AIEPathFinder.cpp

Go to the documentation of this file.

//===- AIEPathFinder.cpp ----------------------------------------*- C++ -*-===//
//
// Copyright (C) 2021-2022 Xilinx, Inc.
// Copyright (C) 2022-2026 Advanced Micro Devices, Inc.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
 
#include "aie/Dialect/AIE/Transforms/AIEPathFinder.h"
#include "aie/Dialect/AIE/Transforms/AIERoutingDiagnostics.h"
#include "d_ary_heap.h"
 
#include "llvm/ADT/MapVector.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/FormatVariadic.h"
 
#include <iterator>
#include <limits>
 
using namespace mlir;
using namespace xilinx;
using namespace xilinx::AIE;
 
#define DEBUG_TYPE "aie-pathfinder"
 
namespace {
// A connection's demand, the cost Dijkstra weighs it by, is
// (demandBase + overCapacityCoeff * iterations it was over capacity) *
// (demandBase + usedCapacityCoeff * streams using it), plus its avoidance.
constexpr double overCapacityCoeff = 0.1;
constexpr double usedCapacityCoeff = 0.02;
constexpr double demandBase = 1.0;
// A full connection's demand grows by this factor, or a prioritized flow's
// by priorityDemandCoeff, each time another stream takes it.
constexpr double demandCoeff = 1.1;
constexpr double priorityDemandCoeff =
    static_cast<double>(std::numeric_limits<int>::max());
constexpr int maxCircuitStreamCapacity = 1;
constexpr int maxPacketStreamCapacity = 32;
// Demand added to a connection into an avoided port. It exceeds what a long
// detour costs, so a route takes the port only when every other is taken.
constexpr double avoidedPortDemand = 100.0;
// History added to a connection each time the routing check rejects it.
constexpr int routingCheckPenalty = 5;
// Iterations spent steering away from a usable routing the check rejects.
constexpr int maxSteers = 16;
// Routings in a row the check rejects only for onlyPriorityMasters before
// routing gives up: the penalties move such a flow between the ports of the
// switchbox it has to leave by.
constexpr int maxPriorityFaults = 16;
// Times the routing check may fault where two trees meet before they stop
// meeting; each fault moves the meeting elsewhere.
constexpr int maxMeetFaults = 4;
// Cost added to a hop that shares an arbiter unit with a flow to avoid.
constexpr double conflictSharePenalty = 4;
// Channels per direction packet streams leave a capped tile by (see
// Pathfinder::relax). A heuristic: fewer channels mean fewer master
// sets per tile, but more flows on each.
constexpr int packetFanoutCap = 2;
// A multicast's next destination may branch off any hop its tree already
// takes, starting at this cost per hop back to the source: enough of a
// discount to share hops, while still preferring the shortest path to each
// destination.
constexpr double treeSeedFactor = 0.9;
// A destination's branch is rerouted only when that saves more than this.
constexpr double rerouteMinSaving = 1e-6;
// Iterations without fewer overused channels before the circuit trees that
// overuse one route first (see findPaths).
constexpr int stallIterations = 50;
// Iterations of a stall that route the losing circuit trees first, without
// fewer overused channels, before the attempt gives up.
constexpr int maxReorderedStall = 300;
// Iterations without fewer overused channels before an attempt that has never
// fit the fabric gives up. In the nightly's designs, none that routed took
// over 275.
constexpr int maxOverusedStall = 400;
// How much faster a stalled routing's overused channels that only circuit
// trees take accrue history, so the trees spread out sooner.
constexpr int stallHistory = 4;
} // namespace
 
void SwitchboxConnect::updateDemand() {
  for (Cell &c : cells)
    c.demand = (demandBase + overCapacityCoeff * c.overCapacity) *
                   (demandBase + usedCapacityCoeff * c.usedCapacity) +
               c.avoidance;
}
 
void SwitchboxConnect::bumpDemand(Cell &c) {
  if (c.usedCapacity >= maxCircuitStreamCapacity)
    c.demand *= c.isPriority ? priorityDemandCoeff : demandCoeff;
}
 
char RoutingFailure::ID = 0;
char DeadlockProneRouting::ID = 0;
char PinnedRoutingFailure::ID = 0;
 
void RoutingFailure::log(llvm::raw_ostream &os) const {
  os << "Unable to find a legal routing";
  if (!reason.empty())
    os << ": " << reason;
}
 
llvm::Error DynamicTileAnalysis::runAnalysis(DeviceOp &device) {
  LLVM_DEBUG(llvm::dbgs() << "\t---Begin DynamicTileAnalysis Constructor---\n");
  // find the maxCol and maxRow
  maxCol = device.getTargetModel().columns();
  maxRow = device.getTargetModel().rows();
 
  pathfinder.initialize(maxCol, maxRow, device.getTargetModel());
  for (const auto &[coords, port] : avoidedPorts)
    pathfinder.avoidPort(coords, port);
 
  // For each flow (circuit + packet) in the device, add it to pathfinder. Each
  // source can map to multiple different destinations (fanout). Control packet
  // flows to be routed (as prioritized routings). Then followed by normal
  // packet flows.
  for (PacketFlowOp pktFlowOp : device.getOps<PacketFlowOp>()) {
    Region &r = pktFlowOp.getPorts();
    Block &b = r.front();
    SmallVector<std::pair<TileID, Port>, 4> sources;
    // Pass 1: collect all sources (order-independent; supports fan-in).
    for (Operation &Op : b.getOperations()) {
      if (auto pktSource = dyn_cast<PacketSourceOp>(Op)) {
        auto srcTile = cast<TileOp>(pktSource.getTile().getDefiningOp());
        sources.push_back(
            {{srcTile.colIndex(), srcTile.rowIndex()}, pktSource.port()});
      }
    }
 
    bool priorityFlow = pktFlowOp.getPriorityRoute().value_or(false);
    // Pass 2: add a flow from every source to every destination so
    // fan-in topologies are routed (not just the last source).
    for (Operation &Op : b.getOperations()) {
      if (auto pktDest = dyn_cast<PacketDestOp>(Op)) {
        auto dstTile = cast<TileOp>(pktDest.getTile().getDefiningOp());
        Port dstPort = pktDest.port();
        TileID dstCoords = {dstTile.colIndex(), dstTile.rowIndex()};
        for (auto &[srcCoords, srcPort] : sources) {
          LLVM_DEBUG(llvm::dbgs()
                     << "\tAdding Packet Flow: (" << srcCoords.col << ", "
                     << srcCoords.row << ")"
                     << stringifyWireBundle(srcPort.bundle) << srcPort.channel
                     << " -> (" << dstCoords.col << ", " << dstCoords.row << ")"
                     << stringifyWireBundle(dstPort.bundle) << dstPort.channel
                     << "\n");
          pathfinder.addFlow(srcCoords, srcPort, dstCoords, dstPort,
                             pktFlowOp.IDInt(), priorityFlow,
                             pktFlowOp.getLoc());
        }
      }
    }
  }
 
  // Add circuit flows.
  for (FlowOp flowOp : device.getOps<FlowOp>()) {
    TileOp srcTile = cast<TileOp>(flowOp.getSource().getDefiningOp());
    TileOp dstTile = cast<TileOp>(flowOp.getDest().getDefiningOp());
    TileID srcCoords = {srcTile.colIndex(), srcTile.rowIndex()};
    TileID dstCoords = {dstTile.colIndex(), dstTile.rowIndex()};
    Port srcPort = {flowOp.getSourceBundle(), flowOp.getSourceChannel()};
    Port dstPort = {flowOp.getDestBundle(), flowOp.getDestChannel()};
    LLVM_DEBUG(llvm::dbgs()
               << "\tAdding Flow: (" << srcCoords.col << ", " << srcCoords.row
               << ")" << stringifyWireBundle(srcPort.bundle) << srcPort.channel
               << " -> (" << dstCoords.col << ", " << dstCoords.row << ")"
               << stringifyWireBundle(dstPort.bundle) << dstPort.channel
               << "\n");
    pathfinder.addFlow(srcCoords, srcPort, dstCoords, dstPort,
                       /*packetId=*/std::nullopt, /*isPriorityFlow=*/false,
                       flowOp.getLoc());
  }
 
  // Canonicalize all flows after both packet and circuit flows are collected.
  pathfinder.sortFlows();
 
  // add existing connections so Pathfinder knows which resources are
  // available search all existing SwitchBoxOps for exising connections
  for (SwitchboxOp switchboxOp : device.getOps<SwitchboxOp>()) {
    if (failed(pathfinder.addFixedConnection(switchboxOp)))
      return llvm::make_error<RoutingFailure>(
          llvm::formatv("cannot add the fixed connections of the switchbox "
                        "at tile ({0}, {1})",
                        switchboxOp.colIndex(), switchboxOp.rowIndex()),
          RoutingFaults{}, switchboxOp.getLoc());
  }
 
  // all flows are now populated, call the congestion-aware pathfinder
  // algorithm
  // check whether the pathfinder algorithm creates a legal routing
  llvm::Expected<Routing> found = pathfinder.findPaths(maxIterations);
  if (!found)
    return found.takeError();
  routing = std::move(*found);
 
  // fill in coords to TileOps, SwitchboxOps, and ShimMuxOps
  coordToTile.clear();
  coordToSwitchbox.clear();
  coordToShimMux.clear();
  for (auto tileOp : device.getOps<TileOp>()) {
    [[maybe_unused]] bool fresh =
        coordToTile.try_emplace(tileOp.getTileID(), tileOp).second;
    assert(fresh);
  }
  for (auto switchboxOp : device.getOps<SwitchboxOp>()) {
    [[maybe_unused]] bool fresh =
        coordToSwitchbox
            .try_emplace({switchboxOp.colIndex(), switchboxOp.rowIndex()},
                         switchboxOp)
            .second;
    assert(fresh);
  }
  for (auto shimmuxOp : device.getOps<ShimMuxOp>()) {
    [[maybe_unused]] bool fresh =
        coordToShimMux
            .try_emplace({shimmuxOp.colIndex(), shimmuxOp.rowIndex()},
                         shimmuxOp)
            .second;
    assert(fresh);
  }
 
  LLVM_DEBUG(llvm::dbgs() << "\t---End DynamicTileAnalysis Constructor---\n");
  return llvm::Error::success();
}
 
TileOp DynamicTileAnalysis::getTile(OpBuilder &builder, int col, int row) {
  TileOp &tileOp = coordToTile[{col, row}];
  if (!tileOp)
    tileOp = TileOp::create(
        builder,
        cast<DeviceOp>(builder.getInsertionBlock()->getParentOp()).getLoc(),
        col, row);
  return tileOp;
}
 
TileOp DynamicTileAnalysis::getTile(OpBuilder &builder, const TileID &tileId) {
  return getTile(builder, tileId.col, tileId.row);
}
 
SwitchboxOp DynamicTileAnalysis::getSwitchbox(OpBuilder &builder, int col,
                                              int row) {
  assert(col >= 0);
  assert(row >= 0);
  if (SwitchboxOp switchboxOp = lookupSwitchbox({col, row}))
    return switchboxOp;
  auto tileOp = getTile(builder, col, row);
  auto switchboxOp = SwitchboxOp::create(builder, tileOp.getLoc(), tileOp);
  SwitchboxOp::ensureTerminator(switchboxOp.getConnections(), builder,
                                tileOp.getLoc());
  coordToSwitchbox[{col, row}] = switchboxOp;
  return switchboxOp;
}
 
ShimMuxOp DynamicTileAnalysis::getShimMux(OpBuilder &builder, int col) {
  assert(col >= 0);
  if (ShimMuxOp shimMuxOp = lookupShimMux(col))
    return shimMuxOp;
  auto tileOp = getTile(builder, col, 0);
  assert(tileOp.isShimNOCorPLTile());
  auto shimMuxOp = ShimMuxOp::create(builder, tileOp.getLoc(), tileOp);
  ShimMuxOp::ensureTerminator(shimMuxOp.getConnections(), builder,
                              tileOp.getLoc());
  coordToShimMux[{col, 0}] = shimMuxOp;
  return shimMuxOp;
}
 
void Pathfinder::initialize(int maxCol, int maxRow,
                            const AIETargetModel &targetModel) {
  // Reset the graph and flows so a Pathfinder can be reused across analyses
  // and devices; the dense-graph cache must be rebuilt for the new topology.
  // The relax state (shareChannels, idsApart, meetApart, relaxStep,
  // cappedTiles, crowdedTiles) survives, so the ladder advances across
  // attempts.
  graph.clear();
  flows.clear();
  packetIdsTo.clear();
  priorityIds.clear();
  flowLocs.clear();
  graphBuilt = false;
  columns = maxCol;
  rows = maxRow;
  nodeIds.clear();
  nodes.clear();
  adjacency.clear();
  wireEdgesBegin.clear();
  distance.clear();
  indexInHeap.clear();
  colors.clear();
  preds.clear();
  predEdge.clear();
 
  std::map<WireBundle, int> maxChannels;
  auto intraconnect = [&](int col, int row) {
    TileID coords = {col, row};
    SwitchboxConnect &sb =
        graph.try_emplace({coords, coords}, coords).first->second;
 
    for (int i = 0, e = getMaxEnumValForWireBundle() + 1; i < e; ++i) {
      WireBundle bundle = symbolizeWireBundle(i).value();
      // get all ports into current switchbox
      int channels =
          targetModel.getNumSourceSwitchboxConnections(col, row, bundle);
      if (channels == 0 && targetModel.isShimNOCorPLTile(col, row)) {
        // wordaround for shimMux
        channels = targetModel.getNumSourceShimMuxConnections(col, row, bundle);
      }
      for (int channel = 0; channel < channels; channel++) {
        sb.srcPorts.push_back(Port{bundle, channel});
      }
      // get all ports out of current switchbox
      channels = targetModel.getNumDestSwitchboxConnections(col, row, bundle);
      if (channels == 0 && targetModel.isShimNOCorPLTile(col, row)) {
        // wordaround for shimMux
        channels = targetModel.getNumDestShimMuxConnections(col, row, bundle);
      }
      for (int channel = 0; channel < channels; channel++) {
        sb.dstPorts.push_back(Port{bundle, channel});
      }
      maxChannels[bundle] = channels;
    }
    sb.resize();
    // A shim's mux reaches its DMA, NOC and PLIO ports from any port.
    auto isMuxed = [&](Port p) {
      return targetModel.isShimNOCorPLTile(col, row) &&
             llvm::is_contained(
                 {WireBundle::DMA, WireBundle::NOC, WireBundle::PLIO},
                 p.bundle);
    };
    for (auto [i, pIn] : llvm::enumerate(sb.srcPorts))
      for (auto [j, pOut] : llvm::enumerate(sb.dstPorts))
        sb.at(i, j).available =
            targetModel.isLegalTileConnection(col, row, pIn.bundle, pIn.channel,
                                              pOut.bundle, pOut.channel) ||
            isMuxed(pIn) || isMuxed(pOut);
  };
 
  auto interconnect = [&](int col, int row, int targetCol, int targetRow,
                          WireBundle srcBundle, WireBundle dstBundle) {
    TileID src = {col, row}, dst = {targetCol, targetRow};
    SwitchboxConnect &sb =
        graph.try_emplace({src, dst}, src, dst).first->second;
    for (int channel = 0; channel < maxChannels[srcBundle]; channel++) {
      sb.srcPorts.push_back(Port{srcBundle, channel});
      sb.dstPorts.push_back(Port{dstBundle, channel});
    }
    sb.resize();
    for (size_t i = 0; i < sb.srcPorts.size(); i++)
      sb.at(i, i).available = true;
  };
 
  for (int row = 0; row <= maxRow; row++) {
    for (int col = 0; col <= maxCol; col++) {
      maxChannels.clear();
      // connections within the same switchbox
      intraconnect(col, row);
 
      // connections between switchboxes
      if (row > 0) {
        // from south to north
        interconnect(col, row, col, row - 1, WireBundle::South,
                     WireBundle::North);
      }
      if (row < maxRow) {
        // from north to south
        interconnect(col, row, col, row + 1, WireBundle::North,
                     WireBundle::South);
      }
      if (col > 0) {
        // from east to west
        interconnect(col, row, col - 1, row, WireBundle::West,
                     WireBundle::East);
      }
      if (col < maxCol) {
        // from west to east
        interconnect(col, row, col + 1, row, WireBundle::East,
                     WireBundle::West);
      }
    }
  }
}
 
// Add a flow from src to dst can have an arbitrary number of dst locations
// due to fanout.
void Pathfinder::addFlow(TileID srcCoords, Port srcPort, TileID dstCoords,
                         Port dstPort, std::optional<int> packetId,
                         bool isPriorityFlow,
                         std::optional<mlir::Location> loc) {
  auto pinnedIds = constraints.pinnedIds.find({srcCoords, srcPort});
  if (constraints.pinned.count({srcCoords, srcPort}))
    isPriorityFlow &= packetId && pinnedIds != constraints.pinnedIds.end() &&
                      pinnedIds->second.count(*packetId);
  else
    isPriorityFlow &= constraints.prioritize;
  if (loc)
    flowLocs[{srcCoords, srcPort}].try_emplace({dstCoords, dstPort}, *loc);
  if (packetId) {
    auto &ids = packetIdsTo[{{srcCoords, srcPort}, {dstCoords, dstPort}}];
    if (!llvm::is_contained(ids, *packetId))
      ids.push_back(*packetId);
    if (isPriorityFlow)
      priorityIds[{srcCoords, srcPort}].insert(*packetId);
  }
  // A source has one flow, with all its destinations.
  PathEndPoint src{srcCoords, srcPort}, dst{dstCoords, dstPort};
  auto flow = llvm::find_if(flows, [&](const Flow &f) { return f.src == src; });
  if (flow == flows.end()) {
    // sortFlows assigns the packet groups.
    flows.push_back(
        Flow{packetId ? 0 : -1, isPriorityFlow, src, {dst}, packetId});
  } else if (isPriorityFlow) {
    flow->isPriorityFlow = true;
    flow->dsts.insert(flow->dsts.begin(), dst);
  } else {
    flow->dsts.push_back(dst);
  }
}
 
// Where the flow from `src` to `dst`, or to any destination if `dst` is null,
// was declared.
std::optional<mlir::Location>
Pathfinder::flowLoc(const PathEndPoint &src, const PathEndPoint *dst) const {
  auto locs = flowLocs.find(src);
  if (locs == flowLocs.end())
    return std::nullopt;
  auto it = dst ? locs->second.find(*dst) : locs->second.begin();
  if (it == locs->second.end())
    return std::nullopt;
  return it->second;
}
 
bool Pathfinder::shareAllChannels() {
  shareChannels = true;
  return llvm::any_of(flows, [](const Flow &f) { return f.packetGroupId > 0; });
}
 
bool Pathfinder::capCrowdedFanOut() {
  size_t capped = cappedTiles.size();
  cappedTiles.insert(crowdedTiles.begin(), crowdedTiles.end());
  return cappedTiles.size() > capped;
}
 
std::map<PathEndPoint, std::set<int>> Pathfinder::idsBySource() const {
  std::map<PathEndPoint, std::set<int>> ids;
  for (const auto &[ends, sent] : packetIdsTo)
    ids[ends.first].insert(sent.begin(), sent.end());
  return ids;
}
 
bool Pathfinder::routeIdsApart() {
  if (idsApart)
    return false;
  idsApart = true;
  shareChannels = false;
  cappedTiles.clear();
  return llvm::any_of(idsBySource(),
                      [](const auto &s) { return s.second.size() > 1; });
}
 
bool Pathfinder::splitSharedIds() {
  if (splitShared)
    return false;
  splitShared = true;
  shareChannels = false;
  cappedTiles.clear();
  std::map<PathEndPoint, std::set<int>> ids = idsBySource();
  for (const auto &[src, srcIds] : ids)
    for (const auto &[other, otherIds] : ids) {
      const std::set<int> &theirs = otherIds;
      if (!(src == other) &&
          llvm::any_of(srcIds, [&](int id) { return theirs.count(id); }) &&
          llvm::any_of(srcIds, [&](int id) { return !theirs.count(id); }))
        return true;
    }
  return false;
}
 
// The steps before it bent the routing around the meetings, so the ladder
// starts over without them.
bool Pathfinder::stopMeeting() {
  if (meetApart || !treesMet)
    return false;
  meetApart = true;
  shareChannels = idsApart = splitShared = false;
  cappedTiles.clear();
  relaxStep = 0;
  return true;
}
 
namespace {
enum class RelaxStep {
  ShareChannels,
  CapCrowdedTiles,
  RouteIdsApart,
  SplitSharedIds,
  StopMeeting
};
// Stopping meetings comes last, and runs the ladder once more: what it routes
// can hold arbiters in a cycle through the receivers trees share.
constexpr RelaxStep relaxLadder[] = {
    RelaxStep::ShareChannels,   RelaxStep::CapCrowdedTiles,
    RelaxStep::RouteIdsApart,   RelaxStep::ShareChannels,
    RelaxStep::CapCrowdedTiles, RelaxStep::SplitSharedIds,
    RelaxStep::ShareChannels,   RelaxStep::CapCrowdedTiles,
    RelaxStep::StopMeeting};
} // namespace
 
bool Pathfinder::relax() {
  if (!packetsFailed) {
    LLVM_DEBUG(llvm::dbgs() << "No packet stream crosses an overused link\n");
    return false;
  }
  while (relaxStep < std::size(relaxLadder)) {
    switch (relaxLadder[relaxStep++]) {
    case RelaxStep::ShareChannels:
      if (shareAllChannels()) {
        LLVM_DEBUG(llvm::dbgs() << "Relax: share channels\n");
        return true;
      }
      break;
    case RelaxStep::CapCrowdedTiles:
      if (capCrowdedFanOut()) {
        LLVM_DEBUG(llvm::dbgs() << "Relax: cap crowded tiles\n");
        return true;
      }
      break;
    case RelaxStep::RouteIdsApart:
      if (routeIdsApart()) {
        LLVM_DEBUG(llvm::dbgs() << "Relax: route ids apart\n");
        return true;
      }
      // With one id per source, the steps up to the last would only repeat.
      relaxStep = std::size(relaxLadder) - 1;
      break;
    case RelaxStep::SplitSharedIds:
      if (splitSharedIds()) {
        LLVM_DEBUG(llvm::dbgs() << "Relax: split shared ids\n");
        return true;
      }
      relaxStep = std::size(relaxLadder) - 1;
      break;
    case RelaxStep::StopMeeting:
      if (stopMeeting()) {
        LLVM_DEBUG(llvm::dbgs() << "Relax: stop meeting\n");
        return true;
      }
      break;
    }
  }
  return false;
}
 
// Sort flows to (1) get deterministic routing, and (2) perform routings on
// prioritized flows before others, for routing consistency on those flows.
void Pathfinder::sortFlows() {
  for (auto &flow : flows)
    llvm::sort(flow.dsts);
 
  // The groups shareAllChannels merges, whatever order the flows were
  // added in: packet flows to a common destination are in one.
  llvm::IntEqClasses groups(flows.size());
  std::map<PathEndPoint, unsigned> firstTo;
  for (auto [k, flow] : llvm::enumerate(flows)) {
    if (flow.packetGroupId < 0)
      continue;
    for (const PathEndPoint &dst : flow.dsts) {
      auto [it, fresh] = firstTo.try_emplace(dst, k);
      if (!fresh)
        groups.join(k, it->second);
    }
  }
  llvm::DenseMap<unsigned, int> groupOf;
  for (auto [k, flow] : llvm::enumerate(flows))
    if (flow.packetGroupId >= 0)
      flow.packetGroupId =
          shareChannels
              ? 0
              : groupOf.try_emplace(groups.findLeader(k), groupOf.size())
                    .first->second;
 
  auto flowRank = [](const Flow &flow) {
    if (flow.isPriorityFlow)
      return 0;
    if (flow.packetGroupId >= 0)
      return 1;
    return 2;
  };
  llvm::sort(flows, [&](const Flow &lhs, const Flow &rhs) {
    return std::make_pair(flowRank(lhs), lhs.src) <
           std::make_pair(flowRank(rhs), rhs.src);
  });
}
 
int xilinx::AIE::shimMuxChannelFrom(Port src) {
  // DMA0 -> N3, DMA1 -> N7; NOC0/1 -> N2/3, NOC2/3 -> N6/7.
  if (src.bundle == WireBundle::DMA)
    return src.channel == 0 ? 3 : 7;
  if (src.bundle == WireBundle::NOC)
    return src.channel >= 2 ? src.channel + 4 : src.channel + 2;
  return src.channel;
}
 
int xilinx::AIE::shimMuxChannelTo(Port dst) {
  // N2 -> DMA0, N3 -> DMA1; N2-5 -> NOC0-3.
  if (dst.bundle == WireBundle::DMA)
    return dst.channel == 0 ? 2 : 3;
  if (dst.bundle == WireBundle::NOC)
    return dst.channel + 2;
  return dst.channel;
}
 
LogicalResult Pathfinder::addFixedConnection(SwitchboxOp switchboxOp) {
  int col = switchboxOp.colIndex();
  int row = switchboxOp.rowIndex();
  TileID coords = {col, row};
  auto &sb = graph[std::make_pair(coords, coords)];
  // Validate every connect against the original connectivity before reserving
  // any resource, so a broadcast (one source fanning out to several dests) does
  // not invalidate its own sibling connects mid-scan. A destination port may be
  // driven only once; a source port may legally recur across a broadcast.
  llvm::SmallVector<std::pair<int, int>, 8> reserved;
  llvm::SmallDenseSet<int, 8> claimedDsts;
  for (ConnectOp connectOp : switchboxOp.getOps<ConnectOp>()) {
    int srcIdx = sb.srcIndex(connectOp.sourcePort());
    int dstIdx = sb.dstIndex(connectOp.destPort());
    // Reject an illegal pair (absent from the switchbox model) or a second
    // driver on the same output port; a repeated source port is a broadcast.
    if (srcIdx < 0 || dstIdx < 0 || !sb.at(srcIdx, dstIdx).available ||
        !claimedDsts.insert(dstIdx).second) {
      return failure();
    }
    reserved.emplace_back(srcIdx, dstIdx);
  }
  // A pre-placed packet-switched output (an aie.masterset) also monopolizes its
  // destination port. That stream-switch output is already configured for
  // packet switching, so no circuit stream may drive it, and the router cannot
  // emit a second masterset on the same port for another packet flow. The
  // circuit pathfinder does not read packet ops, so without this reservation it
  // may route a flow onto an output the masterset owns and produce two ops
  // driving one destination.
  llvm::SmallVector<int, 8> reservedMasterDsts;
  for (MasterSetOp masterSetOp : switchboxOp.getOps<MasterSetOp>()) {
    int dstIdx = sb.dstIndex(masterSetOp.destPort());
    // Reject an output port absent from the switchbox model or already driven
    // by a circuit connect or another masterset.
    if (dstIdx < 0 || !claimedDsts.insert(dstIdx).second) {
      return failure();
    }
    reservedMasterDsts.push_back(dstIdx);
  }
  // A circuit-switched ConnectOp monopolizes both its source port (the stream
  // switch input) and its destination port (the output): no other stream may
  // inject on that input, and the output can carry only this one stream.
  // Reserving the whole column also reserves the outgoing wire, since that wire
  // is reachable only by driving this output port.
  for (auto [srcIdx, dstIdx] : reserved) {
    for (size_t j = 0; j < sb.dstPorts.size(); j++)
      sb.at(srcIdx, j).available = false;
    for (size_t i = 0; i < sb.srcPorts.size(); i++)
      sb.at(i, dstIdx).available = false;
  }
  // A masterset fixes only its output port. Its inputs arrive through arbiters
  // that packet flows share, so the source rows stay free.
  for (int dstIdx : reservedMasterDsts)
    for (size_t i = 0; i < sb.srcPorts.size(); i++)
      sb.at(i, dstIdx).available = false;
  // A fixed op on a shim's South channel claims the port the shim mux carries
  // on it (see shimMuxChannelFrom).
  if (switchboxOp.getTileOp().isShimNOCorPLTile()) {
    auto isMuxed = [](Port p) {
      return llvm::is_contained(
          {WireBundle::DMA, WireBundle::NOC, WireBundle::PLIO}, p.bundle);
    };
    llvm::SmallDenseSet<int, 8> southDsts, southSrcs;
    for (int dstIdx : claimedDsts)
      if (sb.dstPorts[dstIdx].bundle == WireBundle::South)
        southDsts.insert(sb.dstPorts[dstIdx].channel);
    for (auto [srcIdx, dstIdx] : reserved)
      if (sb.srcPorts[srcIdx].bundle == WireBundle::South)
        southSrcs.insert(sb.srcPorts[srcIdx].channel);
    for (size_t j = 0; j < sb.dstPorts.size(); j++)
      if (isMuxed(sb.dstPorts[j]) &&
          southDsts.count(shimMuxChannelTo(sb.dstPorts[j])))
        for (size_t i = 0; i < sb.srcPorts.size(); i++)
          sb.at(i, j).available = false;
    for (size_t i = 0; i < sb.srcPorts.size(); i++)
      if (isMuxed(sb.srcPorts[i]) &&
          southSrcs.count(shimMuxChannelFrom(sb.srcPorts[i])))
        for (size_t j = 0; j < sb.dstPorts.size(); j++)
          sb.at(i, j).available = false;
  }
  for (PacketRulesOp rulesOp : switchboxOp.getOps<PacketRulesOp>()) {
    int srcIdx = sb.srcIndex(rulesOp.sourcePort());
    if (srcIdx < 0)
      return failure();
    sb.packetOnlySrc.set(srcIdx);
  }
  return success();
}
 
void Pathfinder::excludeTile(TileID coords) {
  auto it = graph.find({coords, coords});
  if (it == graph.end())
    return;
  SwitchboxConnect &sb = it->second;
  for (size_t i = 0; i < sb.srcPorts.size(); i++)
    for (size_t j = 0; j < sb.dstPorts.size(); j++)
      sb.at(i, j).available = false;
}
 
void Pathfinder::avoidPort(TileID coords, Port port) {
  auto it = graph.find({coords, coords});
  if (it == graph.end())
    return;
  SwitchboxConnect &sb = it->second;
  int j = sb.dstIndex(port);
  if (j < 0)
    return;
  for (size_t i = 0; i < sb.srcPorts.size(); i++)
    sb.at(i, j).avoidance = avoidedPortDemand;
}
 
static constexpr double INF = std::numeric_limits<double>::max();
 
namespace {
enum Color : int8_t { WHITE = 0, GRAY = 1, BLACK = 2 };
} // namespace
 
int Pathfinder::getOrAddNodeId(const PathEndPoint &pep) {
  auto it = nodeIds.find(pep);
  if (it != nodeIds.end())
    return it->second;
  int id = static_cast<int>(nodes.size());
  nodeIds[pep] = id;
  nodes.push_back(pep);
  return id;
}
 
// Build the dense integer node numbering and per-node adjacency once. The graph
// topology is fixed across congestion iterations (only the demand weights
// change), so this is computed a single time and the edges carry live pointers
// into `graph` for demand lookups. A node's crossbar edges come first, then its
// wire edges, each sorted by the PathEndPoint they reach, so Dijkstra breaks
// ties the same way every run.
void Pathfinder::buildRoutingGraph() {
  // Seed the dense node set with all flow endpoints (the only nodes Dijkstra is
  // ever started from or traced back to). Remaining nodes are discovered as
  // edge destinations below.
  for (auto &f : flows) {
    getOrAddNodeId(f.src);
    for (auto &d : f.dsts)
      getOrAddNodeId(d);
  }
 
  // Process nodes by growing index; getOrAddNodeId() may append new nodes as
  // edge destinations are discovered, so re-read nodes.size() each iteration.
  for (size_t id = 0; id < nodes.size(); id++) {
    PathEndPoint src = nodes[id];
    // The ports the crossbar connects this one to, and the neighbours' ports
    // its wire reaches.
    std::vector<PathEndPoint> dests;
    auto intraIt = graph.find({src.coords, src.coords});
    if (intraIt != graph.end()) {
      auto &sb = intraIt->second;
      for (auto [i, pIn] : llvm::enumerate(sb.srcPorts))
        for (auto [j, pOut] : llvm::enumerate(sb.dstPorts))
          if (pIn == src.port && sb.at(i, j).available)
            dests.emplace_back(src.coords, pOut);
    }
    std::pair<TileID, Port> neighbors[] = {
        {{src.coords.col, src.coords.row - 1},
         {WireBundle::North, src.port.channel}},
        {{src.coords.col - 1, src.coords.row},
         {WireBundle::East, src.port.channel}},
        {{src.coords.col, src.coords.row + 1},
         {WireBundle::South, src.port.channel}},
        {{src.coords.col + 1, src.coords.row},
         {WireBundle::West, src.port.channel}}};
    for (const auto &[neighborCoords, neighborPort] : neighbors) {
      auto nIt = graph.find({src.coords, neighborCoords});
      if (nIt != graph.end() &&
          src.port.bundle == getConnectingBundle(neighborPort.bundle) &&
          llvm::is_contained(nIt->second.dstPorts, neighborPort))
        dests.emplace_back(neighborCoords, neighborPort);
    }
    llvm::sort(dests);
 
    std::vector<Edge> edges;
    edges.reserve(dests.size());
    for (auto &dest : dests) {
      auto &sb = graph.at({src.coords, dest.coords});
      int i = sb.srcIndex(src.port);
      int j = sb.dstIndex(dest.port);
      assert(i >= 0 && j >= 0);
      int destId = getOrAddNodeId(dest);
      edges.push_back(Edge{destId, &sb, i, j});
    }
    auto wires =
        std::stable_partition(edges.begin(), edges.end(), [](const Edge &e) {
          return e.sb->srcCoords == e.sb->dstCoords;
        });
    if (wireEdgesBegin.size() < nodes.size())
      wireEdgesBegin.resize(nodes.size());
    wireEdgesBegin[id] = wires - edges.begin();
    // getOrAddNodeId above may have reallocated `adjacency` via index growth in
    // later iterations, but we only assign this node's edges now.
    if (adjacency.size() < nodes.size())
      adjacency.resize(nodes.size());
    adjacency[id] = std::move(edges);
  }
  size_t n = nodes.size();
  if (adjacency.size() < n)
    adjacency.resize(n);
  wireEdgesBegin.resize(n);
 
  // Size the reusable Dijkstra scratch buffers. These are indexed by state id,
  // i.e. two entries per node -- one per side of the port.
  distance.assign(2 * n, INF);
  indexInHeap.assign(2 * n, 0);
  colors.assign(2 * n, WHITE);
  preds.assign(2 * n, -1);
  predEdge.assign(2 * n, Edge{-1, nullptr, 0, 0});
  graphBuilt = true;
}
 
double Pathfinder::edgeWeight(const Edge &e, std::optional<int> packetId,
                              const llvm::BitVector *avoid,
                              const llvm::BitVector *avoidBranch) const {
  const SwitchboxConnect::Cell &cell = e.sb->at(e.i, e.j);
  double w = cell.demand;
  // Sharing it would take a second stream's capacity, which the demand
  // only shows once the group is routed.
  if (packetId && cell.packetFlowCount > 0 && cell.packetIds.count(*packetId))
    w *= demandCoeff;
  if (e.sb->srcCoords == e.sb->dstCoords)
    for (const llvm::BitVector *flows : {avoid, avoidBranch})
      if (flows && llvm::any_of(e.sb->unitFlows(e.j),
                                [&](int f) { return flows->test(f); }))
        w += conflictSharePenalty;
  return w;
}
 
// Dijkstra over the dense graph from the states in `seeds`, searching states
// (node, PortSide) rather than bare nodes. Fills the `preds` and `predEdge`
// scratch buffers, both indexed by state id.
void Pathfinder::dijkstraShortestPaths(
    ArrayRef<int> seeds, ArrayRef<double> seedCosts,
    std::optional<int> packetId, const llvm::BitVector *avoid,
    const llvm::DenseMap<int, llvm::BitVector> *branchAvoid,
    const llvm::DenseSet<int> *stops, ArrayRef<int> targets,
    llvm::function_ref<bool(int, int)> mayCross) {
  llvm::fill(distance, INF);
  llvm::fill(colors, static_cast<int8_t>(WHITE));
  llvm::fill(preds, -1);
  llvm::fill(indexInHeap, uint64_t{0});
 
  using MutableQueue = d_ary_heap_indirect<
      /*Value=*/int, /*Arity=*/4,
      /*IndexInHeapPropertyMap=*/std::vector<uint64_t> &,
      /*DistanceMap=*/std::vector<double> &,
      /*Compare=*/std::less<>>;
  MutableQueue Q(distance, indexInHeap);
 
  for (auto [seed, cost] : llvm::zip_equal(seeds, seedCosts)) {
    distance[seed] = cost;
    colors[seed] = GRAY;
    Q.push(seed);
  }
  // A settled state's distance and predecessor never change again.
  SmallVector<int, 8> unsettled(targets);
  while (!Q.empty()) {
    int s = Q.top();
    Q.pop();
    if (llvm::is_contained(unsettled, s)) {
      llvm::erase(unsettled, s);
      if (unsettled.empty())
        break;
    }
    if (stops && stops->count(s)) {
      colors[s] = BLACK;
      continue;
    }
    // In takes crossbar edges and lands on the Out side of the port it picks;
    // Out takes the wire to the neighbour and lands on that tile's In side. Any
    // other pairing would either turn the stream around inside a switchbox or
    // ride a wire the crossbar was never set to drive.
    const bool sIsOut = (s & 1) == Out;
    const llvm::BitVector *avoidBranch = nullptr;
    if (branchAvoid)
      if (auto it = branchAvoid->find(s); it != branchAvoid->end())
        avoidBranch = &it->second;
    ArrayRef<Edge> out = adjacency[stateNode(s)];
    size_t wires = wireEdgesBegin[stateNode(s)];
    const bool isIntra = !sIsOut;
    for (const Edge &e :
         sIsOut ? out.drop_front(wires) : out.take_front(wires)) {
      if ((isIntra && !packetId && e.sb->packetOnlySrc[e.i]) ||
          (isIntra && packetId && e.sb->circuitOnlyDst[e.j]))
        continue;
      int dst = stateId(e.dst, isIntra ? Out : In);
      if (colors[dst] == BLACK || (isIntra && mayCross && !mayCross(s, dst)))
        continue;
      double w = edgeWeight(e, packetId, avoid, avoidBranch);
      if (distance[s] + w >= distance[dst])
        continue;
      distance[dst] = distance[s] + w;
      preds[dst] = s;
      predEdge[dst] = e;
      if (colors[dst] == WHITE) {
        colors[dst] = GRAY;
        Q.push(dst);
      } else {
        Q.update(dst);
      }
    }
    colors[s] = BLACK;
  }
}
 
// What findPaths keeps from one flow and iteration to the next.
struct Pathfinder::RouteState {
  explicit RouteState(const Pathfinder &pf);
 
  int groupOf(const Flow &f) const;
  SmallVector<int, 4> idsTo(int flow, int dstState) const;
  void relateParts();
  int splitPart(int flow, const std::set<int> &ids);
  bool isPinned(const Flow &f) const;
 
  const Pathfinder &pf;
  Routing routing;
  // Stamp-based "processed" set (avoids O(n) clears per flow).
  std::vector<uint32_t> processedStamp;
  uint32_t curStamp = 0;
  // The flows to route: one per source, less the packets split off into parts
  // of their own (see below), which route as flows from the same source.
  std::vector<Flow> parts;
  std::map<PathEndPoint, SmallVector<int, 2>> partsOf;
  // group flows based on packetGroupId; pinned trees go in first, so the
  // flows routed around them see them.
  llvm::MapVector<int, SmallVector<int, 8>> groupedFlows;
  // Packet flows that conflict, by the ids each carries or by
  // RoutingFaults::apart.
  std::vector<llvm::BitVector> conflicting;
  std::set<std::pair<PathEndPoint, PathEndPoint>> apartSources;
  std::set<std::pair<PathEndPoint, PathEndPoint>> togetherSources;
  // The packet ids each flow carries, in all and to each destination.
  std::vector<std::set<int>> flowIds;
  std::vector<SmallVector<int, 4>> sameId;
  // Each packet flow's tree as routed so far this iteration: the state each
  // hop reaches, from which state and by which edge; and its destinations.
  std::vector<llvm::DenseMap<int, std::pair<int, Edge>>> treeOf;
  // Each circuit flow's hops this iteration, which treeOf keeps for packet
  // flows only.
  std::vector<SmallVector<Edge, 8>> circuitHops;
  std::vector<SmallVector<int, 4>> treeDsts;
  // The hops each flow takes only by joining another flow's tree, by the flow
  // it joined. A join the routing check faults is not made again.
  std::vector<SmallVector<std::pair<int, Edge>, 8>> joinedHops;
  std::set<std::pair<int, int>> noJoin;
  // Where the routing check split a flow's tree: the tile it branches at, the
  // ids to branch apart there, and the state of the destination that reaches
  // the tile apart, if one does.
  struct IdSplit {
    TileID at;
    int a, b;
    std::optional<int> apart;
    bool operator<(const IdSplit &other) const {
      return std::tie(at, a, b, apart) <
             std::tie(other.at, other.a, other.b, other.apart);
    }
  };
  std::vector<std::set<IdSplit>> splitsOf;
  // A split one tree cannot make, since a destination takes both ids, moves
  // the second id to a part of its own. Parts of a source split apart at a
  // tile leave it by different master ports: the part routed later keeps off
  // those the other's tree takes there.
  std::vector<std::set<std::pair<TileID, int>>> partSplits;
  // Flows that found no one switchbox to meet a tree routed before them at,
  // by that tree's flow; each such pair routes the other way round once.
  std::set<std::pair<int, int>> unmet, reordered;
  // A tree branching for two destinations at its source switchbox may leave
  // no slave port there to meet it by. Each of an unmet pair then reaches the
  // destinations it shares with the other by one master port out of it.
  std::set<std::pair<int, int>> trunked;
  // Sources whose trunk took their tree back through a switchbox it holds an
  // arbiter in (RoutingFaults::untrunk), which branch freely from then on.
  std::set<PathEndPoint> untrunked;
  // The flows that met a tree this iteration, by its flow, and how often the
  // routing check faulted a meeting of each pair.
  std::set<std::pair<int, int>> met;
  std::map<std::pair<int, int>, int> meetFaults;
  // Joined pairs the routing check faulted along with hops neither joined,
  // which were left to the penalties on those hops once.
  std::set<std::pair<int, int>> spared;
  // A control-packet reload keeps the master sets the prioritized flows' trees
  // leave each switchbox by, so another flow leaving by one of those master
  // ports leaves by all of one such set and no others.
  llvm::DenseSet<int> priorityMasters;
  std::vector<SmallVector<int, 4>> prioritySets;
  bool mayLeave(ArrayRef<int> masters, int next) const;
  bool reorder(int later, int earlier, bool again = false);
};
 
Pathfinder::RouteState::RouteState(const Pathfinder &pf)
    : pf(pf), processedStamp(2 * pf.nodes.size(), 0), parts(pf.flows),
      conflicting(parts.size(), llvm::BitVector(parts.size())),
      flowIds(parts.size()), treeOf(parts.size()), circuitHops(parts.size()),
      treeDsts(parts.size()), joinedHops(parts.size()), splitsOf(parts.size()),
      partSplits(parts.size()) {
  for (auto [k, f] : llvm::enumerate(parts))
    partsOf[f.src].push_back(k);
  for (auto [k, f] : llvm::enumerate(parts))
    groupedFlows[groupOf(f)].push_back(k);
  for (const auto &[ends, ids] : pf.packetIdsTo)
    flowIds[partsOf.at(ends.first).front()].insert(ids.begin(), ids.end());
  relateParts();
  // A pinned source's other packets follow the pinned tree where they go
  // everywhere it goes, so they leave each switchbox by its master sets, and
  // otherwise route as a part of their own.
  for (size_t k = 0, n = parts.size(); k < n; k++) {
    if (!isPinned(parts[k]))
      continue;
    const PathEndPoint &src = parts[k].src;
    const std::set<int> &prioritized = pf.priorityIds.at(src);
    std::set<PathEndPoint> treeDsts;
    std::map<int, std::set<PathEndPoint>> dstsOf;
    for (const auto &[ends, ids] : pf.packetIdsTo)
      if (ends.first == src)
        for (int id : ids)
          (prioritized.count(id) ? treeDsts : dstsOf[id]).insert(ends.second);
    std::set<int> others;
    for (const auto &[id, dsts] : dstsOf)
      if (!prioritized.count(id) && dsts != treeDsts)
        others.insert(id);
    if (!others.empty())
      splitPart(k, others);
  }
  for (const auto &[src, tree] : pf.constraints.pinned) {
    std::map<PathEndPoint, SmallVector<int, 4>> sets;
    for (const TreeHop &h : tree) {
      auto to = pf.nodeIds.find(h.to);
      if (h.from.coords == h.to.coords && to != pf.nodeIds.end())
        sets[h.from].push_back(stateId(to->second, Out));
    }
    for (auto &[_, set] : sets) {
      llvm::sort(set);
      priorityMasters.insert(set.begin(), set.end());
      prioritySets.push_back(std::move(set));
    }
  }
}
 
// Route `later` before `earlier` from the next iteration on, unless the two
// were reordered before and this is not `again`.
bool Pathfinder::RouteState::reorder(int later, int earlier, bool again) {
  if (!again && (reordered.count({earlier, later}) ||
                 !reordered.insert({later, earlier}).second))
    return false;
  SmallVector<int, 8> &group = groupedFlows[groupOf(parts[later])];
  if (!llvm::is_contained(group, earlier))
    return false;
  group.erase(llvm::find(group, later));
  group.insert(llvm::find(group, earlier), later);
  return true;
}
 
// Whether a tree whose packets leave a switchbox by `masters` from one slave
// port may leave it by `next` too; see priorityMasters.
bool Pathfinder::RouteState::mayLeave(ArrayRef<int> masters, int next) const {
  if (!priorityMasters.count(next) &&
      llvm::none_of(masters, [&](int m) { return priorityMasters.count(m); }))
    return true;
  return llvm::any_of(prioritySets, [&](const SmallVector<int, 4> &set) {
    return llvm::is_contained(set, next) && llvm::all_of(masters, [&](int m) {
             return llvm::is_contained(set, m);
           });
  });
}
 
bool Pathfinder::RouteState::isPinned(const Flow &f) const {
  return f.isPriorityFlow && pf.constraints.pinned.count(f.src);
}
 
int Pathfinder::RouteState::groupOf(const Flow &f) const {
  return isPinned(f) ? std::numeric_limits<int>::min() : f.packetGroupId;
}
 
SmallVector<int, 4> Pathfinder::RouteState::idsTo(int flow,
                                                  int dstState) const {
  SmallVector<int, 4> ids;
  auto it =
      pf.packetIdsTo.find({parts[flow].src, pf.nodes[stateNode(dstState)]});
  if (it != pf.packetIdsTo.end())
    for (int id : it->second)
      if (flowIds[flow].count(id))
        ids.push_back(id);
  return ids;
}
 
void Pathfinder::RouteState::relateParts() {
  sameId.assign(parts.size(), {});
  conflicting.assign(parts.size(), llvm::BitVector(parts.size()));
  for (size_t a = 0; a < parts.size(); a++)
    for (size_t b = 0; b < parts.size(); b++) {
      // Trees with an id in common join where they meet, so are never apart.
      bool same = llvm::any_of(flowIds[a],
                               [&](int id) { return flowIds[b].count(id); });
      if (a != b && same)
        sameId[a].push_back(b);
      if (a < b && parts[a].packetId && parts[b].packetId &&
          ((!same &&
            apartSources.count(std::minmax(parts[a].src, parts[b].src))) ||
           (pf.constraints.conflict &&
            pf.constraints.conflict(parts[a].src, flowIds[a], parts[b].src,
                                    flowIds[b])))) {
        conflicting[a].set(b);
        conflicting[b].set(a);
      }
    }
}
 
int Pathfinder::RouteState::splitPart(int flow, const std::set<int> &ids) {
  int part = parts.size();
  Flow f = parts[flow];
  LLVM_DEBUG({
    llvm::dbgs() << "\t\tRouting ids";
    for (int id : ids)
      llvm::dbgs() << ' ' << id;
    llvm::dbgs() << " from " << describeTilePort(f.src.coords, f.src.port)
                 << " apart\n";
  });
  for (int id : ids)
    flowIds[flow].erase(id);
  flowIds.push_back(ids);
  auto carries = [&](int k, const PathEndPoint &p) {
    auto it = pf.packetIdsTo.find({f.src, p});
    return it != pf.packetIdsTo.end() &&
           llvm::any_of(it->second, [&](int i) { return flowIds[k].count(i); });
  };
  llvm::erase_if(f.dsts,
                 [&](const PathEndPoint &p) { return !carries(part, p); });
  llvm::erase_if(parts[flow].dsts,
                 [&](const PathEndPoint &p) { return !carries(flow, p); });
  f.packetId = *ids.begin();
  std::optional<int> &flowId = parts[flow].packetId;
  if (flowId && ids.count(*flowId))
    flowId = *flowIds[flow].begin();
  auto prioritized = [&](const std::set<int> &carried) {
    auto prio = pf.priorityIds.find(f.src);
    return prio != pf.priorityIds.end() && llvm::any_of(carried, [&](int id) {
             return prio->second.count(id);
           });
  };
  f.isPriorityFlow = prioritized(ids);
  parts[flow].isPriorityFlow = prioritized(flowIds[flow]);
  parts.push_back(f);
  partsOf[f.src].push_back(part);
  groupedFlows[groupOf(f)].push_back(part);
  relateParts();
  treeOf.emplace_back();
  circuitHops.emplace_back();
  treeDsts.emplace_back();
  joinedHops.emplace_back();
  for (auto [a, b] : std::set<std::pair<int, int>>(noJoin))
    if (a == flow || b == flow)
      noJoin.insert({a == flow ? part : a, b == flow ? part : b});
  splitsOf.push_back(splitsOf[flow]);
  partSplits.push_back(partSplits[flow]);
  for (auto [at, other] : partSplits[flow])
    partSplits[other].insert({at, part});
  for (auto [at, a, b, apart] : splitsOf[flow])
    if (ids.count(a) != ids.count(b) &&
        flowIds[flow].count(ids.count(a) ? b : a)) {
      partSplits[flow].insert({at, part});
      partSplits[part].insert({at, flow});
    }
  return part;
}
 
// A link with a channel no flow takes and a free master port driving it
// was overused only by the way the flows went; its flows could spread.
bool Pathfinder::hasRoom(const SwitchboxConnect &sb) const {
  if (sb.srcCoords == sb.dstCoords)
    return true;
  auto xbar = graph.find({sb.srcCoords, sb.srcCoords});
  for (size_t i = 0; i < sb.srcPorts.size(); i++)
    for (size_t j = 0; j < sb.dstPorts.size(); j++) {
      const SwitchboxConnect::Cell &c = sb.at(i, j);
      if (!c.available || c.usedCapacity > 0)
        continue;
      if (xbar == graph.end())
        return true;
      const SwitchboxConnect &x = xbar->second;
      int k = x.dstIndex(sb.srcPorts[i]);
      if (k < 0)
        return true;
      for (size_t row = 0; row < x.srcPorts.size(); row++)
        if (x.at(row, k).available)
          return true;
    }
  return false;
}
 
llvm::Error Pathfinder::explainNoRouting(const RouteState &st) const {
  // A prioritized flow keeps the route it takes alone, so the others
  // may have had to fit around it.
  auto overused = [](const SwitchboxConnect &sb) {
    return sb.srcCoords != sb.dstCoords &&
           llvm::any_of(sb.cells, [](const SwitchboxConnect::Cell &c) {
             return c.usedCapacity > maxCircuitStreamCapacity;
           });
  };
  auto link = [](const SwitchboxConnect &sb) -> std::string {
    return llvm::formatv("from tile ({0}, {1}) to ({2}, {3})", sb.srcCoords.col,
                         sb.srcCoords.row, sb.dstCoords.col, sb.dstCoords.row);
  };
  const Flow *prioritized = nullptr;
  llvm::SetVector<const SwitchboxConnect *> held;
  for (auto [k, f] : llvm::enumerate(st.parts)) {
    if (!st.isPinned(f))
      continue;
    prioritized = prioritized ? prioritized : &f;
    for (const auto &[_, hop] : st.treeOf[k]) {
      if (overused(*hop.second.sb)) {
        return llvm::make_error<PinnedRoutingFailure>(
            describePrioritized(describeTilePort(f.src.coords, f.src.port)) +
            ", and it holds a channel " + link(*hop.second.sb) +
            " the other flows need.");
      }
      if (hop.second.sb->srcCoords != hop.second.sb->dstCoords)
        held.insert(hop.second.sb);
    }
  }
  if (prioritized && llvm::any_of(graph, [&](const auto &entry) {
        return overused(entry.second);
      })) {
    return llvm::make_error<PinnedRoutingFailure>(
        describePrioritized(
            describeTilePort(prioritized->src.coords, prioritized->src.port)) +
        ", and the router found no routing for the other flows around the "
        "channels it holds " +
        joinNames(llvm::to_vector(
            llvm::map_range(llvm::make_pointee_range(held), link))) +
        ".");
  }
  // The routing check says more than the overuse it led to.
  if (!checkReason.empty())
    return llvm::make_error<RoutingFailure>(checkReason);
  // Name the channel the last iteration overused that was overused in the
  // most iterations, on a link with no room if there is one, and the flows
  // the last one routed through it.
  const SwitchboxConnect *worst = nullptr;
  int worstI = 0, worstJ = 0;
  std::pair<bool, int> worstRank{false, 0};
  for (const auto &[_, sb] : graph) {
    std::optional<bool> roomless;
    for (size_t i = 0; i < sb.srcPorts.size(); i++)
      for (size_t j = 0; j < sb.dstPorts.size(); j++) {
        if (sb.at(i, j).usedCapacity <= maxCircuitStreamCapacity)
          continue;
        if (!roomless)
          roomless = !hasRoom(sb);
        std::pair<bool, int> rank{*roomless, sb.at(i, j).overCapacity};
        if (rank > worstRank) {
          worst = &sb;
          worstI = i;
          worstJ = j;
          worstRank = rank;
        }
      }
  }
  if (!worst)
    return llvm::make_error<RoutingFailure>("");
  bool crossbar = worst->srcCoords == worst->dstCoords;
  std::vector<std::string> users;
  for (const auto &[src, settings] : st.routing.settings) {
    auto it = settings.find(worst->srcCoords);
    if (it == settings.end())
      continue;
    const SwitchSetting &s = it->second;
    bool uses = false;
    for (size_t k = 0; k < s.dsts.size() && !uses; k++)
      uses = crossbar
                 ? k < s.srcs.size() && s.srcs[k] == worst->srcPorts[worstI] &&
                       s.dsts[k] == worst->dstPorts[worstJ]
                 : llvm::is_contained(worst->srcPorts, s.dsts[k]);
    if (uses)
      users.push_back(describeTilePort(src.coords, src.port));
  }
  std::string where =
      crossbar ? llvm::formatv("the connection from {0} to {1} at tile ({2}, "
                               "{3})",
                               describePort(worst->srcPorts[worstI]),
                               describePort(worst->dstPorts[worstJ]),
                               worst->srcCoords.col, worst->srcCoords.row)
                     .str()
               : "the links " + link(*worst);
  if (users.empty())
    return llvm::make_error<RoutingFailure>(
        "the router found no routing that fits " + where + ".");
  return llvm::make_error<RoutingFailure>(
      "the flows from " + joinNames(users) + " need " + where +
      ", and the router found no routing that fits them.");
}
 
llvm::Error Pathfinder::cutOverflow() const {
  // Each circuit tree crossing a boundary needs a channel of its own, and the
  // packet flows one more, or one each for streams no two of which may share
  // an arbiter, since a channel's master port has one. Channels fixed
  // connections hold are not the router's to use, so this rejects only what
  // it could not route anyway.
  auto onDevice = [&](TileID t) { return t.col < columns && t.row < rows; };
  std::map<std::tuple<bool, int, bool>, size_t> channels;
  for (const auto &[ends, sb] : graph) {
    const auto &[a, b] = ends;
    auto xbar = graph.find({a, a});
    if (a == b || !onDevice(a) || !onDevice(b) || xbar == graph.end())
      continue;
    bool rows = a.col == b.col;
    int below = rows ? std::min(a.row, b.row) : std::min(a.col, b.col);
    bool up = rows ? b.row > a.row : b.col > a.col;
    const SwitchboxConnect &x = xbar->second;
    // A boundary with no available channel at all (every one is a fixed
    // connection's) still needs an entry, so flows that must cross it are
    // not skipped as if the boundary did not exist.
    channels[{rows, below, up}] += 0;
    for (Port port : sb.srcPorts) {
      int k = x.dstIndex(port);
      if (k >= 0 &&
          llvm::any_of(llvm::seq<size_t>(0, x.srcPorts.size()),
                       [&](size_t i) { return x.at(i, k).available; }))
        channels[{rows, below, up}]++;
    }
  }
  for (const auto &[cut, available] : channels) {
    bool rows = std::get<0>(cut), up = std::get<2>(cut);
    int below = std::get<1>(cut);
    auto low = [&](TileID t) { return (rows ? t.row : t.col) <= below; };
    std::vector<std::string> circuits;
    bool packets = false;
    for (const Flow &f : flows) {
      if (low(f.src.coords) != up ||
          llvm::none_of(f.dsts, [&](const PathEndPoint &d) {
            return low(d.coords) != up;
          }))
        continue;
      if (f.packetId)
        packets = true;
      else
        circuits.push_back(describeTilePort(f.src.coords, f.src.port));
    }
    PacketsApart apart;
    if (packets && constraints.apartAcross && available > circuits.size())
      apart = constraints.apartAcross(low, up, available - circuits.size());
    size_t needed =
        circuits.size() + std::max<size_t>(packets, apart.flows.size());
    LLVM_DEBUG(llvm::dbgs() << "Cut " << (rows ? "row " : "column ") << below
                            << (up ? " up" : " down") << ": " << needed
                            << " of " << available << " channels\n");
    if (needed <= available)
      continue;
    int from = up ? below : below + 1, to = up ? below + 1 : below;
    auto channel = [](size_t n) { return n == 1 ? "channel" : "channels"; };
    std::string who =
        circuits.empty() ? "" : "the circuit flows from " + joinNames(circuits);
    if (apart.flows.size() > 1)
      who += (who.empty() ? "" : ", and ") + joinNames(apart.flows) +
             ", no two of which can share an arbiter,";
    else if (packets)
      who =
          circuits.empty() ? "the packet flows" : who + ", with packet flows,";
    std::string why =
        apart.flows.size() > 1 ? " For example, " + apart.why : "";
    return llvm::make_error<RoutingFailure>(llvm::formatv(
        "{0} cross from {1} {2} to {1} {3}, which takes {4} {5} across, and "
        "it has {6} {7}.{8}",
        who, rows ? "row" : "column", from, to, needed, channel(needed),
        available, channel(available), why));
  }
  return llvm::Error::success();
}
 
// One flow's tree, grown by routePart.
struct Pathfinder::TreeBuilder {
  TreeBuilder(Pathfinder &pf, RouteState &st, int flow);
 
  // A destination port is driven by its switchbox, so it is reached on
  // the Out side.
  int dstState(const PathEndPoint &p) const {
    return stateId(pf.nodeIds.at(p), Out);
  }
  bool isPending(int state) const;
  void reach(ArrayRef<int> dsts);
  bool joinable(int at, ArrayRef<int> dsts) const;
  void findJoins();
  void meet();
  void meet(int owner);
  void search(const llvm::DenseSet<int> &drop, ArrayRef<int> targets,
              const llvm::DenseSet<int> &off = {});
  bool trace(int state);
  llvm::DenseSet<int> splitOff(int dst) const;
  llvm::DenseSet<int> trunkOff(int dst) const;
  llvm::Error placePinned();
  llvm::Error grow();
  void reroute();
  void claim();
  bool join(int state, int predId, const Edge &e);
  void joinTrees();
  void record();
 
  Pathfinder &pf;
  RouteState &st;
  int flow;
  const Flow &part;
  const llvm::BitVector *avoid;
  // The route the flow takes alone, if it is pinned to it.
  const std::vector<TreeHop> *pinned = nullptr;
  SwitchSettings switchSettings;
  // The states the tree reaches, and how many hops from the source each is.
  SmallVector<int, 16> tree, treeHops;
  SmallVector<int, 16> seeds;
  SmallVector<double, 16> seedCosts;
  // The tree's hops, by the state each reaches, from which state and by
  // which edge, in the order they were traced. They take effect once the
  // tree is final.
  llvm::MapVector<int, std::pair<int, Edge>> planned;
  llvm::DenseMap<int, int> children;
  // A branch off a port the tree already crosses joins that port's unit
  // (see planArbiters), so it avoids the flows conflicting with any flow
  // on those arbiters too.
  llvm::DenseMap<int, llvm::BitVector> branchAvoid;
  SmallVector<PathEndPoint, 4> pending;
  bool toSelf = false;
  // The destination to reach first, if not the nearest.
  std::optional<PathEndPoint> first;
  // A switchbox routes on the id alone, so packets that reach a master
  // port another source's tree takes an id they share by go wherever
  // that id goes from there. The flow may join the tree there only if
  // it still has to reach each of those destinations, with just the ids
  // they share.
  llvm::DenseMap<int, SmallVector<int, 4>> joins;
  llvm::DenseMap<int, SmallVector<int, 2>> joinOwners;
  llvm::DenseSet<int> stops, unjoinable;
  // The destinations the flow still has to reach that each other source's
  // tree reaches with the ids they share, less the trees it may not join.
  llvm::MapVector<int, SmallVector<int, 4>> sharedDsts;
  llvm::DenseSet<int> disagree, foreign;
  // The destinations the flow reaches where it meets another tree.
  SmallVector<int, 4> met;
  // The master ports the source's other parts take at the tiles the flow
  // was split apart from them at.
  llvm::DenseSet<int> partOff;
  // The destinations the flow reaches by one master port out of its source
  // switchbox (see RouteState::trunked).
  llvm::DenseSet<int> trunkDsts;
  SmallVector<int, 4> reached;
  SmallVector<std::pair<int, const SmallVector<int, 4> *>, 2> joinedAt;
  SmallVector<std::pair<int, std::pair<int, Edge>>, 8> pinnedJoins;
  SmallVector<int, 4> pinnedJoinDsts;
};
 
Pathfinder::TreeBuilder::TreeBuilder(Pathfinder &pf, RouteState &st, int flow)
    : pf(pf), st(st), flow(flow), part(st.parts[flow]),
      avoid(part.packetId ? &st.conflicting[flow] : nullptr) {
  if (st.isPinned(part))
    pinned = &pf.constraints.pinned.at(part.src);
  // The flow source port feeds into its switchbox, so the tree starts
  // on its In side and the first edge taken is necessarily a crossbar
  // hop.
  int srcId = pf.nodeIds.at(part.src);
  tree.push_back(stateId(srcId, In));
  treeHops.push_back(0);
  st.processedStamp[tree.front()] = ++st.curStamp;
  for (const PathEndPoint &endPoint : part.dsts) {
    // Route to self: the port is both ends. Where its switchbox cannot
    // connect it to itself (Core to Core), the stream has to leave and
    // come back, which Dijkstra finds from the In side to the Out side.
    // A tree the flow joins may reach the port for it instead. A port in
    // priorityMasters is reached like any other destination, so mayLeave
    // still holds.
    int self = stateId(srcId, Out);
    if (endPoint == part.src && !st.priorityMasters.count(self) &&
        llvm::any_of(pf.adjacency[srcId],
                     [&](const Edge &e) { return e.dst == srcId; })) {
      toSelf = true;
      continue;
    }
    pending.push_back(endPoint);
  }
  findJoins();
  for (auto it = st.trunked.lower_bound({flow, 0});
       !st.untrunked.count(part.src) && it != st.trunked.end() &&
       it->first == flow;
       ++it) {
    SmallVector<int, 4> shared;
    for (const PathEndPoint &dst : st.parts[it->second].dsts)
      if (llvm::is_contained(part.dsts, dst))
        shared.push_back(dstState(dst));
    if (shared.size() > 1)
      trunkDsts.insert(shared.begin(), shared.end());
  }
  for (auto [at, other] : st.partSplits[flow])
    for (const auto &[state, _] : st.treeOf[other])
      if ((state & 1) == Out && pf.nodes[stateNode(state)].coords == at)
        partOff.insert(state);
}
 
bool Pathfinder::TreeBuilder::isPending(int state) const {
  return (toSelf && state == dstState(part.src)) ||
         llvm::any_of(pending, [&](const PathEndPoint &p) {
           return dstState(p) == state;
         });
}
 
void Pathfinder::TreeBuilder::reach(ArrayRef<int> dsts) {
  llvm::erase_if(pending, [&](const PathEndPoint &p) {
    return llvm::is_contained(dsts, dstState(p));
  });
  if (llvm::is_contained(dsts, dstState(part.src)))
    toSelf = false;
}
 
bool Pathfinder::TreeBuilder::joinable(int at, ArrayRef<int> dsts) const {
  return !unjoinable.count(at) &&
         llvm::all_of(dsts, [&](int dst) { return isPending(dst); });
}
 
void Pathfinder::TreeBuilder::findJoins() {
  auto shared = [&](ArrayRef<int> ids, int other) {
    std::set<int> common;
    for (int id : ids)
      if (st.flowIds[other].count(id))
        common.insert(id);
    return common;
  };
  for (int other : st.sameId[flow]) {
    // A tree reaching its own source port takes no hop for it.
    const Flow &o = st.parts[other];
    int self = dstState(o.src);
    if (!st.treeDsts[other].empty() && llvm::is_contained(o.dsts, o.src) &&
        isPending(self) && !shared(st.idsTo(other, self), flow).empty())
      sharedDsts[other].push_back(self);
    for (int dst : st.treeDsts[other]) {
      std::set<int> common = shared(st.idsTo(other, dst), flow);
      if (common.empty())
        continue;
      // Joining shares the other flow's arbiters below the join with the
      // packets it takes there. A prioritized flow's tree is pinned, so it
      // joins only trees pinned with it. A destination of the other flow alone
      // keeps the flow off the hops toward it, as no join there is joinable.
      bool agree =
          (!isPending(dst) || common == shared(st.idsTo(flow, dst), other)) &&
          !(pf.constraints.conflict &&
            pf.constraints.conflict(part.src, common, o.src,
                                    st.flowIds[other])) &&
          !st.noJoin.count({flow, other}) &&
          (!part.isPriorityFlow || st.parts[other].isPriorityFlow);
      if (!agree)
        disagree.insert(other);
      else if (isPending(dst))
        sharedDsts[other].push_back(dst);
      for (auto it = st.treeOf[other].find(dst); it != st.treeOf[other].end();
           it = st.treeOf[other].find(it->second.first)) {
        int up = it->second.first;
        if ((up & 1) != Out)
          continue;
        stops.insert(up);
        if (!agree)
          unjoinable.insert(up);
        if (!llvm::is_contained(joins[up], dst))
          joins[up].push_back(dst);
        if (!llvm::is_contained(joinOwners[up], other))
          joinOwners[up].push_back(other);
      }
    }
  }
  // A tree with other ids reaching two of the flow's destinations is met the
  // same way, the flow taking its hops below the meeting with its own ids.
  // Not for a destination a tree with one of its ids also reaches, which the
  // flow has to meet on the way there instead.
  if (!part.packetId || part.isPriorityFlow)
    return;
  llvm::DenseSet<int> sameIdDsts;
  for (int other : st.sameId[flow])
    for (const PathEndPoint &dst : st.parts[other].dsts)
      if (!shared(st.idsTo(other, dstState(dst)), flow).empty())
        sameIdDsts.insert(dstState(dst));
  for (auto [other, o] : llvm::enumerate(st.parts)) {
    int k = other;
    if (k == flow || o.src == part.src || !o.packetId || o.isPriorityFlow ||
        st.treeDsts[k].empty() || llvm::is_contained(st.sameId[flow], k) ||
        st.conflicting[flow].test(k) || st.noJoin.count({flow, k}))
      continue;
    SmallVector<int, 4> dsts;
    for (int dst : st.treeDsts[k])
      if (isPending(dst) && dst != dstState(part.src) &&
          !sameIdDsts.count(dst) && st.treeOf[k].count(dst))
        dsts.push_back(dst);
    if (dsts.size() > 1) {
      sharedDsts[k] = std::move(dsts);
      foreign.insert(k);
    }
  }
}
 
// Trees from two sources wait on each other wherever they meet (see HoldCycle),
// so two trees meeting at two switchboxes can each hold one arbiter and wait at
// the other. The flow meets each tree it shares destinations with at one
// switchbox, those it shares the most with first, on that tree's way from its
// source to where it branches for them, by a slave port that takes each master
// port the tree takes there toward them. Only a packet going to two of them can
// hold the arbiter where the trees meet for one and wait where they meet for
// the other, so two trees meet only when each sends some id to two shared
// destinations.
void Pathfinder::TreeBuilder::meet() {
  if (pf.meetApart)
    return;
  auto spans = [&](int k, ArrayRef<int> dsts) {
    return llvm::any_of(st.flowIds[k], [&](int id) {
      return llvm::count_if(dsts, [&](int dst) {
               return llvm::is_contained(st.idsTo(k, dst), id);
             }) > 1;
    });
  };
  auto mustMeet = [&](int other) {
    return spans(flow, sharedDsts[other]) && spans(other, sharedDsts[other]);
  };
  SmallVector<int, 4> owners;
  for (int other : llvm::make_first_range(sharedDsts))
    if (!disagree.count(other) && mustMeet(other))
      owners.push_back(other);
  llvm::stable_sort(owners, [&](int a, int b) {
    return sharedDsts[a].size() > sharedDsts[b].size();
  });
  for (int owner : owners) {
    llvm::erase_if(sharedDsts[owner], [&](int dst) { return !isPending(dst); });
    if (mustMeet(owner))
      meet(owner);
  }
}
 
void Pathfinder::TreeBuilder::meet(int owner) {
  st.unmet.insert({flow, owner});
  pf.treesMet = true;
  bool other = foreign.count(owner);
  const auto &t = st.treeOf[owner];
  const Flow &o = st.parts[owner];
  int root = stateId(pf.nodeIds.at(o.src), In);
  // The owner's states from its source down to each shared destination.
  SmallVector<SmallVector<int, 16>, 4> paths;
  for (int dst : sharedDsts[owner]) {
    SmallVector<int, 16> &path = paths.emplace_back(1, dst);
    for (auto it = t.find(dst); it != t.end(); it = t.find(it->second.first))
      path.push_back(it->second.first);
    if (path.size() == 1)
      path.push_back(root);
    if (path.back() != root)
      return;
    std::reverse(path.begin(), path.end());
  }
  size_t trunk = 0;
  while (llvm::all_of(paths, [&](const auto &path) {
    return trunk + 1 < path.size() && path[trunk] == paths[0][trunk];
  }))
    trunk++;
  struct Meeting {
    int in;
    SmallVector<std::pair<int, Edge>, 4> hops;
    double cost;
    size_t at;
  };
  SmallVector<Meeting, 8> meetings;
  SmallVector<int, 8> targets;
  // Below a meeting with other ids the flow takes the owner's hops itself.
  auto below = [&](size_t k) {
    llvm::MapVector<int, std::pair<int, Edge>> hops;
    for (const auto &path : paths)
      for (size_t l = k + 1; l + 1 < path.size(); l++)
        hops.insert({path[l + 1], t.find(path[l + 1])->second});
    return hops;
  };
  for (size_t k = 0; k < trunk; k++) {
    int at = paths[0][k];
    if ((at & 1) != In)
      continue;
    SetVector<int> next;
    for (const auto &path : paths)
      next.insert(path[k + 1]);
    if (!other && llvm::any_of(next, [&](int s) {
          return !isPending(s) && !(joins.count(s) && joinable(s, joins[s]));
        }))
      continue;
    auto taken = [&](int s) {
      return st.processedStamp[s] == st.curStamp || stops.count(s) ||
             partOff.count(s);
    };
    if (other && (llvm::any_of(next, taken) ||
                  llvm::any_of(below(k), [&](const auto &hop) {
                    const Edge &e = hop.second.second;
                    return taken(hop.first) ||
                           (e.sb->srcCoords == e.sb->dstCoords &&
                            e.sb->circuitOnlyDst[e.j]);
                  })))
      continue;
    SmallVector<int, 4> leaving;
    if (llvm::any_of(next, [&](int s) {
          bool ok = st.mayLeave(leaving, s);
          leaving.push_back(s);
          return !ok;
        }))
      continue;
    TileID tile = pf.nodes[stateNode(at)].coords;
    auto sb = pf.graph.find({tile, tile});
    if (sb == pf.graph.end())
      continue;
    for (Port port : sb->second.srcPorts) {
      auto node = pf.nodeIds.find({tile, port});
      if (node == pf.nodeIds.end())
        continue;
      int in = stateId(node->second, In);
      if (in == at || t.count(in))
        continue;
      Meeting m{in, {}, 0, k};
      for (int s : next)
        for (const Edge &e : pf.adjacency[node->second])
          if (e.dst == stateNode(s) && e.sb == &sb->second &&
              !(part.packetId && e.sb->circuitOnlyDst[e.j])) {
            m.hops.push_back({s, e});
            m.cost += pf.edgeWeight(e, part.packetId, avoid, nullptr);
            break;
          }
      if (m.hops.size() == next.size()) {
        meetings.push_back(std::move(m));
        targets.push_back(in);
      }
    }
  }
  if (meetings.empty())
    return;
  llvm::DenseSet<int> off;
  if (other)
    for (const auto &[s, _] : below(0))
      off.insert(s);
  search({}, targets, off);
  const Meeting *best = nullptr;
  for (const Meeting &m : meetings)
    if (pf.distance[m.in] < INF &&
        (!best ||
         pf.distance[m.in] + m.cost < pf.distance[best->in] + best->cost))
      best = &m;
  if (!best || !trace(best->in))
    return;
  st.unmet.erase({flow, owner});
  st.met.insert({flow, owner});
  int hops = treeHops[llvm::find(tree, best->in) - tree.begin()] + 1;
  auto add = [&](int s, int from, const Edge &e, int depth) {
    planned.insert({s, {from, e}});
    ++children[from];
    st.processedStamp[s] = st.curStamp;
    tree.push_back(s);
    treeHops.push_back(depth);
  };
  for (const auto &[s, e] : best->hops) {
    add(s, best->in, e, hops);
    if (other) {
      st.joinedHops[flow].push_back({owner, e});
      continue;
    }
    if (isPending(s)) {
      met.push_back(s);
      reach(s);
      continue;
    }
    const SmallVector<int, 4> &dsts = joins[s];
    reach(dsts);
    joinedAt.push_back({s, &dsts});
    ++children[s];
  }
  if (!other)
    return;
  for (const auto &[s, hop] : below(best->at)) {
    const auto &[from, e] = hop;
    add(s, from, e, treeHops[llvm::find(tree, from) - tree.begin()] + 1);
    st.joinedHops[flow].push_back({owner, e});
  }
  for (int dst : sharedDsts[owner]) {
    met.push_back(dst);
    reach(dst);
  }
}
 
// Dijkstra from the tree, less the states in `drop`, and not through
// those in `off`, until the states in `targets` are settled.
void Pathfinder::TreeBuilder::search(const llvm::DenseSet<int> &drop,
                                     ArrayRef<int> targets,
                                     const llvm::DenseSet<int> &off) {
  branchAvoid.clear();
  llvm::DenseMap<int, llvm::BitVector> onArbiter;
  if (avoid)
    for (const auto &[state, hop] : planned) {
      const auto &[from, e] = hop;
      if (e.sb->srcCoords != e.sb->dstCoords || drop.count(state))
        continue;
      llvm::BitVector &away =
          branchAvoid.try_emplace(from, st.conflicting.size()).first->second;
      llvm::BitVector &on =
          onArbiter.try_emplace(from, st.conflicting.size()).first->second;
      for (int other : e.sb->unitFlows(e.j)) {
        on.set(other);
        if (other != flow)
          away |= st.conflicting[other];
      }
    }
  // A flow sharing an arbiter with itself is no conflict, and flows
  // already on those arbiters share them whatever the branch does.
  for (auto &[from, away] : branchAvoid) {
    away.reset(onArbiter.find(from)->second);
    away.reset(flow);
  }
  seeds.clear();
  seedCosts.clear();
  for (auto [state, hops] : llvm::zip_equal(tree, treeHops))
    if (!drop.count(state) && !off.count(state)) {
      seeds.push_back(state);
      seedCosts.push_back(treeSeedFactor * hops);
    }
  llvm::DenseSet<int> blocked;
  if (!off.empty()) {
    blocked = stops;
    blocked.insert(off.begin(), off.end());
  }
  llvm::DenseMap<int, SmallVector<int, 4>> masters;
  bool limited = !st.priorityMasters.empty();
  if (limited)
    for (const auto &[state, hop] : planned)
      if ((hop.first & 1) == In && !drop.count(state))
        masters[hop.first].push_back(state);
  auto mayCross = [&](int from, int to) {
    auto it = masters.find(from);
    return st.mayLeave(it == masters.end() ? ArrayRef<int>{} : it->second, to);
  };
  pf.dijkstraShortestPaths(
      seeds, seedCosts, part.packetId, avoid, &branchAvoid,
      off.empty() ? &stops : &blocked, targets,
      limited ? llvm::function_ref<bool(int, int)>(mayCross) : nullptr);
}
 
// Trace the path Dijkstra found to `state` back to the tree.
bool Pathfinder::TreeBuilder::trace(int state) {
  size_t grown = tree.size();
  while (st.processedStamp[state] != st.curStamp) {
    // If Dijkstra never reached this node it has no predecessor; the
    // destination is unroutable under the current demand.
    int pred = pf.preds[state];
    if (pred < 0)
      return false;
    planned.insert({state, {pred, pf.predEdge[state]}});
    ++children[pred];
    st.processedStamp[state] = st.curStamp;
    tree.push_back(state);
    state = pred;
  }
  // The new hops were traced from the destination back to the tree.
  int hops = treeHops[llvm::find(tree, state) - tree.begin()] +
             static_cast<int>(tree.size() - grown);
  while (treeHops.size() < tree.size())
    treeHops.push_back(hops--);
  return true;
}
 
// The path to `dst` stays off the hops another destination's path
// takes below where the check split the two apart, and off the
// slave port it takes there too if one of them has to reach the tile
// on its own.
llvm::DenseSet<int> Pathfinder::TreeBuilder::splitOff(int dst) const {
  llvm::DenseSet<int> off = partOff;
  auto carries = [&](int d, int id) {
    return llvm::is_contained(st.idsTo(flow, d), id);
  };
  auto only = [&](int d, int id, int other) {
    return carries(d, id) && !carries(d, other);
  };
  for (auto [at, a, b, apart] : st.splitsOf[flow])
    for (int other : reached) {
      bool splits = !apart ? (only(dst, a, b) && only(other, b, a)) ||
                                 (only(dst, b, a) && only(other, a, b))
                           : (only(dst, a, b) && other == *apart) ||
                                 (dst == *apart && only(other, a, b));
      if (!splits)
        continue;
      SmallVector<int, 8> below;
      int s = other;
      auto entersAt = [&, tile = at](int state) {
        return (state & 1) == In && pf.nodes[stateNode(state)].coords == tile;
      };
      for (auto *hop = planned.find(s); !entersAt(s) && hop != planned.end();
           hop = planned.find(s)) {
        below.push_back(s);
        s = hop->second.first;
      }
      if (!entersAt(s))
        continue;
      off.insert(below.begin(), below.end());
      if (apart)
        off.insert(s);
    }
  return off;
}
 
// The path to a trunked destination leaves the tree below the master port
// the others it has reached leave the source switchbox by.
llvm::DenseSet<int> Pathfinder::TreeBuilder::trunkOff(int dst) const {
  llvm::DenseSet<int> off;
  if (!trunkDsts.count(dst))
    return off;
  int root = tree.front();
  auto exitOf = [&](int s) {
    for (const auto *it = planned.find(s);
         it != planned.end() && it->second.first != root; it = planned.find(s))
      s = it->second.first;
    return s;
  };
  const auto *other = llvm::find_if(reached, [&](int d) {
    return d != dst && trunkDsts.count(d) && planned.count(d);
  });
  if (other == reached.end())
    return off;
  int exit = exitOf(*other);
  for (int s : tree)
    if (s == root || exitOf(s) != exit)
      off.insert(s);
  return off;
}
 
// Lay the tree along the route the flow takes alone.
llvm::Error Pathfinder::TreeBuilder::placePinned() {
  for (const auto &[from, to, joined] : *pinned) {
    if (toSelf && from == to)
      continue;
    bool intra = from.coords == to.coords;
    auto fromId = pf.nodeIds.find(from), toId = pf.nodeIds.find(to);
    const Edge *e = nullptr;
    if (fromId != pf.nodeIds.end() && toId != pf.nodeIds.end())
      for (const Edge &out : pf.adjacency[fromId->second])
        if (out.dst == toId->second &&
            (out.sb->srcCoords == out.sb->dstCoords) == intra)
          e = &out;
    if (!e)
      return llvm::make_error<RoutingFailure>(
          "the route packet flows from " +
              describeTilePort(part.src.coords, part.src.port) +
              " take alone does not fit this design: it goes from " +
              describeTilePort(from.coords, from.port) + " to " +
              describeTilePort(to.coords, to.port) +
              ", which the design's own switchboxes leave no connection for.",
          RoutingFaults{}, pf.flowLoc(part.src, nullptr));
    std::pair<int, std::pair<int, Edge>> hop{
        stateId(toId->second, intra ? Out : In),
        {stateId(fromId->second, intra ? In : Out), *e}};
    if (joined)
      pinnedJoins.push_back(hop);
    else
      planned.insert(hop);
  }
  int self = dstState(part.src);
  if (toSelf && llvm::is_contained(llvm::make_first_range(pinnedJoins), self)) {
    toSelf = false;
    pinnedJoinDsts.push_back(self);
  }
  for (const PathEndPoint &p : pending)
    (planned.count(dstState(p)) ? reached : pinnedJoinDsts)
        .push_back(dstState(p));
  pending.clear();
  return llvm::Error::success();
}
 
// Grow the tree one destination at a time: Dijkstra, given the current
// demand, from everything the tree reaches so far to the next destination,
// whose path is then traced back to the tree. Growing from the tree rather
// than the source lets destinations share hops; see treeSeedFactor for what
// a branch off the tree costs.
llvm::Error Pathfinder::TreeBuilder::grow() {
  // A path to another tree can leave the destination to reach first no way
  // to it, so the tree meets the others once it reaches it.
  bool metTrees = !first || !llvm::is_contained(pending, *first);
  if (metTrees)
    meet();
  while (!pending.empty()) {
    SmallVector<int, 8> targets;
    for (const PathEndPoint &p : pending)
      targets.push_back(dstState(p));
    for (const auto &[at, dsts] : joins)
      if (joinable(at, dsts))
        targets.push_back(at);
    search({}, targets);
    // The nearest destination joins the tree next, or the nearest join
    // brings every destination below it.
    auto *nearest =
        first && llvm::is_contained(pending, *first)
            ? llvm::find(pending, *first)
            : llvm::min_element(
                  pending, [&](const PathEndPoint &a, const PathEndPoint &b) {
                    return pf.distance[dstState(a)] < pf.distance[dstState(b)];
                  });
    PathEndPoint endPoint = *nearest;
    int currId = dstState(endPoint);
    llvm::DenseSet<int> off = splitOff(currId);
    llvm::DenseSet<int> trunk = trunkOff(currId);
    off.insert(trunk.begin(), trunk.end());
    if (!off.empty()) {
      search({}, targets, off);
      if (pf.distance[currId] == INF)
        search({}, targets);
    }
    const SmallVector<int, 4> *joined = nullptr;
    for (const auto &[at, dsts] : joins)
      if (pf.distance[at] < pf.distance[currId] && joinable(at, dsts)) {
        currId = at;
        joined = &dsts;
      }
    if (joined) {
      reach(*joined);
      joinedAt.push_back({currId, joined});
      // The tree it joins goes on below.
      ++children[currId];
    } else {
      pending.erase(nearest);
      reached.push_back(currId);
    }
    if (!trace(currId))
      return llvm::make_error<RoutingFailure>(
          "no path leads from " +
              describeTilePort(part.src.coords, part.src.port) + " to " +
              describeTilePort(endPoint.coords, endPoint.port) +
              " through the connections the switchboxes allow and existing "
              "routing leaves free.",
          RoutingFaults{}, pf.flowLoc(part.src, &endPoint));
    if (!metTrees) {
      metTrees = true;
      meet();
    }
  }
  return llvm::Error::success();
}
 
// A destination's path was chosen before the tree reached the later
// ones, so reroute each destination's own branch from the rest of the
// tree where that is cheaper.
void Pathfinder::TreeBuilder::reroute() {
  for (int dst : reached) {
    llvm::DenseSet<int> branch;
    int top = dst;
    for (int below = 0; top != tree.front() && children.lookup(top) == below;
         below = 1) {
      branch.insert(top);
      top = planned.find(top)->second.first;
    }
    if (branch.empty())
      continue;
    llvm::DenseSet<int> off = splitOff(dst), trunk = trunkOff(dst);
    off.insert(trunk.begin(), trunk.end());
    search(branch, dst, off);
    double cost =
        treeSeedFactor * treeHops[llvm::find(tree, top) - tree.begin()];
    for (int s = dst; s != top;) {
      const auto &[from, e] = planned.find(s)->second;
      auto away = branchAvoid.find(from);
      cost +=
          pf.edgeWeight(e, part.packetId, avoid,
                        away == branchAvoid.end() ? nullptr : &away->second);
      s = from;
    }
    if (pf.distance[dst] + rerouteMinSaving >= cost)
      continue;
    for (int s : branch) {
      st.processedStamp[s] = 0;
      planned.erase(s);
      children.erase(s);
    }
    --children[top];
    for (size_t k = tree.size(); k-- > 0;)
      if (branch.count(tree[k])) {
        tree.erase(tree.begin() + k);
        treeHops.erase(treeHops.begin() + k);
      }
    [[maybe_unused]] bool traced = trace(dst);
    assert(traced && "a rerouted branch reaches its destination");
  }
}
 
// Take the channels the tree's hops cross.
void Pathfinder::TreeBuilder::claim() {
  if (toSelf) {
    switchSettings[part.src.coords].srcs.push_back(part.src.port);
    switchSettings[part.src.coords].dsts.push_back(part.src.port);
    if (part.packetId)
      st.routing.packetTrees[part.src].push_back({part.src, part.src, false});
  }
  const std::optional<int> &packetId = part.packetId;
  int packetGroupId = part.packetGroupId;
  llvm::DenseMap<int, std::pair<SwitchboxConnect *, int>> branchPort;
  for (const auto &[currId, hop] : planned) {
    const auto &[predId, e] = hop;
    const PathEndPoint &curr = pf.nodes[stateNode(currId)];
    const PathEndPoint &pred = pf.nodes[stateNode(predId)];
    SwitchboxConnect &sb = *e.sb;
    int i = e.i;
    int j = e.j;
    SwitchboxConnect::Cell &cell = sb.at(i, j);
    if (packetId)
      st.treeOf[flow].try_emplace(currId, predId, e);
    else
      st.circuitHops[flow].push_back(e);
    cell.isPriority |= part.isPriorityFlow;
    // Two trees with the same id may merge onto one only where nothing fans out
    // after, or where both take the id to the same destinations, so a merged id
    // never fans back out to one tree's destinations alone. The flow's own tree
    // branching at a port never merges back.
    // packetGroupId only becomes >= 0 when packetId has a value (see
    // Pathfinder::addFlow), so the dereferences below are safe; the
    // checker just can't correlate the two across this loop's back edge.
    // NOLINTBEGIN(bugprone-unchecked-optional-access)
    auto seen =
        packetId ? cell.packetIds.find(*packetId) : cell.packetIds.end();
    auto mergeable = [&] {
      if (!isDirectional(sb.dstPorts[j].bundle))
        return true;
      auto reached = [&](const Flow &f) {
        std::set<PathEndPoint> dsts;
        for (const PathEndPoint &dst : f.dsts)
          if (auto ids = pf.packetIdsTo.find({f.src, dst});
              ids != pf.packetIdsTo.end() &&
              llvm::is_contained(ids->second, *packetId))
            dsts.insert(dst);
        return dsts;
      };
      return reached(part) == reached(st.parts[seen->second]);
    };
    bool sameGroupUnseen =
        packetGroupId >= 0 && packetId.has_value() &&
        (cell.packetGroupId == -1 || cell.packetGroupId == packetGroupId) &&
        (seen == cell.packetIds.end() || seen->second == flow || mergeable());
    if (sameGroupUnseen) {
      int packetIdValue = *packetId;
      // NOLINTEND(bugprone-unchecked-optional-access)
      auto claim = [&](SwitchboxConnect::Cell &c) {
        c.packetGroupId = packetGroupId;
        c.packetIds.try_emplace(packetIdValue, flow);
      };
      for (size_t k = 0; k < sb.srcPorts.size(); k++)
        claim(sb.at(k, j));
      for (size_t l = 0; l < sb.dstPorts.size(); l++)
        if (l != static_cast<size_t>(j))
          claim(sb.at(i, l));
      // maximum packet stream sharing per channel
      if (++cell.packetFlowCount >= maxPacketStreamCapacity) {
        cell.packetFlowCount = 0;
        cell.usedCapacity++;
      }
    } else {
      cell.usedCapacity++;
    }
    // if at capacity, bump demand to discourage using this Channel
    // this means the order matters!
    SwitchboxConnect::bumpDemand(cell);
    if (pred.coords == curr.coords) {
      switchSettings[pred.coords].srcs.push_back(pred.port);
      switchSettings[curr.coords].dsts.push_back(curr.port);
      if (packetId) {
        sb.addToUnit(j, flow);
        auto [it, first] = branchPort.try_emplace(predId, &sb, j);
        if (!first)
          sb.joinUnits(it->second.second, j);
      }
    }
  }
  if (packetId) {
    st.treeDsts[flow].append(reached.begin(), reached.end());
    st.treeDsts[flow].append(met.begin(), met.end());
    for (const auto &[currId, hop] : planned)
      st.routing.packetTrees[part.src].push_back(
          {pf.nodes[stateNode(hop.first)], pf.nodes[stateNode(currId)], false});
  }
}
 
// Below a join the flow's packets follow the tree they joined.
bool Pathfinder::TreeBuilder::join(int state, int predId, const Edge &e) {
  if (!st.treeOf[flow].try_emplace(state, predId, e).second)
    return false;
  const PathEndPoint &pred = pf.nodes[stateNode(predId)];
  const PathEndPoint &curr = pf.nodes[stateNode(state)];
  st.routing.packetTrees[part.src].push_back({pred, curr, true});
  if (pred.coords == curr.coords) {
    switchSettings[pred.coords].srcs.push_back(pred.port);
    switchSettings[curr.coords].dsts.push_back(curr.port);
    e.sb->addToUnit(e.j, flow);
  }
  return true;
}
 
void Pathfinder::TreeBuilder::joinTrees() {
  for (const auto &[joinAt, joined] : joinedAt) {
    for (int other : joinOwners[joinAt]) {
      st.joinedHops[flow].push_back(
          {other, planned.find(joinAt)->second.second});
      for (int dst : *joined) {
        const auto &t = st.treeOf[other];
        SmallVector<std::pair<int, std::pair<int, Edge>>, 8> path;
        auto it = t.find(dst);
        for (; it != t.end() && it->first != joinAt;
             it = t.find(it->second.first))
          path.push_back(*it);
        if (it == t.end())
          continue;
        for (const auto &[state, hop] : path)
          if (join(state, hop.first, hop.second))
            st.joinedHops[flow].push_back({other, hop.second});
      }
    }
    st.treeDsts[flow].append(joined->begin(), joined->end());
  }
  for (const auto &[state, hop] : pinnedJoins)
    join(state, hop.first, hop.second);
  st.treeDsts[flow].append(pinnedJoinDsts.begin(), pinnedJoinDsts.end());
}
 
// Add the tree to the routing.
void Pathfinder::TreeBuilder::record() {
  const PathEndPoint &src = part.src;
  if (st.partsOf.at(src).size() == 1) {
    st.routing.settings[src] = switchSettings;
    return;
  }
  for (int id : st.flowIds[flow])
    st.routing.idSettings[{src, id}] = switchSettings;
  for (const auto &[tile, setting] : switchSettings) {
    SwitchSetting &all = st.routing.settings[src][tile];
    for (auto [in, out] : llvm::zip(setting.srcs, setting.dsts))
      if (!llvm::is_contained(llvm::zip(all.srcs, all.dsts),
                              std::make_tuple(in, out))) {
        all.srcs.push_back(in);
        all.dsts.push_back(out);
      }
  }
}
 
llvm::Error Pathfinder::routePart(RouteState &st, int flow) {
  std::optional<TreeBuilder> tree;
  tree.emplace(*this, st, flow);
  llvm::Error err = tree->pinned ? tree->placePinned() : tree->grow();
  // Kept to the prioritized flows' master sets, the branch a tree takes first
  // can leave it no way to another destination; each is then tried first.
  if (err && !tree->pinned && !st.priorityMasters.empty())
    for (const PathEndPoint &dst : st.parts[flow].dsts) {
      for (auto *pairs : {&st.unmet, &st.met})
        pairs->erase(pairs->lower_bound({flow, 0}),
                     pairs->lower_bound({flow + 1, 0}));
      st.joinedHops[flow].clear();
      tree.emplace(*this, st, flow);
      tree->first = dst;
      if (llvm::Error retry = tree->grow()) {
        llvm::consumeError(std::move(retry));
        continue;
      }
      llvm::consumeError(std::move(err));
      break;
    }
  if (err)
    return err;
  if (!tree->pinned && tree->reached.size() + tree->joinedAt.size() > 1)
    tree->reroute();
  tree->claim();
  tree->joinTrees();
  tree->record();
  return llvm::Error::success();
}
 
int Pathfinder::applyRoutingFaults(RouteState &st,
                                   const RoutingFaults &faults) {
  int illegalEdges = 0;
  for (const TreeSplit &split : faults.splits) {
    auto src = st.partsOf.find(split.src);
    if (src == st.partsOf.end())
      continue;
    auto partWith = [&](int id) {
      for (int k : src->second)
        if (st.flowIds[k].count(id))
          return k;
      return -1;
    };
    int flow = partWith(split.a), other = partWith(split.b);
    if (flow < 0 || other < 0)
      continue;
    std::optional<int> apart;
    if (split.apart) {
      auto it = nodeIds.find(*split.apart);
      if (it == nodeIds.end())
        continue;
      apart = stateId(it->second, Out);
    }
    // Whether a destination taking both ids is reached through the tile.
    auto inseparable = [&] {
      const Flow &f = st.parts[flow];
      for (const PathEndPoint &dst : f.dsts) {
        auto ids = packetIdsTo.find({f.src, dst});
        if (ids == packetIdsTo.end() ||
            !llvm::is_contained(ids->second, split.a) ||
            !llvm::is_contained(ids->second, split.b))
          continue;
        const auto &tree = st.treeOf[flow];
        auto it = tree.find(stateId(nodeIds.at(dst), Out));
        if (it == tree.end() && dst == f.src && dst.coords == split.at)
          return true;
        for (; it != tree.end(); it = tree.find(it->second.first)) {
          int up = it->second.first;
          if ((up & 1) == In && nodes[stateNode(up)].coords == split.at)
            return true;
        }
      }
      return false;
    };
    if (idsApart && flow == other && !split.apart &&
        !st.parts[flow].isPriorityFlow && inseparable())
      other = st.splitPart(flow, {split.b});
    if (flow != other) {
      if (st.partSplits[flow].insert({split.at, other}).second)
        illegalEdges++;
      st.partSplits[other].insert({split.at, flow});
    } else if (st.splitsOf[flow]
                   .insert({split.at, split.a, split.b, apart})
                   .second) {
      LLVM_DEBUG(llvm::dbgs()
                 << "Split ids " << split.a << " and " << split.b << " from "
                 << describeTilePort(split.src.coords, split.src.port)
                 << " at tile (" << split.at.col << ", " << split.at.row
                 << ")\n");
      illegalEdges++;
    }
  }
  crowdedTiles.insert(faults.crowded.begin(), faults.crowded.end());
  // Trees with an id in common join where they meet, so the ids a source
  // sends that the other does not route apart as a part of their own.
  auto splitOwnIds = [&](const std::pair<PathEndPoint, PathEndPoint> &pair) {
    for (auto [src, other] : {pair, std::pair{pair.second, pair.first}}) {
      auto srcParts = st.partsOf.find(src);
      auto otherParts = st.partsOf.find(other);
      if (srcParts == st.partsOf.end() || otherParts == st.partsOf.end())
        continue;
      std::set<int> otherIds;
      for (int k : otherParts->second)
        otherIds.insert(st.flowIds[k].begin(), st.flowIds[k].end());
      for (int k : SmallVector<int, 2>(srcParts->second)) {
        std::set<int> own;
        for (int id : st.flowIds[k])
          if (!otherIds.count(id))
            own.insert(id);
        if (!st.parts[k].isPriorityFlow && !own.empty() &&
            own.size() < st.flowIds[k].size())
          st.splitPart(k, own);
      }
    }
  };
  bool related = false;
  for (const auto &pair : faults.apart) {
    if (!st.apartSources.insert(pair).second)
      continue;
    related = true;
    LLVM_DEBUG(llvm::dbgs()
               << "Route apart: "
               << describeTilePort(pair.first.coords, pair.first.port)
               << " and "
               << describeTilePort(pair.second.coords, pair.second.port)
               << "\n");
    if (splitShared)
      splitOwnIds(pair);
  }
  for (const auto &pair : faults.together) {
    if (!st.togetherSources.insert(pair).second)
      continue;
    related = true;
    LLVM_DEBUG(llvm::dbgs()
               << "Route together: "
               << describeTilePort(pair.first.coords, pair.first.port)
               << " and "
               << describeTilePort(pair.second.coords, pair.second.port)
               << "\n");
    splitOwnIds(pair);
  }
  if (related) {
    illegalEdges++;
    st.relateParts();
  }
  for (const PathEndPoint &src : faults.untrunk)
    if (st.untrunked.insert(src).second) {
      LLVM_DEBUG(llvm::dbgs()
                 << "Untrunk: " << describeTilePort(src.coords, src.port)
                 << "\n");
      illegalEdges++;
    }
  std::set<std::pair<int, int>> faulted;
  bool unjoined = false;
  for (const auto &[tile, conn] : faults.connections) {
    illegalEdges++;
    auto it = graph.find({tile, tile});
    if (it == graph.end())
      continue;
    SwitchboxConnect &sb = it->second;
    int i = sb.srcIndex(conn.src);
    int j = sb.dstIndex(conn.dst);
    if (i < 0 || j < 0)
      continue;
    sb.at(i, j).overCapacity += routingCheckPenalty;
    bool joined = false;
    for (auto [flow, hops] : llvm::enumerate(st.joinedHops))
      for (const auto &[other, e] : hops)
        if (e.sb == &sb && sb.srcPorts[e.i] == conn.src &&
            sb.dstPorts[e.j] == conn.dst) {
          faulted.insert({static_cast<int>(flow), other});
          joined = true;
        }
    unjoined |= !joined;
  }
  // Moving the hops neither joined may be enough, so a joined pair is first
  // left to their penalties.
  for (auto [flow, other] : faulted)
    if (unjoined && st.spared.insert({flow, other}).second)
      continue;
    else if (st.met.count({flow, other}) &&
             ++st.meetFaults[{std::min(flow, other), std::max(flow, other)}] <=
                 maxMeetFaults)
      st.reorder(flow, other, /*again=*/true);
    else
      st.noJoin.insert({flow, other});
  return illegalEdges;
}
 
// Perform congestion-aware routing for all flows which have been added.
// Use Dijkstra's shortest path to find routes, and use "demand" as the
// weights. If the routing finds too much congestion, update the demand
// weights and repeat the process until a valid solution is found. Returns
// the switchbox settings for all flows, or a RoutingFailure if no legal
// routing is found after maxIterations.
llvm::Expected<Routing> Pathfinder::findPaths(const int maxIterations) {
  LLVM_DEBUG(llvm::dbgs() << "\t---Begin Pathfinder::findPaths---\n");
  checkReason.clear();
  packetsFailed = true;
  // Build the dense routing graph once; topology is invariant across
  // iterations.
  if (!graphBuilt)
    buildRoutingGraph();
  if (llvm::Error err = cutOverflow()) {
    packetsFailed = false;
    return std::move(err);
  }
  crowdedTiles.clear();
  // initialize all Channel histories to 0
  for (auto &[_, sb] : graph) {
    if (sb.srcCoords == sb.dstCoords)
      for (auto [j, port] : llvm::enumerate(sb.dstPorts))
        sb.circuitOnlyDst[j] = cappedTiles.contains(sb.srcCoords) &&
                               port.channel >= packetFanoutCap &&
                               isDirectional(port.bundle);
    for (SwitchboxConnect::Cell &c : sb.cells) {
      c.usedCapacity = 0;
      c.overCapacity = 0;
      c.isPriority = false;
    }
  }
 
  RouteState st(*this);
 
  int iterationCount = -1;
  int illegalEdges = 0;
  std::optional<Routing> usable;
  int usableAt = 0;
  int fewestIllegal = std::numeric_limits<int>::max(), sinceFewest = 0;
  // Iterations of the current stall that moved circuit trees first.
  int reorderedStall = 0;
  int priorityFaults = 0;
  do {
    if (usable && (iterationCount + 1 >= maxIterations ||
                   iterationCount - usableAt >= maxSteers)) {
      LLVM_DEBUG(llvm::dbgs() << "\t\tKeeping the usable routing\n");
      return std::move(*usable);
    }
    // if reach maxIterations, throw an error since no routing can be found;
    // so too once the overuse stalls for good, or routing the losing circuit
    // trees first has stopped helping
    if (++iterationCount >= maxIterations ||
        (fewestIllegal > 0 && sinceFewest >= maxOverusedStall) ||
        reorderedStall >= maxReorderedStall) {
      LLVM_DEBUG(llvm::dbgs()
                 << "\t\tPathfinder: giving up after " << iterationCount
                 << " iterations ("
                 << (iterationCount >= maxIterations ? "the iteration limit"
                     : reorderedStall >= maxReorderedStall
                         ? "circuit trees routed first stopped helping"
                         : "the overuse stalled")
                 << ")...unable to find routing for flows.\n");
      packetsFailed =
          !checkReason.empty() || llvm::any_of(graph, [](const auto &entry) {
            ArrayRef<SwitchboxConnect::Cell> cells = entry.second.cells;
            return llvm::any_of(cells,
                                [](const SwitchboxConnect::Cell &c) {
                                  return c.packetGroupId >= 0;
                                }) &&
                   llvm::any_of(cells, [](const SwitchboxConnect::Cell &c) {
                     return c.usedCapacity > maxCircuitStreamCapacity;
                   });
          });
      return explainNoRouting(st);
    }
 
    LLVM_DEBUG(llvm::dbgs() << "\t\t---Begin findPaths iteration #"
                            << iterationCount << "---\n");
    // update demand at the beginning of each iteration
    for (auto &[_, sb] : graph) {
      sb.updateDemand();
    }
 
    // "rip up" all routes
    illegalEdges = 0;
    st.routing = {};
    for (auto &[_, sb] : graph) {
      for (SwitchboxConnect::Cell &c : sb.cells) {
        c.usedCapacity = 0;
        c.packetFlowCount = 0;
        c.packetGroupId = -1;
        c.packetIds.clear();
      }
      sb.resetUnits();
    }
    for (auto &tree : st.treeOf)
      tree.clear();
    for (auto &hops : st.circuitHops)
      hops.clear();
    for (auto &dsts : st.treeDsts)
      dsts.clear();
    for (auto &hops : st.joinedHops)
      hops.clear();
    st.unmet.clear();
    st.met.clear();
 
    // for each flow, find the shortest path from source to destination
    // update used_capacity for the path between them
 
    for (const auto &[_, group] : st.groupedFlows) {
      for (int flow : group)
        if (llvm::Error err = routePart(st, flow))
          return std::move(err);
      for (auto &[_, sb] : graph) {
        for (SwitchboxConnect::Cell &c : sb.cells) {
          // fix used capacity for packet flows
          if (c.packetFlowCount > 0) {
            c.packetFlowCount = 0;
            c.usedCapacity++;
          }
          SwitchboxConnect::bumpDemand(c);
        }
      }
    }
 
    // The tree routed first may branch where none from elsewhere can meet it
    // at one switchbox, though it could meet a tree routed before it, or one
    // that leaves its source switchbox by one master port for them.
    for (auto [later, earlier] : st.unmet) {
      bool steered = st.reorder(later, earlier);
      steered |= st.trunked.insert({later, earlier}).second;
      steered |= st.trunked.insert({earlier, later}).second;
      if (steered)
        illegalEdges++;
    }
 
    for (auto &[_, sb] : graph) {
      for (size_t i = 0; i < sb.srcPorts.size(); i++) {
        for (size_t j = 0; j < sb.dstPorts.size(); j++) {
          SwitchboxConnect::Cell &c = sb.at(i, j);
          // check that every channel does not exceed max capacity
          if (c.usedCapacity > maxCircuitStreamCapacity) {
            c.overCapacity +=
                sinceFewest >= stallIterations && c.packetGroupId < 0
                    ? stallHistory
                    : 1;
            illegalEdges++;
            LLVM_DEBUG(llvm::dbgs()
                       << "\t\t\tToo much capacity on (" << sb.srcCoords.col
                       << "," << sb.srcCoords.row << ") "
                       << sb.srcPorts[i].bundle << sb.srcPorts[i].channel
                       << " -> (" << sb.dstCoords.col << "," << sb.dstCoords.row
                       << ") " << sb.dstPorts[j].bundle
                       << sb.dstPorts[j].channel << ", used_capacity = "
                       << c.usedCapacity << ", demand = " << c.demand
                       << ", over_capacity_count = " << c.overCapacity << "\n");
          }
        }
      }
    }
 
    // Once the overuse stalls, circuit trees that overuse a circuit-only
    // channel route first, so the same tree stops losing it. Packet-shared
    // overuse is left to the packet steering.
    if (illegalEdges < fewestIllegal) {
      fewestIllegal = illegalEdges;
      sinceFewest = reorderedStall = 0;
    } else {
      sinceFewest++;
    }
    if (illegalEdges && sinceFewest >= stallIterations) {
      auto losing = [&](int flow) {
        return !st.parts[flow].packetId &&
               llvm::any_of(st.circuitHops[flow], [](const Edge &e) {
                 const SwitchboxConnect::Cell &c = e.sb->at(e.i, e.j);
                 return c.usedCapacity > maxCircuitStreamCapacity &&
                        c.packetGroupId < 0;
               });
      };
      bool moved = false;
      for (auto &[_, group] : st.groupedFlows) {
        moved |= llvm::any_of(group, losing);
        std::stable_partition(group.begin(), group.end(), losing);
      }
      reorderedStall += moved;
    }
    // Each stall period without a legal routing, the packet trees drop their
    // id splits: the routing that faulted them may be gone, and the routing
    // check adds back any still needed.
    if (sinceFewest >= stallIterations && sinceFewest % stallIterations == 0) {
      LLVM_DEBUG(llvm::dbgs() << "Drop the id splits after " << sinceFewest
                              << " stalled iterations\n");
      for (auto &splits : st.splitsOf)
        splits.clear();
    }
 
    // A routing that fits the fabric can still be one the caller cannot use;
    // steer away from the connections it names as if they were overused. One
    // it rejects naming nothing to move is as far as steering gets, leaving
    // the usable routing found, if any, or the rejection.
    bool stuck = false;
    llvm::Error unmoved =
        illegalEdges != 0 || !constraints.check
            ? llvm::Error::success()
            : llvm::handleErrors(
                  constraints.check(st.routing),
                  [&](std::unique_ptr<RoutingFailure> rejected) -> llvm::Error {
                    LLVM_DEBUG(llvm::dbgs() << "Routing rejected: "
                                            << rejected->reason << '\n');
                    illegalEdges += applyRoutingFaults(st, rejected->faults);
                    priorityFaults = rejected->faults.onlyPriorityMasters
                                         ? priorityFaults + 1
                                         : 0;
                    stuck = illegalEdges == 0;
                    if (rejected->isA(DeadlockProneRouting::classID())) {
                      if (!usable) {
                        usable = st.routing;
                        usableAt = iterationCount;
                      }
                      return llvm::Error::success();
                    }
                    if (stuck)
                      return llvm::Error(std::move(rejected));
                    checkReason = std::move(rejected->reason);
                    return llvm::Error::success();
                  });
 
    LLVM_DEBUG({
      for (const auto &[src, settings] : st.routing.settings)
        llvm::dbgs() << "\t\t\tFlow starting at (" << src.coords.col << ","
                     << src.coords.row << "):\t" << settings;
      // total path length, across switchboxes
      int totalPathLength = 0;
      for (const auto &[_, sb] : graph)
        if (sb.srcCoords != sb.dstCoords)
          for (const SwitchboxConnect::Cell &c : sb.cells)
            totalPathLength += c.usedCapacity;
      llvm::dbgs() << "\t\t---End findPaths iteration #" << iterationCount
                   << " , illegal edges count = " << illegalEdges
                   << ", total path length = " << totalPathLength << "---\n";
    });
    if (stuck && usable) {
      llvm::consumeError(std::move(unmoved));
      return std::move(*usable);
    }
    if (unmoved)
      return std::move(unmoved);
    if (priorityFaults >= maxPriorityFaults) {
      LLVM_DEBUG(llvm::dbgs() << "\t\tPathfinder: the routing check rejects "
                                 "only master sets of the prioritized flows ("
                              << priorityFaults << " routings in a row)\n");
      if (usable)
        return std::move(*usable);
      packetsFailed = false;
      return explainNoRouting(st);
    }
    // continue iterations until a legal routing is found
  } while (illegalEdges > 0);
 
  LLVM_DEBUG(llvm::dbgs() << "\t---End Pathfinder::findPaths---\n");
  return std::move(st.routing);
}