ++j) {
250 PBQPNum min = eCosts[0][j] + xCosts[0];
251 for (unsigned i = 1; i < xCosts.getLength(); ++i) {
252 PBQPNum c = eCosts[i][j] + xCosts[i];
258 h.handleRemoveEdge(eItr, ynItr);
260 Graph::NodeItr ynItr = g.getEdgeNode1(eItr);
261 Vector &yCosts = g.getNodeCosts(ynItr);
262 for (unsigned i = 0; i < yCosts.getLength(); ++i) {
263 PBQPNum min = eCosts[i][0] + xCosts[0];
264 for (unsigned j = 1; j < xCosts.getLength(); ++j) {
265 PBQPNum c = eCosts[i][j] + xCosts[j];
271 h.handleRemoveEdge(eItr, ynItr);
273 removeSolverEdge(eItr);
274 assert(nd.getSolverDegree() == 0 &&
275 "Degree 1 with edge removed should be 0.");
279 /// \brief Apply rule R2.
280 /// @param xnItr Node iterator for node to apply R2 to.
282 /// Node will be automatically pushed to the solver stack.
283 void applyR2(Graph::NodeItr xnItr) {
284 assert(getSolverNodeData(xnItr).getSolverDegree() == 2 &&
285 "R2 applied to node with degree != 2.");
287 NodeData &nd = getSolverNodeData(xnItr);
288 const Vector &xCosts = g.getNodeCosts(xnItr);
290 SolverEdgeItr aeItr = nd.solverEdgesBegin();
291 Graph::EdgeItr yxeItr = *aeItr,
294 Graph::NodeItr ynItr = g.getEdgeOtherNode(yxeItr, xnItr),
295 znItr = g.getEdgeOtherNode(zxeItr, xnItr);
297 bool flipEdge1 = (g.getEdgeNode1(yxeItr) == xnItr),
298 flipEdge2 = (g.getEdgeNode1(zxeItr) == xnItr);
300 const Matrix *yxeCosts = flipEdge1 ?
301 new Matrix(g.getEdgeCosts(yxeItr).transpose()) :
302 &g.getEdgeCosts(yxeItr);
304 const Matrix *zxeCosts = flipEdge2 ?
305 new Matrix(g.getEdgeCosts(zxeItr).transpose()) :
306 &g.getEdgeCosts(zxeItr);
308 unsigned xLen = xCosts.getLength(),
309 yLen = yxeCosts->getRows(),
310 zLen = zxeCosts->getRows();
312 Matrix delta(yLen, zLen);
314 for (unsigned i = 0; i < yLen; ++i) {
315 for (unsigned j = 0; j < zLen; ++j) {
316 PBQPNum min = (*yxeCosts)[i][0] + (*zxeCosts)[j][0] + xCosts[0];
317 for (unsigned k = 1; k < xLen; ++k) {
318 PBQPNum c = (*yxeCosts)[i][k] + (*zxeCosts)[j][k] + xCosts[k];
333 Graph::EdgeItr yzeItr = g.findEdge(ynItr, znItr);
334 bool addedEdge = false;
336 if (yzeItr == g.edgesEnd()) {
337 yzeItr = g.addEdge(ynItr, znItr, delta);
340 Matrix &yzeCosts = g.getEdgeCosts(yzeItr);
341 h.preUpdateEdgeCosts(yzeItr);
342 if (ynItr == g.getEdgeNode1(yzeItr)) {
345 yzeCosts += delta.transpose();
349 bool nullCostEdge = tryNormaliseEdgeMatrix(yzeItr);
352 // If we modified the edge costs let the heuristic know.
353 h.postUpdateEdgeCosts(yzeItr);
357 // If this edge ended up null remove it.
359 // We didn't just add it, so we need to notify the heuristic
360 // and remove it from the solver.
361 h.handleRemoveEdge(yzeItr, ynItr);
362 h.handleRemoveEdge(yzeItr, znItr);
363 removeSolverEdge(yzeItr);
365 g.removeEdge(yzeItr);
366 } else if (addedEdge) {
367 // If the edge was added, and non-null, finish setting it up, add it to
368 // the solver & notify heuristic.
369 edgeDataList.push_back(EdgeData());
370 g.setEdgeData(yzeItr, &edgeDataList.back());
371 addSolverEdge(yzeItr);
372 h.handleAddEdge(yzeItr);
375 h.handleRemoveEdge(yxeItr, ynItr);
376 removeSolverEdge(yxeItr);
377 h.handleRemoveEdge(zxeItr, znItr);
378 removeSolverEdge(zxeItr);
385 NodeData& getSolverNodeData(Graph::NodeItr nItr) {
386 return *static_cast<NodeData*>(g.getNodeData(nItr));
389 EdgeData& getSolverEdgeData(Graph::EdgeItr eItr) {
390 return *static_cast<EdgeData*>(g.getEdgeData(eItr));
393 void addSolverEdge(Graph::EdgeItr eItr) {
394 EdgeData &eData = getSolverEdgeData(eItr);
395 NodeData &n1Data = getSolverNodeData(g.getEdgeNode1(eItr)),
396 &n2Data = getSolverNodeData(g.getEdgeNode2(eItr));
398 eData.setN1SolverEdgeItr(n1Data.addSolverEdge(eItr));
399 eData.setN2SolverEdgeItr(n2Data.addSolverEdge(eItr));
403 if (h.solverRunSimplify()) {
407 // Create node data objects.
408 for (Graph::NodeItr nItr = g.nodesBegin(), nEnd = g.nodesEnd();
409 nItr != nEnd; ++nItr) {
410 nodeDataList.push_back(NodeData());
411 g.setNodeData(nItr, &nodeDataList.back());
414 // Create edge data objects.
415 for (Graph::EdgeItr eItr = g.edgesBegin(), eEnd = g.edgesEnd();
416 eItr != eEnd; ++eItr) {
417 edgeDataList.push_back(EdgeData());
418 g.setEdgeData(eItr, &edgeDataList.back());
424 disconnectTrivialNodes();
425 eliminateIndependentEdges();
428 // Eliminate trivial nodes.
429 void disconnectTrivialNodes() {
430 unsigned numDisconnected = 0;
432 for (Graph::NodeItr nItr = g.nodesBegin(), nEnd = g.nodesEnd();
433 nItr != nEnd; ++nItr) {
435 if (g.getNodeCosts(nItr).getLength() == 1) {
437 std::vector<Graph::EdgeItr> edgesToRemove;
439 for (Graph::AdjEdgeItr aeItr = g.adjEdgesBegin(nItr),
440 aeEnd = g.adjEdgesEnd(nItr);
441 aeItr != aeEnd; ++aeItr) {
443 Graph::EdgeItr eItr = *aeItr;
445 if (g.getEdgeNode1(eItr) == nItr) {
446 Graph::NodeItr otherNodeItr = g.getEdgeNode2(eItr);
447 g.getNodeCosts(otherNodeItr) +=
448 g.getEdgeCosts(eItr).getRowAsVector(0);
451 Graph::NodeItr otherNodeItr = g.getEdgeNode1(eItr);
452 g.getNodeCosts(otherNodeItr) +=
453 g.getEdgeCosts(eItr).getColAsVector(0);
456 edgesToRemove.push_back(eItr);
459 if (!edgesToRemove.empty())
462 while (!edgesToRemove.empty()) {
463 g.removeEdge(edgesToRemove.back());
464 edgesToRemove.pop_back();
470 void eliminateIndependentEdges() {
471 std::vector<Graph::EdgeItr> edgesToProcess;
472 unsigned numEliminated = 0;
474 for (Graph::EdgeItr eItr = g.edgesBegin(), eEnd = g.edgesEnd();
475 eItr != eEnd; ++eItr) {
476 edgesToProcess.push_back(eItr);
479 while (!edgesToProcess.empty()) {
480 if (tryToEliminateEdge(edgesToProcess.back()))
482 edgesToProcess.pop_back();
486 bool tryToEliminateEdge(Graph::EdgeItr eItr) {
487 if (tryNormaliseEdgeMatrix(eItr)) {
494 bool tryNormaliseEdgeMatrix(Graph::EdgeItr &eItr) {
496 const PBQPNum infinity = std::numeric_limits<PBQPNum>::infinity();
498 Matrix &edgeCosts = g.getEdgeCosts(eItr);
499 Vector &uCosts = g.getNodeCosts(g.getEdgeNode1(eItr)),
500 &vCosts = g.getNodeCosts(g.getEdgeNode2(eItr));
502 for (unsigned r = 0; r < edgeCosts.getRows(); ++r) {
503 PBQPNum rowMin = infinity;
505 for (unsigned c = 0; c < edgeCosts.getCols(); ++c) {
506 if (vCosts[c] != infinity && edgeCosts[r][c] < rowMin)
507 rowMin = edgeCosts[r][c];
512 if (rowMin != infinity) {
513 edgeCosts.subFromRow(r, rowMin);
516 edgeCosts.setRow(r, 0);
520 for (unsigned c = 0; c < edgeCosts.getCols(); ++c) {
521 PBQPNum colMin = infinity;
523 for (unsigned r = 0; r < edgeCosts.getRows(); ++r) {
524 if (uCosts[r] != infinity && edgeCosts[r][c] < colMin)
525 colMin = edgeCosts[r][c];
530 if (colMin != infinity) {
531 edgeCosts.subFromCol(c, colMin);
534 edgeCosts.setCol(c, 0);
538 return edgeCosts.isZero();
541 void backpropagate() {
542 while (!stack.empty()) {
543 computeSolution(stack.back());
548 void computeSolution(Graph::NodeItr nItr) {
550 NodeData &nodeData = getSolverNodeData(nItr);
552 Vector v(g.getNodeCosts(nItr));
554 // Solve based on existing solved edges.
555 for (SolverEdgeItr solvedEdgeItr = nodeData.solverEdgesBegin(),
556 solvedEdgeEnd = nodeData.solverEdgesEnd();
557 solvedEdgeItr != solvedEdgeEnd; ++solvedEdgeItr) {
559 Graph::EdgeItr eItr(*solvedEdgeItr);
560 Matrix &edgeCosts = g.getEdgeCosts(eItr);
562 if (nItr == g.getEdgeNode1(eItr)) {
563 Graph::NodeItr adjNode(g.getEdgeNode2(eItr));
564 unsigned adjSolution = s.getSelection(adjNode);
565 v += edgeCosts.getColAsVector(adjSolution);
568 Graph::NodeItr adjNode(g.getEdgeNode1(eItr));
569 unsigned adjSolution = s.getSelection(adjNode);
570 v += edgeCosts.getRowAsVector(adjSolution);
575 setSolution(nItr, v.minIndex());
580 nodeDataList.clear();
581 edgeDataList.clear();
585 /// \brief PBQP heuristic solver class.
587 /// Given a PBQP Graph g representing a PBQP problem, you can find a solution
589 /// <tt>Solution s = HeuristicSolver<H>::solve(g);</tt>
591 /// The choice of heuristic for the H parameter will affect both the solver
592 /// speed and solution quality. The heuristic should be chosen based on the
593 /// nature of the problem being solved.
594 /// Currently the only solver included with LLVM is the Briggs heuristic for
595 /// register allocation.
596 template <typename HImpl>
597 class HeuristicSolver {
599 static Solution solve(Graph &g) {
600 HeuristicSolverImpl<HImpl> hs(g);
601 return hs.computeSolution();
607 #endif // LLVM_CODEGEN_PBQP_HEURISTICSOLVER_H