llvm/tools/llvm-exegesis/lib/Clustering.cpp

//===-- Clustering.cpp ------------------------------------------*- C++ -*-===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//

#include "Clustering.h"
#include <string>
#include <unordered_set>

namespace exegesis {

// The clustering problem has the following characteristics:
//  (A) - Low dimension (dimensions are typically proc resource units,
//    typically < 10).
//  (B) - Number of points : ~thousands (points are measurements of an MCInst)
//  (C) - Number of clusters: ~tens.
//  (D) - The number of clusters is not known /a priory/.
//  (E) - The amount of noise is relatively small.
// The problem is rather small. In terms of algorithms, (D) disqualifies
// k-means and makes algorithms such as DBSCAN[1] or OPTICS[2] more applicable.
//
// We've used DBSCAN here because it's simple to implement. This is a pretty
// straightforward and inefficient implementation of the pseudocode in [2].
//
// [1] https://en.wikipedia.org/wiki/DBSCAN
// [2] https://en.wikipedia.org/wiki/OPTICS_algorithm

namespace {

// Finds the points at distance less than sqrt(EpsilonSquared) of Q (not
// including Q).
std::vector<size_t> rangeQuery(const std::vector<InstructionBenchmark> &Points,
                               const size_t Q, const double EpsilonSquared) {
  std::vector<size_t> Neighbors;
  const auto &QMeasurements = Points[Q].Measurements;
  for (size_t P = 0, NumPoints = Points.size(); P < NumPoints; ++P) {
    if (P == Q)
      continue;
    const auto &PMeasurements = Points[P].Measurements;
    if (PMeasurements.empty()) // Error point.
      continue;
    double DistanceSquared = 0;
    for (size_t I = 0, E = QMeasurements.size(); I < E; ++I) {
      const auto Diff = PMeasurements[I].Value - QMeasurements[I].Value;
      DistanceSquared += Diff * Diff;
    }
    if (DistanceSquared <= EpsilonSquared) {
      Neighbors.push_back(P);
    }
  }
  return Neighbors;
}

} // namespace

InstructionBenchmarkClustering::InstructionBenchmarkClustering(
    const std::vector<InstructionBenchmark> &Points)
    : Points_(Points), NoiseCluster_(ClusterId::noise()),
      ErrorCluster_(ClusterId::error()) {}

llvm::Error InstructionBenchmarkClustering::validateAndSetup() {
  ClusterIdForPoint_.resize(Points_.size());
  // Mark erroneous measurements out.
  // All points must have the same number of dimensions, in the same order.
  const std::vector<BenchmarkMeasure> *LastMeasurement = nullptr;
  for (size_t P = 0, NumPoints = Points_.size(); P < NumPoints; ++P) {
    const auto &Point = Points_[P];
    if (!Point.Error.empty()) {
      ClusterIdForPoint_[P] = ClusterId::error();
      ErrorCluster_.PointIndices.push_back(P);
      continue;
    }
    const auto *CurMeasurement = &Point.Measurements;
    if (LastMeasurement) {
      if (LastMeasurement->size() != CurMeasurement->size()) {
        return llvm::make_error<llvm::StringError>(
            "inconsistent measurement dimensions",
            llvm::inconvertibleErrorCode());
      }
      for (size_t I = 0, E = LastMeasurement->size(); I < E; ++I) {
        if (LastMeasurement->at(I).Key != CurMeasurement->at(I).Key) {
          return llvm::make_error<llvm::StringError>(
              "inconsistent measurement dimensions keys",
              llvm::inconvertibleErrorCode());
        }
      }
    }
    LastMeasurement = CurMeasurement;
  }
  if (LastMeasurement) {
    NumDimensions_ = LastMeasurement->size();
  }
  return llvm::Error::success();
}

void InstructionBenchmarkClustering::dbScan(const size_t MinPts,
                                            const double EpsilonSquared) {
  for (size_t P = 0, NumPoints = Points_.size(); P < NumPoints; ++P) {
    if (!ClusterIdForPoint_[P].isUndef())
      continue; // Previously processed in inner loop.
    const auto Neighbors = rangeQuery(Points_, P, EpsilonSquared);
    if (Neighbors.size() + 1 < MinPts) { // Density check.
      // The region around P is not dense enough to create a new cluster, mark
      // as noise for now.
      ClusterIdForPoint_[P] = ClusterId::noise();
      continue;
    }

    // Create a new cluster, add P.
    Clusters_.emplace_back(ClusterId::makeValid(Clusters_.size()));
    Cluster &CurrentCluster = Clusters_.back();
    ClusterIdForPoint_[P] = CurrentCluster.Id; /* Label initial point */
    CurrentCluster.PointIndices.push_back(P);

    // Process P's neighbors.
    std::unordered_set<size_t> ToProcess(Neighbors.begin(), Neighbors.end());
    while (!ToProcess.empty()) {
      // Retrieve a point from the set.
      const size_t Q = *ToProcess.begin();
      ToProcess.erase(Q);

      if (ClusterIdForPoint_[Q].isNoise()) {
        // Change noise point to border point.
        ClusterIdForPoint_[Q] = CurrentCluster.Id;
        CurrentCluster.PointIndices.push_back(Q);
        continue;
      }
      if (!ClusterIdForPoint_[Q].isUndef()) {
        continue; // Previously processed.
      }
      // Add Q to the current custer.
      ClusterIdForPoint_[Q] = CurrentCluster.Id;
      CurrentCluster.PointIndices.push_back(Q);
      // And extend to the neighbors of Q if the region is dense enough.
      const auto Neighbors = rangeQuery(Points_, Q, EpsilonSquared);
      if (Neighbors.size() + 1 >= MinPts) {
        ToProcess.insert(Neighbors.begin(), Neighbors.end());
      }
    }
  }

  // Add noisy points to noise cluster.
  for (size_t P = 0, NumPoints = Points_.size(); P < NumPoints; ++P) {
    if (ClusterIdForPoint_[P].isNoise()) {
      NoiseCluster_.PointIndices.push_back(P);
    }
  }
}

llvm::Expected<InstructionBenchmarkClustering>
InstructionBenchmarkClustering::create(
    const std::vector<InstructionBenchmark> &Points, const size_t MinPts,
    const double Epsilon) {
  InstructionBenchmarkClustering Clustering(Points);
  if (auto Error = Clustering.validateAndSetup()) {
    return std::move(Error);
  }
  if (Clustering.ErrorCluster_.PointIndices.size() == Points.size()) {
    return Clustering; // Nothing to cluster.
  }

  Clustering.dbScan(MinPts, Epsilon * Epsilon);
  return Clustering;
}

} // namespace exegesis