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+//===- ReductionRules.h - Reduction Rules -----------------------*- C++ -*-===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// Reduction Rules.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_CODEGEN_PBQP_REDUCTIONRULES_H
+#define LLVM_CODEGEN_PBQP_REDUCTIONRULES_H
+
+#include "Graph.h"
+#include "Math.h"
+#include "Solution.h"
+#include <cassert>
+#include <limits>
+
+namespace llvm {
+namespace PBQP {
+
+ /// \brief Reduce a node of degree one.
+ ///
+ /// Propagate costs from the given node, which must be of degree one, to its
+ /// neighbor. Notify the problem domain.
+ template <typename GraphT>
+ void applyR1(GraphT &G, typename GraphT::NodeId NId) {
+ using NodeId = typename GraphT::NodeId;
+ using EdgeId = typename GraphT::EdgeId;
+ using Vector = typename GraphT::Vector;
+ using Matrix = typename GraphT::Matrix;
+ using RawVector = typename GraphT::RawVector;
+
+ assert(G.getNodeDegree(NId) == 1 &&
+ "R1 applied to node with degree != 1.");
+
+ EdgeId EId = *G.adjEdgeIds(NId).begin();
+ NodeId MId = G.getEdgeOtherNodeId(EId, NId);
+
+ const Matrix &ECosts = G.getEdgeCosts(EId);
+ const Vector &XCosts = G.getNodeCosts(NId);
+ RawVector YCosts = G.getNodeCosts(MId);
+
+ // Duplicate a little to avoid transposing matrices.
+ if (NId == G.getEdgeNode1Id(EId)) {
+ for (unsigned j = 0; j < YCosts.getLength(); ++j) {
+ PBQPNum Min = ECosts[0][j] + XCosts[0];
+ for (unsigned i = 1; i < XCosts.getLength(); ++i) {
+ PBQPNum C = ECosts[i][j] + XCosts[i];
+ if (C < Min)
+ Min = C;
+ }
+ YCosts[j] += Min;
+ }
+ } else {
+ for (unsigned i = 0; i < YCosts.getLength(); ++i) {
+ PBQPNum Min = ECosts[i][0] + XCosts[0];
+ for (unsigned j = 1; j < XCosts.getLength(); ++j) {
+ PBQPNum C = ECosts[i][j] + XCosts[j];
+ if (C < Min)
+ Min = C;
+ }
+ YCosts[i] += Min;
+ }
+ }
+ G.setNodeCosts(MId, YCosts);
+ G.disconnectEdge(EId, MId);
+ }
+
+ template <typename GraphT>
+ void applyR2(GraphT &G, typename GraphT::NodeId NId) {
+ using NodeId = typename GraphT::NodeId;
+ using EdgeId = typename GraphT::EdgeId;
+ using Vector = typename GraphT::Vector;
+ using Matrix = typename GraphT::Matrix;
+ using RawMatrix = typename GraphT::RawMatrix;
+
+ assert(G.getNodeDegree(NId) == 2 &&
+ "R2 applied to node with degree != 2.");
+
+ const Vector &XCosts = G.getNodeCosts(NId);
+
+ typename GraphT::AdjEdgeItr AEItr = G.adjEdgeIds(NId).begin();
+ EdgeId YXEId = *AEItr,
+ ZXEId = *(++AEItr);
+
+ NodeId YNId = G.getEdgeOtherNodeId(YXEId, NId),
+ ZNId = G.getEdgeOtherNodeId(ZXEId, NId);
+
+ bool FlipEdge1 = (G.getEdgeNode1Id(YXEId) == NId),
+ FlipEdge2 = (G.getEdgeNode1Id(ZXEId) == NId);
+
+ const Matrix *YXECosts = FlipEdge1 ?
+ new Matrix(G.getEdgeCosts(YXEId).transpose()) :
+ &G.getEdgeCosts(YXEId);
+
+ const Matrix *ZXECosts = FlipEdge2 ?
+ new Matrix(G.getEdgeCosts(ZXEId).transpose()) :
+ &G.getEdgeCosts(ZXEId);
+
+ unsigned XLen = XCosts.getLength(),
+ YLen = YXECosts->getRows(),
+ ZLen = ZXECosts->getRows();
+
+ RawMatrix Delta(YLen, ZLen);
+
+ for (unsigned i = 0; i < YLen; ++i) {
+ for (unsigned j = 0; j < ZLen; ++j) {
+ PBQPNum Min = (*YXECosts)[i][0] + (*ZXECosts)[j][0] + XCosts[0];
+ for (unsigned k = 1; k < XLen; ++k) {
+ PBQPNum C = (*YXECosts)[i][k] + (*ZXECosts)[j][k] + XCosts[k];
+ if (C < Min) {
+ Min = C;
+ }
+ }
+ Delta[i][j] = Min;
+ }
+ }
+
+ if (FlipEdge1)
+ delete YXECosts;
+
+ if (FlipEdge2)
+ delete ZXECosts;
+
+ EdgeId YZEId = G.findEdge(YNId, ZNId);
+
+ if (YZEId == G.invalidEdgeId()) {
+ YZEId = G.addEdge(YNId, ZNId, Delta);
+ } else {
+ const Matrix &YZECosts = G.getEdgeCosts(YZEId);
+ if (YNId == G.getEdgeNode1Id(YZEId)) {
+ G.updateEdgeCosts(YZEId, Delta + YZECosts);
+ } else {
+ G.updateEdgeCosts(YZEId, Delta.transpose() + YZECosts);
+ }
+ }
+
+ G.disconnectEdge(YXEId, YNId);
+ G.disconnectEdge(ZXEId, ZNId);
+
+ // TODO: Try to normalize newly added/modified edge.
+ }
+
+#ifndef NDEBUG
+ // Does this Cost vector have any register options ?
+ template <typename VectorT>
+ bool hasRegisterOptions(const VectorT &V) {
+ unsigned VL = V.getLength();
+
+ // An empty or spill only cost vector does not provide any register option.
+ if (VL <= 1)
+ return false;
+
+ // If there are registers in the cost vector, but all of them have infinite
+ // costs, then ... there is no available register.
+ for (unsigned i = 1; i < VL; ++i)
+ if (V[i] != std::numeric_limits<PBQP::PBQPNum>::infinity())
+ return true;
+
+ return false;
+ }
+#endif
+
+ // \brief Find a solution to a fully reduced graph by backpropagation.
+ //
+ // Given a graph and a reduction order, pop each node from the reduction
+ // order and greedily compute a minimum solution based on the node costs, and
+ // the dependent costs due to previously solved nodes.
+ //
+ // Note - This does not return the graph to its original (pre-reduction)
+ // state: the existing solvers destructively alter the node and edge
+ // costs. Given that, the backpropagate function doesn't attempt to
+ // replace the edges either, but leaves the graph in its reduced
+ // state.
+ template <typename GraphT, typename StackT>
+ Solution backpropagate(GraphT& G, StackT stack) {
+ using NodeId = GraphBase::NodeId;
+ using Matrix = typename GraphT::Matrix;
+ using RawVector = typename GraphT::RawVector;
+
+ Solution s;
+
+ while (!stack.empty()) {
+ NodeId NId = stack.back();
+ stack.pop_back();
+
+ RawVector v = G.getNodeCosts(NId);
+
+#ifndef NDEBUG
+ // Although a conservatively allocatable node can be allocated to a register,
+ // spilling it may provide a lower cost solution. Assert here that spilling
+ // is done by choice, not because there were no register available.
+ if (G.getNodeMetadata(NId).wasConservativelyAllocatable())
+ assert(hasRegisterOptions(v) && "A conservatively allocatable node "
+ "must have available register options");
+#endif
+
+ for (auto EId : G.adjEdgeIds(NId)) {
+ const Matrix& edgeCosts = G.getEdgeCosts(EId);
+ if (NId == G.getEdgeNode1Id(EId)) {
+ NodeId mId = G.getEdgeNode2Id(EId);
+ v += edgeCosts.getColAsVector(s.getSelection(mId));
+ } else {
+ NodeId mId = G.getEdgeNode1Id(EId);
+ v += edgeCosts.getRowAsVector(s.getSelection(mId));
+ }
+ }
+
+ s.setSelection(NId, v.minIndex());
+ }
+
+ return s;
+ }
+
+} // end namespace PBQP
+} // end namespace llvm
+
+#endif // LLVM_CODEGEN_PBQP_REDUCTIONRULES_H