CD_LoadBalancingImplem.H

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/* chombo-discharge
 * Copyright © 2021 SINTEF Energy Research.
 * Please refer to Copyright.txt and LICENSE in the chombo-discharge root directory.
 */
 
#ifndef CD_LoadBalanceImplem_H
#define CD_LoadBalanceImplem_H
 
// Std includes
#include <algorithm>
#include <random>
#include <chrono>
#include <limits>
#include <array>
#include <tuple>
 
// Chombo includes
#include <LoadBalance.H>
#include <BoxLayout.H>
#include <ParmParse.H>
#include <CH_Timer.H>
 
// Our includes
#include <CD_LoadBalancing.H>
#include <CD_NamespaceHeader.H>
 
template <class T>
void
LoadBalancing::makeBalance(Vector<int>& a_ranks, const Vector<T>& a_loads, const Vector<Box>& a_boxes)
{
  CH_TIME("LoadBalancing::makeBalance");
 
  //  LoadBalance(a_ranks, a_loads, a_boxes);
  Loads rankLoads;
  LoadBalancing::makeBalance<T>(a_ranks, rankLoads, a_loads, a_boxes);
}
 
template <class T>
void
LoadBalancing::makeBalance(Vector<int>&       a_ranks,
                           Loads&             a_rankLoads,
                           const Vector<T>&   a_boxLoads,
                           const Vector<Box>& a_boxes)
{
  CH_TIME("LoadBalancing::makeBalance");
 
  // Convert everything to floating points
  Vector<Real> boxLoads;
  for (int i = 0; i < a_boxLoads.size(); i++) {
    boxLoads.push_back(1.0 * a_boxLoads[i]);
  }
 
  // Minimum number of grid subsets is the number of boxe, and the maximum number of grid subsets
  // is the number of ranks.
  const int numBoxes   = a_boxes.size();
  const int numRanks   = numProc();
  const int numSubsets = std::min(numBoxes, numRanks);
 
  a_ranks.resize(numBoxes);
 
  if (numSubsets > 0) {
 
    // Figure out the total and target load (load per subset) on this level.
    Real totalLoad = 0.0;
    for (int ibox = 0; ibox < numBoxes; ibox++) {
      totalLoad += boxLoads[ibox];
    }
 
    Real staticTargetLoad = totalLoad / numSubsets;
 
    // Build the grid subsets. When we do this we iterate through the boxes and try to ensure that we partition
    // the subsets such that the subsetLoad is as close to the dynamic targetLoad as possible.
    //
    // The pair contains the starting index for the subset and the computational load for the subset.
    using Span   = std::pair<int, int>;
    using Subset = std::pair<Span, Real>;
 
    std::vector<Subset> subsets(numSubsets);
 
    int firstSubsetBox = 0;
 
    Real remainingLoad = totalLoad;
 
    for (int curSubset = 0; curSubset < numSubsets; curSubset++) {
 
      // The firstSubsetBox is the index for the first box in this subset (always assigned).
      Real subsetLoad = boxLoads[firstSubsetBox];
 
      int lastSubsetBox = firstSubsetBox;
 
      const int subsetsLeft = numSubsets - (curSubset + 1);
      const int boxesLeft   = numBoxes - (firstSubsetBox + 1);
 
      if (boxesLeft > subsetsLeft) {
        for (int ibox = firstSubsetBox + 1; ibox < numBoxes; ibox++) {
 
          // Hook for catching case when we add too many boxes to this subset. Each remaining subset must have at least one box.
          if (numBoxes - lastSubsetBox - 1 <= subsetsLeft) {
            break;
          }
 
          // Check if we should add this box - we do this by making sure that the dynamically moving target load stays as close
          // to the static load as possible.
          //
          // In the below, '1' is the load without ibox, and '2' is the load with ibox
          const Real load1 = subsetLoad;
          const Real load2 = subsetLoad + boxLoads[ibox];
 
          // Check if we should add this box.
          bool addBoxToSubset = false;
 
          if (boxLoads[ibox] <= std::numeric_limits<Real>::epsilon()) {
            addBoxToSubset = true;
          }
          else if (load1 > staticTargetLoad) {
            addBoxToSubset = false;
          }
          else if (load2 <= staticTargetLoad) {
            addBoxToSubset = true;
          }
          else if (load1 <= staticTargetLoad && load2 > staticTargetLoad) {
            // Compute the new average load if we add or don't add this box to the current subset. Accept the answer
            // that leads to a smallest deviation from the static target load.
            const Real loadErrWithoutBox = std::abs(load1 - staticTargetLoad);
            const Real loadErrWithBox    = std::abs(load2 - staticTargetLoad);
 
            if (loadErrWithBox <= loadErrWithoutBox) {
              addBoxToSubset = true;
            }
          }
 
          // Add box or break out of box iteration.
          if (addBoxToSubset) {
            subsetLoad    = subsetLoad + boxLoads[ibox];
            lastSubsetBox = ibox;
 
            continue;
          }
          else {
            lastSubsetBox = ibox - 1;
 
            break;
          }
        }
      }
 
      // Create the subset
      subsets[curSubset] = std::make_pair(std::make_pair(firstSubsetBox, lastSubsetBox), subsetLoad);
 
      // Update the remaining load.
      remainingLoad    = remainingLoad - subsetLoad;
      staticTargetLoad = remainingLoad / subsetsLeft;
 
      // Update start box for next iteration.
      firstSubsetBox = lastSubsetBox + 1;
    }
 
    // Sort the subsets from largest to smallest computational load.
    std::sort(subsets.begin(), subsets.end(), [](const Subset& A, const Subset& B) -> bool {
      return A.second > B.second;
    });
 
    // Get the accumulated loads per rank, sorted by lowest-to-highest load.
    const std::vector<std::pair<int, Real>> sortedRankLoads = a_rankLoads.getSortedLoads();
 
    // Assign the most expensive grid subset to the rank with the lowest accumulated load.
    for (int i = 0; i < subsets.size(); i++) {
      const int  startIndex = subsets[i].first.first;
      const int  endIndex   = subsets[i].first.second;
      const Real subsetLoad = subsets[i].second;
      const int  rank       = sortedRankLoads[i].first;
 
      // Assign to rank
      for (int ibox = startIndex; ibox <= endIndex; ibox++) {
        a_ranks[ibox] = rank;
      }
 
      // Update load on this rank.
      a_rankLoads.incrementLoad(rank, subsetLoad);
    }
  }
  else {
    a_ranks.resize(0);
  }
}
 
template <class T>
std::vector<std::pair<Box, T>>
LoadBalancing::packPairs(const Vector<Box>& a_boxes, const Vector<T>& a_loads)
{
  CH_TIME("LoadBalancing::packPairs");
 
  std::vector<std::pair<Box, T>> vec;
  for (int i = 0; i < a_boxes.size(); i++) {
    vec.emplace_back(a_boxes[i], a_loads[i]);
  }
 
  return vec;
}
 
template <class T>
void
LoadBalancing::unpackPairs(Vector<Box>& a_boxes, Vector<T>& a_loads, const std::vector<std::pair<Box, T>>& a_pairs)
{
  CH_TIME("LoadBalancing::unpackPairs");
 
  // Reconstruct boxes and loads
  a_boxes.resize(0);
  a_loads.resize(0);
 
  for (const auto& v : a_pairs) {
    a_boxes.push_back(v.first);
    a_loads.push_back(v.second);
  }
}
 
template <typename T>
void
LoadBalancing::sort(Vector<Vector<Box>>& a_boxes, Vector<Vector<T>>& a_loads, const BoxSorting a_which)
{
  CH_TIME("LoadBalancing::sort");
 
  for (int lvl = 0; lvl < a_boxes.size(); lvl++) {
    LoadBalancing::sort(a_boxes[lvl], a_loads[lvl], a_which);
  }
}
 
template <typename T>
void
LoadBalancing::sort(Vector<Box>& a_boxes, Vector<T>& a_loads, const BoxSorting a_which)
{
  CH_TIME("LoadBalancing::sort");
 
  switch (a_which) {
  case BoxSorting::None: {
    break;
  }
  case BoxSorting::Std: {
    LoadBalancing::standardSort(a_boxes, a_loads);
 
    break;
  }
  case BoxSorting::Shuffle: {
    LoadBalancing::shuffleSort(a_boxes, a_loads);
 
    break;
  }
  case BoxSorting::Morton: {
    LoadBalancing::sortSFC<T, SpaceDim>(a_boxes, a_loads, LoadBalancing::mortonIndex<SpaceDim>);
 
    break;
  }
  case BoxSorting::Hilbert: {
    LoadBalancing::sortSFC<T, SpaceDim>(a_boxes, a_loads, LoadBalancing::hilbertIndex<SpaceDim>);
 
    break;
  }
  default: {
    MayDay::Abort("LoadBalancing::sort_boxes - unknown algorithm requested");
 
    break;
  }
  }
}
 
template <class T>
void
LoadBalancing::standardSort(Vector<Box>& a_boxes, Vector<T>& a_loads)
{
  CH_TIME("LoadBalancing::standardSort");
 
  std::vector<std::pair<Box, T>> vec = packPairs(a_boxes, a_loads);
 
  // Call std::sort, using box1 < box2 lambda as sorting criterion.
  std::sort(std::begin(vec), std::end(vec), [](const std::pair<Box, T>& v1, const std::pair<Box, T>& v2) {
    return v1.first < v2.first;
  });
 
  unpackPairs(a_boxes, a_loads, vec);
}
 
template <class T>
void
LoadBalancing::shuffleSort(Vector<Box>& a_boxes, Vector<T>& a_loads)
{
  CH_TIME("LoadBalancing::shuffleSort");
 
  auto vec = packPairs(a_boxes, a_loads);
 
  // Set up RNG
  int seed = std::chrono::system_clock::now().time_since_epoch().count();
#ifdef CH_MPI // Broadcast
  MPI_Bcast(&seed, 1, MPI_INT, 0, Chombo_MPI::comm);
#endif
 
  // Shuffle vector
  std::default_random_engine e(seed);
  std::shuffle(vec.begin(), vec.end(), e);
 
  // Split boxes and loads
  unpackPairs(a_boxes, a_loads, vec);
}
 
template <class T, int DIM>
void
LoadBalancing::sortSFC(Vector<Box>&                                                    a_boxes,
                       Vector<T>&                                                      a_loads,
                       const std::function<uint64_t(const std::array<uint32_t, DIM>)>& a_sfcEncoder) noexcept
 
{
  CH_TIME("LoadBalancing::sortSFC");
 
  using Bundle = std::tuple<Box, T, uint64_t>;
 
  const int n = a_boxes.size();
  if (n == 0 || n != a_loads.size()) {
    return;
  }
 
  // Pack data into a vector of tuples. Tuple contains (box, load, key).
  std::vector<Bundle> buf;
  for (std::size_t i = 0; i < n; ++i) {
    buf.emplace_back(std::move(a_boxes[i]), std::move(a_loads[i]), uint64_t{0});
  }
 
  // Compute Hilbert keys
  for (std::size_t i = 0; i < n; ++i) {
    const auto& b  = std::get<0>(buf[i]);
    const auto  iv = b.smallEnd();
 
    std::array<uint32_t, SpaceDim> c;
 
    for (int d = 0; d < SpaceDim; ++d) {
      c[d] = static_cast<uint32_t>(iv[d]);
    }
 
    std::get<2>(buf[i]) = a_sfcEncoder(c);
  }
 
  // 3) Sort by hilbert key.
  std::sort(buf.begin(), buf.end(), [](const Bundle& a, const Bundle& b) noexcept {
    return std::get<2>(a) < std::get<2>(b);
  });
 
  // Unpack into original containers.
  for (std::size_t i = 0; i < n; ++i) {
    a_boxes[i] = std::move(std::get<0>(buf[i]));
    a_loads[i] = std::move(std::get<1>(buf[i]));
  }
}
 
template <int DIM>
uint64_t
LoadBalancing::mortonIndex(const std::array<uint32_t, DIM> a_coords) noexcept
{
  uint64_t code = 0;
 
  // If this fails then we can't compute a Morton code using a 64-bit integer. We must either scale back the boxes
  // by their blocking factors, or switch to 128/256 bit integers.
  const int maxDim = std::pow(2, 21);
 
  for (int dir = 0; dir < SpaceDim; dir++) {
    if (a_coords[dir] > maxDim) {
      MayDay::Abort("LoadBalancing::mortonIndex - logic bust");
    }
  }
 
  for (int bit = 20; bit >= 0; --bit) {
    for (int dir = CH_SPACEDIM - 1; dir >= 0; --dir) {
      const uint64_t b = (static_cast<uint64_t>(static_cast<uint32_t>(a_coords[dir])) >> bit) & 1ull;
 
      code = (code << 1) | b;
    }
  }
 
  return code;
}
 
template <int DIM>
uint64_t
LoadBalancing::hilbertIndex(const std::array<uint32_t, DIM>& a_coords)
{
  CH_TIME("LoadBalancing::hilbertIndex");
 
  constexpr int nbits = 21;
 
  uint32_t x[DIM];
 
  for (int i = 0; i < DIM; ++i) {
    x[i] = a_coords[i];
  }
 
  const uint32_t M = 1u << (nbits - 1);
 
  for (uint32_t Q = M; Q > 1; Q >>= 1) {
    const uint32_t P = Q - 1;
 
    for (int i = 0; i < DIM; ++i) {
      if (x[i] & Q) {
        x[0] ^= P;
      }
      else {
        const uint32_t t = (x[0] ^ x[i]) & P;
 
        x[0] ^= t;
        x[i] ^= t;
      }
    }
  }
 
  for (int i = 1; i < DIM; ++i) {
    x[i] ^= x[i - 1];
  }
 
  uint32_t t = 0;
  for (uint32_t Q = M; Q > 1; Q >>= 1) {
    if (x[DIM - 1] & Q) {
      t ^= (Q - 1);
    }
  }
 
  for (int i = 0; i < DIM; ++i) {
    x[i] ^= t;
  }
 
  uint64_t idx = 0;
 
  for (int b = nbits - 1; b >= 0; --b) {
    for (int i = 0; i < DIM; ++i) {
      idx = (idx << 1) | ((x[i] >> b) & 1u);
    }
  }
 
  return idx;
}
 
#include <CD_NamespaceFooter.H>
 
#endif