Tpetra_Map_def.hpp

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// @HEADER
// *****************************************************************************
//          Tpetra: Templated Linear Algebra Services Package
//
// Copyright 2008 NTESS and the Tpetra contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
 
 
#ifndef TPETRA_MAP_DEF_HPP
#define TPETRA_MAP_DEF_HPP
 
#include <memory>
#include <sstream>
#include <stdexcept>
#include <typeinfo>
 
#include "Teuchos_as.hpp"
#include "Teuchos_TypeNameTraits.hpp"
#include "Teuchos_CommHelpers.hpp"
 
#include "Tpetra_Directory.hpp"  // must include for implicit instantiation to work
#include "Tpetra_Details_Behavior.hpp"
#include "Tpetra_Details_FixedHashTable.hpp"
#include "Tpetra_Details_gathervPrint.hpp"
#include "Tpetra_Details_printOnce.hpp"
#include "Tpetra_Core.hpp"
#include "Tpetra_Util.hpp"
#include "Tpetra_Details_mpiIsInitialized.hpp"
#include "Tpetra_Details_extractMpiCommFromTeuchos.hpp"  // teuchosCommIsAnMpiComm
#include "Tpetra_Details_initializeKokkos.hpp"
#include "Tpetra_Details_Profiling.hpp"
 
namespace {  // (anonymous)
 
void checkMapInputArray(const char ctorName[],
                        const void* indexList,
                        const size_t indexListSize,
                        const Teuchos::Comm<int>* const comm) {
  using Tpetra::Details::Behavior;
 
  const bool debug = Behavior::debug("Map");
  if (debug) {
    using std::endl;
    using Teuchos::outArg;
    using Teuchos::REDUCE_MIN;
    using Teuchos::reduceAll;
 
    const int myRank   = comm == nullptr ? 0 : comm->getRank();
    const bool verbose = Behavior::verbose("Map");
    std::ostringstream lclErrStrm;
    int lclSuccess = 1;
 
    if (indexListSize != 0 && indexList == nullptr) {
      lclSuccess = 0;
      if (verbose) {
        lclErrStrm << "Proc " << myRank << ": indexList is null, "
                                           "but indexListSize="
                   << indexListSize << " != 0." << endl;
      }
    }
    int gblSuccess = 0;  // output argument
    reduceAll(*comm, REDUCE_MIN, lclSuccess, outArg(gblSuccess));
    if (gblSuccess != 1) {
      std::ostringstream gblErrStrm;
      gblErrStrm << "Tpetra::Map constructor " << ctorName << " detected a problem with the input array "
                                                              "(raw array, Teuchos::ArrayView, or Kokkos::View) "
                                                              "of global indices."
                 << endl;
      if (verbose) {
        using ::Tpetra::Details::gathervPrint;
        gathervPrint(gblErrStrm, lclErrStrm.str(), *comm);
      }
      TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, gblErrStrm.str());
    }
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class ViewType>
void computeConstantsOnDevice(const ViewType& entryList, GlobalOrdinal& minMyGID, GlobalOrdinal& maxMyGID, GlobalOrdinal& firstContiguousGID, GlobalOrdinal& lastContiguousGID_val, LocalOrdinal& lastContiguousGID_loc) {
  using LO                  = LocalOrdinal;
  using GO                  = GlobalOrdinal;
  using exec_space          = typename ViewType::device_type::execution_space;
  using range_policy        = Kokkos::RangePolicy<exec_space, Kokkos::IndexType<LO>>;
  const LO numLocalElements = entryList.extent(0);
 
  // We're going to use the minloc backwards because we need to have it sort on the "location" and have the "value" along for the
  // ride, rather than the other way around
  typedef typename Kokkos::MinLoc<LO, GO>::value_type minloc_type;
  minloc_type myMinLoc;
 
  // Find the initial sequence of parallel gids
  // To find the lastContiguousGID_, we find the first guy where entryList[i] - entryList[0] != i-0.  That's the first non-contiguous guy.
  // We want the one *before* that guy.
  Kokkos::parallel_reduce(
      range_policy(0, numLocalElements), KOKKOS_LAMBDA(const LO& i, GO& l_myMin, GO& l_myMax, GO& l_firstCont, minloc_type& l_lastCont) {
        GO entry_0 = entryList[0];
        GO entry_i = entryList[i];
 
        // Easy stuff
        l_myMin     = (l_myMin < entry_i) ? l_myMin : entry_i;
        l_myMax     = (l_myMax > entry_i) ? l_myMax : entry_i;
        l_firstCont = entry_0;
 
        if (entry_i - entry_0 != i && l_lastCont.val >= i) {
          // We're non-contiguous, so the guy before us could be the last contiguous guy
          l_lastCont.val = i - 1;
          l_lastCont.loc = entryList[i - 1];
        } else if (i == numLocalElements - 1 && i < l_lastCont.val) {
          // If we're last, we always think we're the last contiguous guy, unless someone non-contiguous is already here
          l_lastCont.val = i;
          l_lastCont.loc = entry_i;
        }
      },
      Kokkos::Min<GO>(minMyGID), Kokkos::Max<GO>(maxMyGID), Kokkos::Min<GO>(firstContiguousGID), Kokkos::MinLoc<LO, GO>(myMinLoc));
 
  // This switch is intentional, since we're using MinLoc backwards
  lastContiguousGID_val = myMinLoc.loc;
  lastContiguousGID_loc = myMinLoc.val;
}
 
}  // namespace
 
namespace Tpetra {
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Map<LocalOrdinal, GlobalOrdinal, Node>::
    Map()
  : comm_(new Teuchos::SerialComm<int>())
  , indexBase_(0)
  , numGlobalElements_(0)
  , numLocalElements_(0)
  , minMyGID_(Tpetra::Details::OrdinalTraits<GlobalOrdinal>::invalid())
  , maxMyGID_(Tpetra::Details::OrdinalTraits<GlobalOrdinal>::invalid())
  , minAllGID_(Tpetra::Details::OrdinalTraits<GlobalOrdinal>::invalid())
  , maxAllGID_(Tpetra::Details::OrdinalTraits<GlobalOrdinal>::invalid())
  , firstContiguousGID_(Tpetra::Details::OrdinalTraits<GlobalOrdinal>::invalid())
  , lastContiguousGID_(Tpetra::Details::OrdinalTraits<GlobalOrdinal>::invalid())
  , uniform_(false)
  ,  // trivially
  contiguous_(false)
  , distributed_(false)
  ,  // no communicator yet
  directory_(new Directory<LocalOrdinal, GlobalOrdinal, Node>()) {
  Tpetra::Details::initializeKokkos();
  Tpetra::Details::Behavior::reject_unrecognized_env_vars();
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Map<LocalOrdinal, GlobalOrdinal, Node>::
    Map(const global_size_t numGlobalElements,
        const global_ordinal_type indexBase,
        const Teuchos::RCP<const Teuchos::Comm<int>>& comm,
        const LocalGlobal lOrG)
  : comm_(comm)
  , uniform_(true)
  , directory_(new Directory<LocalOrdinal, GlobalOrdinal, Node>()) {
  using std::endl;
  using Teuchos::as;
  using Teuchos::broadcast;
  using Teuchos::outArg;
  using Teuchos::REDUCE_MAX;
  using Teuchos::REDUCE_MIN;
  using Teuchos::reduceAll;
  using Teuchos::typeName;
  using GO              = global_ordinal_type;
  using GST             = global_size_t;
  const GST GSTI        = Tpetra::Details::OrdinalTraits<GST>::invalid();
  const char funcName[] = "Map(gblNumInds,indexBase,comm,LG)";
  const char exPfx[] =
      "Tpetra::Map::Map(gblNumInds,indexBase,comm,LG): ";
 
  const bool debug   = Details::Behavior::debug("Map");
  const bool verbose = Details::Behavior::verbose("Map");
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(
        comm_.getRawPtr(), "Map", funcName);
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    std::cerr << os.str();
  }
  Tpetra::Details::initializeKokkos();
  Tpetra::Details::Behavior::reject_unrecognized_env_vars();
 
  // In debug mode only, check whether numGlobalElements and
  // indexBase are the same over all processes in the communicator.
  if (debug) {
    GST proc0NumGlobalElements = numGlobalElements;
    broadcast(*comm_, 0, outArg(proc0NumGlobalElements));
    GST minNumGlobalElements = numGlobalElements;
    GST maxNumGlobalElements = numGlobalElements;
    reduceAll(*comm, REDUCE_MIN, numGlobalElements,
              outArg(minNumGlobalElements));
    reduceAll(*comm, REDUCE_MAX, numGlobalElements,
              outArg(maxNumGlobalElements));
    TEUCHOS_TEST_FOR_EXCEPTION(minNumGlobalElements != maxNumGlobalElements ||
                                   numGlobalElements != minNumGlobalElements,
                               std::invalid_argument, exPfx << "All processes must "
                                                               "provide the same number of global elements.  Process 0 set "
                                                               "numGlobalElements="
                                                            << proc0NumGlobalElements << ".  The "
                                                                                         "calling process "
                                                            << comm->getRank() << " set "
                                                                                  "numGlobalElements="
                                                            << numGlobalElements << ".  The min "
                                                                                    "and max values over all processes are "
                                                            << minNumGlobalElements << " resp. " << maxNumGlobalElements << ".");
 
    GO proc0IndexBase = indexBase;
    broadcast<int, GO>(*comm_, 0, outArg(proc0IndexBase));
    GO minIndexBase = indexBase;
    GO maxIndexBase = indexBase;
    reduceAll(*comm, REDUCE_MIN, indexBase, outArg(minIndexBase));
    reduceAll(*comm, REDUCE_MAX, indexBase, outArg(maxIndexBase));
    TEUCHOS_TEST_FOR_EXCEPTION(minIndexBase != maxIndexBase || indexBase != minIndexBase,
                               std::invalid_argument, exPfx << "All processes must "
                                                               "provide the same indexBase argument.  Process 0 set "
                                                               "indexBase="
                                                            << proc0IndexBase << ".  The calling process " << comm->getRank() << " set indexBase=" << indexBase << ".  The min and max values over all processes are " << minIndexBase << " resp. " << maxIndexBase << ".");
  }
 
  // Distribute the elements across the processes in the given
  // communicator so that global IDs (GIDs) are
  //
  // - Nonoverlapping (only one process owns each GID)
  // - Contiguous (the sequence of GIDs is nondecreasing, and no two
  //   adjacent GIDs differ by more than one)
  // - As evenly distributed as possible (the numbers of GIDs on two
  //   different processes do not differ by more than one)
 
  // All processes have the same numGlobalElements, but we still
  // need to check that it is valid.  numGlobalElements must be
  // positive and not the "invalid" value (GSTI).
  //
  // This comparison looks funny, but it avoids compiler warnings
  // for comparing unsigned integers (numGlobalElements_in is a
  // GST, which is unsigned) while still working if we
  // later decide to make GST signed.
  TEUCHOS_TEST_FOR_EXCEPTION(
      (numGlobalElements < 1 && numGlobalElements != 0),
      std::invalid_argument, exPfx << "numGlobalElements (= " << numGlobalElements << ") must be nonnegative.");
 
  TEUCHOS_TEST_FOR_EXCEPTION(numGlobalElements == GSTI, std::invalid_argument, exPfx << "You provided numGlobalElements = Teuchos::OrdinalTraits<"
                                                                                        "Tpetra::global_size_t>::invalid().  This version of the "
                                                                                        "constructor requires a valid value of numGlobalElements.  "
                                                                                        "You probably mistook this constructor for the \"contiguous "
                                                                                        "nonuniform\" constructor, which can compute the global "
                                                                                        "number of elements for you if you set numGlobalElements to "
                                                                                        "Teuchos::OrdinalTraits<Tpetra::global_size_t>::invalid().");
 
  size_t numLocalElements = 0;  // will set below
  if (lOrG == GloballyDistributed) {
    // Compute numLocalElements:
    //
    // If numGlobalElements == numProcs * B + remainder,
    // then Proc r gets B+1 elements if r < remainder,
    // and B elements if r >= remainder.
    //
    // This strategy is valid for any value of numGlobalElements and
    // numProcs, including the following border cases:
    //   - numProcs == 1
    //   - numLocalElements < numProcs
    //
    // In the former case, remainder == 0 && numGlobalElements ==
    // numLocalElements.  In the latter case, remainder ==
    // numGlobalElements && numLocalElements is either 0 or 1.
    const GST numProcs  = static_cast<GST>(comm_->getSize());
    const GST myRank    = static_cast<GST>(comm_->getRank());
    const GST quotient  = numGlobalElements / numProcs;
    const GST remainder = numGlobalElements - quotient * numProcs;
 
    GO startIndex;
    if (myRank < remainder) {
      numLocalElements = static_cast<size_t>(1) + static_cast<size_t>(quotient);
      // myRank was originally an int, so it should never overflow
      // reasonable GO types.
      startIndex = as<GO>(myRank) * as<GO>(numLocalElements);
    } else {
      numLocalElements = as<size_t>(quotient);
      startIndex       = as<GO>(myRank) * as<GO>(numLocalElements) +
                   as<GO>(remainder);
    }
 
    minMyGID_    = indexBase + startIndex;
    maxMyGID_    = indexBase + startIndex + numLocalElements - 1;
    minAllGID_   = indexBase;
    maxAllGID_   = indexBase + numGlobalElements - 1;
    distributed_ = (numProcs > 1);
  } else {  // lOrG == LocallyReplicated
    numLocalElements = as<size_t>(numGlobalElements);
    minMyGID_        = indexBase;
    maxMyGID_        = indexBase + numGlobalElements - 1;
    distributed_     = false;
  }
 
  minAllGID_          = indexBase;
  maxAllGID_          = indexBase + numGlobalElements - 1;
  indexBase_          = indexBase;
  numGlobalElements_  = numGlobalElements;
  numLocalElements_   = numLocalElements;
  firstContiguousGID_ = minMyGID_;
  lastContiguousGID_  = maxMyGID_;
  contiguous_         = true;
 
  // Create the Directory on demand in getRemoteIndexList().
  // setupDirectory ();
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done" << endl;
    std::cerr << os.str();
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Map<LocalOrdinal, GlobalOrdinal, Node>::
    Map(const global_size_t numGlobalElements,
        const size_t numLocalElements,
        const global_ordinal_type indexBase,
        const Teuchos::RCP<const Teuchos::Comm<int>>& comm)
  : comm_(comm)
  , uniform_(false)
  , directory_(new Directory<LocalOrdinal, GlobalOrdinal, Node>()) {
  using std::endl;
  using Teuchos::as;
  using Teuchos::broadcast;
  using Teuchos::outArg;
  using Teuchos::REDUCE_MAX;
  using Teuchos::REDUCE_MIN;
  using Teuchos::REDUCE_SUM;
  using Teuchos::reduceAll;
  using Teuchos::scan;
  using GO       = global_ordinal_type;
  using GST      = global_size_t;
  const GST GSTI = Tpetra::Details::OrdinalTraits<GST>::invalid();
  const char funcName[] =
      "Map(gblNumInds,lclNumInds,indexBase,comm)";
  const char exPfx[] =
      "Tpetra::Map::Map(gblNumInds,lclNumInds,indexBase,comm): ";
  const char suffix[] =
      ".  Please report this bug to the Tpetra developers.";
 
  const bool debug   = Details::Behavior::debug("Map");
  const bool verbose = Details::Behavior::verbose("Map");
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(
        comm_.getRawPtr(), "Map", funcName);
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    std::cerr << os.str();
  }
  Tpetra::Details::initializeKokkos();
  Tpetra::Details::Behavior::reject_unrecognized_env_vars();
 
  // Global sum of numLocalElements over all processes.
  // Keep this for later debug checks.
  GST debugGlobalSum{};
  if (debug) {
    debugGlobalSum = initialNonuniformDebugCheck(exPfx,
                                                 numGlobalElements, numLocalElements, indexBase, comm);
  }
 
  // Distribute the elements across the nodes so that they are
  // - non-overlapping
  // - contiguous
 
  // This differs from the first Map constructor (that only takes a
  // global number of elements) in that the user has specified the
  // number of local elements, so that the elements are not
  // (necessarily) evenly distributed over the processes.
 
  // Compute my local offset.  This is an inclusive scan, so to get
  // the final offset, we subtract off the input.
  GO scanResult = 0;
  scan<int, GO>(*comm, REDUCE_SUM, numLocalElements, outArg(scanResult));
  const GO myOffset = scanResult - numLocalElements;
 
  if (numGlobalElements != GSTI) {
    numGlobalElements_ = numGlobalElements;  // Use the user's value.
  } else {
    // Inclusive scan means that the last process has the final sum.
    // Rather than doing a reduceAll to get the sum of
    // numLocalElements, we can just have the last process broadcast
    // its result.  That saves us a round of log(numProcs) messages.
    const int numProcs = comm->getSize();
    GST globalSum      = scanResult;
    if (numProcs > 1) {
      broadcast(*comm, numProcs - 1, outArg(globalSum));
    }
    numGlobalElements_ = globalSum;
 
    if (debug) {
      // No need for an all-reduce here; both come from collectives.
      TEUCHOS_TEST_FOR_EXCEPTION(globalSum != debugGlobalSum, std::logic_error, exPfx << "globalSum = " << globalSum << " != debugGlobalSum = " << debugGlobalSum << suffix);
    }
  }
  numLocalElements_   = numLocalElements;
  indexBase_          = indexBase;
  minAllGID_          = (numGlobalElements_ == 0) ? std::numeric_limits<GO>::max() : indexBase;
  maxAllGID_          = (numGlobalElements_ == 0) ? std::numeric_limits<GO>::lowest() : indexBase + GO(numGlobalElements_) - GO(1);
  minMyGID_           = (numLocalElements_ == 0) ? std::numeric_limits<GO>::max() : indexBase + GO(myOffset);
  maxMyGID_           = (numLocalElements_ == 0) ? std::numeric_limits<GO>::lowest() : indexBase + myOffset + GO(numLocalElements) - GO(1);
  firstContiguousGID_ = minMyGID_;
  lastContiguousGID_  = maxMyGID_;
  contiguous_         = true;
  distributed_        = checkIsDist();
 
  // Create the Directory on demand in getRemoteIndexList().
  // setupDirectory ();
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done" << endl;
    std::cerr << os.str();
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
global_size_t
Map<LocalOrdinal, GlobalOrdinal, Node>::
    initialNonuniformDebugCheck(
        const char errorMessagePrefix[],
        const global_size_t numGlobalElements,
        const size_t numLocalElements,
        const global_ordinal_type indexBase,
        const Teuchos::RCP<const Teuchos::Comm<int>>& comm) const {
  const bool debug = Details::Behavior::debug("Map");
  if (!debug) {
    return global_size_t(0);
  }
 
  using Teuchos::broadcast;
  using Teuchos::outArg;
  using Teuchos::ptr;
  using Teuchos::REDUCE_MAX;
  using Teuchos::REDUCE_MIN;
  using Teuchos::REDUCE_SUM;
  using Teuchos::reduceAll;
  using GO       = global_ordinal_type;
  using GST      = global_size_t;
  const GST GSTI = Tpetra::Details::OrdinalTraits<GST>::invalid();
 
  // The user has specified the distribution of indices over the
  // processes.  The distribution is not necessarily contiguous or
  // equally shared over the processes.
  //
  // We assume that the number of local elements can be stored in a
  // size_t.  The instance member numLocalElements_ is a size_t, so
  // this variable and that should have the same type.
 
  GST debugGlobalSum = 0;  // Will be global sum of numLocalElements
  reduceAll<int, GST>(*comm, REDUCE_SUM, static_cast<GST>(numLocalElements),
                      outArg(debugGlobalSum));
  // In debug mode only, check whether numGlobalElements and
  // indexBase are the same over all processes in the communicator.
  {
    GST proc0NumGlobalElements = numGlobalElements;
    broadcast<int, GST>(*comm_, 0, outArg(proc0NumGlobalElements));
    GST minNumGlobalElements = numGlobalElements;
    GST maxNumGlobalElements = numGlobalElements;
    reduceAll<int, GST>(*comm, REDUCE_MIN, numGlobalElements,
                        outArg(minNumGlobalElements));
    reduceAll<int, GST>(*comm, REDUCE_MAX, numGlobalElements,
                        outArg(maxNumGlobalElements));
    TEUCHOS_TEST_FOR_EXCEPTION(minNumGlobalElements != maxNumGlobalElements ||
                                   numGlobalElements != minNumGlobalElements,
                               std::invalid_argument, errorMessagePrefix << "All processes "
                                                                            "must provide the same number of global elements, even if "
                                                                            "that argument is "
                                                                            "Teuchos::OrdinalTraits<Tpetra::global_size_t>::invalid() "
                                                                            "(which signals that the Map should compute the global "
                                                                            "number of elements).  Process 0 set numGlobalElements"
                                                                            "="
                                                                         << proc0NumGlobalElements << ".  The calling process " << comm->getRank() << " set numGlobalElements=" << numGlobalElements << ".  The min and max values over all "
                                                                                                                                                                                                        "processes are "
                                                                         << minNumGlobalElements << " resp. " << maxNumGlobalElements << ".");
 
    GO proc0IndexBase = indexBase;
    broadcast<int, GO>(*comm_, 0, outArg(proc0IndexBase));
    GO minIndexBase = indexBase;
    GO maxIndexBase = indexBase;
    reduceAll<int, GO>(*comm, REDUCE_MIN, indexBase, outArg(minIndexBase));
    reduceAll<int, GO>(*comm, REDUCE_MAX, indexBase, outArg(maxIndexBase));
    TEUCHOS_TEST_FOR_EXCEPTION(minIndexBase != maxIndexBase || indexBase != minIndexBase,
                               std::invalid_argument, errorMessagePrefix << "All processes must provide the same indexBase argument.  "
                                                                            "Process 0 set indexBase = "
                                                                         << proc0IndexBase << ".  The "
                                                                                              "calling process "
                                                                         << comm->getRank() << " set indexBase=" << indexBase << ".  The min and max values over all "
                                                                                                                                 "processes are "
                                                                         << minIndexBase << " resp. " << maxIndexBase << ".");
 
    // Make sure that the sum of numLocalElements over all processes
    // equals numGlobalElements.
    TEUCHOS_TEST_FOR_EXCEPTION(numGlobalElements != GSTI &&
                                   debugGlobalSum != numGlobalElements,
                               std::invalid_argument,
                               errorMessagePrefix << "The sum of each process' number of "
                                                     "indices over all processes, "
                                                  << debugGlobalSum << ", != "
                                                  << "numGlobalElements=" << numGlobalElements << ".  If you "
                                                                                                  "would like this constructor to compute numGlobalElements "
                                                                                                  "for you, you may set numGlobalElements="
                                                                                                  "Teuchos::OrdinalTraits<Tpetra::global_size_t>::invalid() "
                                                                                                  "on input.  Please note that this is NOT necessarily -1.");
  }
  return debugGlobalSum;
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
void Map<LocalOrdinal, GlobalOrdinal, Node>::
    initWithNonownedHostIndexList(
        const char errorMessagePrefix[],
        const global_size_t numGlobalElements,
        const Kokkos::View<const global_ordinal_type*,
                           Kokkos::LayoutLeft,
                           Kokkos::HostSpace,
                           Kokkos::MemoryUnmanaged>& entryList_host,
        const global_ordinal_type indexBase,
        const Teuchos::RCP<const Teuchos::Comm<int>>& comm) {
  Tpetra::Details::ProfilingRegion pr("Map::initWithNonownedHostIndexList()");
 
  using Kokkos::LayoutLeft;
  using Kokkos::subview;
  using Kokkos::View;
  using Kokkos::view_alloc;
  using Kokkos::WithoutInitializing;
  using Teuchos::as;
  using Teuchos::broadcast;
  using Teuchos::outArg;
  using Teuchos::ptr;
  using Teuchos::REDUCE_MAX;
  using Teuchos::REDUCE_MIN;
  using Teuchos::REDUCE_SUM;
  using Teuchos::reduceAll;
  using LO       = local_ordinal_type;
  using GO       = global_ordinal_type;
  using GST      = global_size_t;
  const GST GSTI = Tpetra::Details::OrdinalTraits<GST>::invalid();
  // Make sure that Kokkos has been initialized (Github Issue #513).
  TEUCHOS_TEST_FOR_EXCEPTION(!Kokkos::is_initialized(), std::runtime_error,
                             errorMessagePrefix << "The Kokkos execution space "
                                                << Teuchos::TypeNameTraits<execution_space>::name()
                                                << " has not been initialized.  "
                                                   "Please initialize it before creating a Map.")
 
  // The user has specified the distribution of indices over the
  // processes, via the input array of global indices on each
  // process.  The distribution is not necessarily contiguous or
  // equally shared over the processes.
 
  // The length of the input array on this process is the number of
  // local indices to associate with this process, even though the
  // input array contains global indices.  We assume that the number
  // of local indices on a process can be stored in a size_t;
  // numLocalElements_ is a size_t, so this variable and that should
  // have the same type.
  const size_t numLocalElements(entryList_host.size());
 
  initialNonuniformDebugCheck(errorMessagePrefix, numGlobalElements,
                              numLocalElements, indexBase, comm);
 
  // NOTE (mfh 20 Feb 2013, 10 Oct 2016) In some sense, this global
  // reduction is redundant, since the directory Map will have to do
  // the same thing.  Thus, we could do the scan and broadcast for
  // the directory Map here, and give the computed offsets to the
  // directory Map's constructor.  However, a reduction costs less
  // than a scan and broadcast, so this still saves time if users of
  // this Map don't ever need the Directory (i.e., if they never
  // call getRemoteIndexList on this Map).
  if (numGlobalElements != GSTI) {
    numGlobalElements_ = numGlobalElements;  // Use the user's value.
  } else {                                   // The user wants us to compute the sum.
    reduceAll(*comm, REDUCE_SUM,
              static_cast<GST>(numLocalElements),
              outArg(numGlobalElements_));
  }
 
  // mfh 20 Feb 2013: We've never quite done the right thing for
  // duplicate GIDs here.  Duplicate GIDs have always been counted
  // distinctly in numLocalElements_, and thus should get a
  // different LID.  However, we've always used std::map or a hash
  // table for the GID -> LID lookup table, so distinct GIDs always
  // map to the same LID.  Furthermore, the order of the input GID
  // list matters, so it's not desirable to sort for determining
  // uniqueness.
  //
  // I've chosen for now to write this code as if the input GID list
  // contains no duplicates.  If this is not desired, we could use
  // the lookup table itself to determine uniqueness: If we haven't
  // seen the GID before, it gets a new LID and it's added to the
  // LID -> GID and GID -> LID tables.  If we have seen the GID
  // before, it doesn't get added to either table.  I would
  // implement this, but it would cost more to do the double lookups
  // in the table (one to check, and one to insert).
  //
  // More importantly, since we build the GID -> LID table in (a
  // thread-) parallel (way), the order in which duplicate GIDs may
  // get inserted is not defined.  This would make the assignment of
  // LID to GID nondeterministic.
 
  numLocalElements_ = numLocalElements;
  indexBase_        = indexBase;
 
  minMyGID_ = indexBase_;
  maxMyGID_ = indexBase_;
 
  // NOTE (mfh 27 May 2015): While finding the initial contiguous
  // GID range requires looking at all the GIDs in the range,
  // dismissing an interval of GIDs only requires looking at the
  // first and last GIDs.  Thus, we could do binary search backwards
  // from the end in order to catch the common case of a contiguous
  // interval followed by noncontiguous entries.  On the other hand,
  // we could just expose this case explicitly as yet another Map
  // constructor, and avoid the trouble of detecting it.
  if (numLocalElements_ > 0) {
    // Find contiguous GID range, with the restriction that the
    // beginning of the range starts with the first entry.  While
    // doing so, fill in the LID -> GID table.
    typename decltype(lgMap_)::non_const_type lgMap(view_alloc("lgMap", WithoutInitializing), numLocalElements_);
    auto lgMap_host =
        Kokkos::create_mirror_view(Kokkos::HostSpace(), lgMap);
 
    // The input array entryList_host is already on host, so we
    // don't need to take a host view of it.
    // auto entryList_host =
    //   Kokkos::create_mirror_view (Kokkos::HostSpace (), entryList);
    // Kokkos::deep_copy (entryList_host, entryList);
 
    firstContiguousGID_ = entryList_host[0];
    lastContiguousGID_  = firstContiguousGID_ + 1;
 
    // FIXME (mfh 23 Sep 2015) We need to copy the input GIDs
    // anyway, so we have to look at them all.  The logical way to
    // find the first noncontiguous entry would thus be to "reduce,"
    // where the local reduction result is whether entryList[i] + 1
    // == entryList[i+1].
 
    lgMap_host[0] = firstContiguousGID_;
    size_t i      = 1;
    for (; i < numLocalElements_; ++i) {
      const GO curGid = entryList_host[i];
      const LO curLid = as<LO>(i);
 
      if (lastContiguousGID_ != curGid) break;
 
      // Add the entry to the LID->GID table only after we know that
      // the current GID is in the initial contiguous sequence, so
      // that we don't repeat adding it in the first iteration of
      // the loop below over the remaining noncontiguous GIDs.
      lgMap_host[curLid] = curGid;
      ++lastContiguousGID_;
    }
    --lastContiguousGID_;
    // NOTE: i is the first non-contiguous index.
 
    // [firstContiguousGID_, lastContigousGID_] is the initial
    // sequence of contiguous GIDs.  We can start the min and max
    // GID using this range.
    minMyGID_ = firstContiguousGID_;
    maxMyGID_ = lastContiguousGID_;
 
    // Compute the GID -> LID lookup table, _not_ including the
    // initial sequence of contiguous GIDs.
    LO firstNonContiguous_loc = i;
    {
      const std::pair<size_t, size_t> ncRange(i, entryList_host.extent(0));
      auto nonContigGids_host = subview(entryList_host, ncRange);
      TEUCHOS_TEST_FOR_EXCEPTION(static_cast<size_t>(nonContigGids_host.extent(0)) !=
                                     static_cast<size_t>(entryList_host.extent(0) - i),
                                 std::logic_error,
                                 "Tpetra::Map noncontiguous constructor: "
                                 "nonContigGids_host.extent(0) = "
                                     << nonContigGids_host.extent(0)
                                     << " != entryList_host.extent(0) - i = "
                                     << (entryList_host.extent(0) - i) << " = "
                                     << entryList_host.extent(0) << " - " << i
                                     << ".  Please report this bug to the Tpetra developers.");
 
      // FixedHashTable's constructor expects an owned device View,
      // so we must deep-copy the subview of the input indices.
      View<GO*, LayoutLeft, device_type>
          nonContigGids(view_alloc("nonContigGids", WithoutInitializing),
                        nonContigGids_host.size());
 
      // DEEP_COPY REVIEW - HOST-TO-DEVICE
      Kokkos::deep_copy(execution_space(), nonContigGids, nonContigGids_host);
      Kokkos::fence("Map::initWithNonownedHostIndexList");  // for UVM issues below - which will be refatored soon so FixedHashTable can build as pure CudaSpace - then I think remove this fence
 
      glMap_ = global_to_local_table_type(nonContigGids,
                                          firstNonContiguous_loc);
      // Make host version - when memory spaces match these just do trivial assignment
      glMapHost_ = global_to_local_table_host_type(glMap_);
    }
 
    // FIXME (mfh 10 Oct 2016) When we construct the global-to-local
    // table above, we have to look at all the (noncontiguous) input
    // indices anyway.  Thus, why not have the constructor compute
    // and return the min and max?
 
    for (; i < numLocalElements_; ++i) {
      const GO curGid    = entryList_host[i];
      const LO curLid    = static_cast<LO>(i);
      lgMap_host[curLid] = curGid;  // LID -> GID table
 
      // While iterating through entryList, we compute its
      // (process-local) min and max elements.
      if (curGid < minMyGID_) {
        minMyGID_ = curGid;
      }
      if (curGid > maxMyGID_) {
        maxMyGID_ = curGid;
      }
    }
 
    // We filled lgMap on host above; now sync back to device.
    // DEEP_COPY REVIEW - HOST-TO-DEVICE
    Kokkos::deep_copy(execution_space(), lgMap, lgMap_host);
 
    // "Commit" the local-to-global lookup table we filled in above.
    lgMap_ = lgMap;
    // We've already created this, so use it.
    lgMapHost_ = lgMap_host;
 
  } else {
    minMyGID_ = std::numeric_limits<GlobalOrdinal>::max();
    maxMyGID_ = std::numeric_limits<GlobalOrdinal>::lowest();
    // This insures tests for GIDs in the range
    // [firstContiguousGID_, lastContiguousGID_] fail for processes
    // with no local elements.
    firstContiguousGID_ = indexBase_ + 1;
    lastContiguousGID_  = indexBase_;
    // glMap_ was default constructed, so it's already empty.
  }
 
  // Compute the min and max of all processes' GIDs.  If
  // numLocalElements_ == 0 on this process, minMyGID_ and maxMyGID_
  // are both indexBase_.  This is wrong, but fixing it would
  // require either a fancy sparse all-reduce, or a custom reduction
  // operator that ignores invalid values ("invalid" means
  // Tpetra::Details::OrdinalTraits<GO>::invalid()).
  //
  // Also, while we're at it, use the same all-reduce to figure out
  // if the Map is distributed.  "Distributed" means that there is
  // at least one process with a number of local elements less than
  // the number of global elements.
  //
  // We're computing the min and max of all processes' GIDs using a
  // single MAX all-reduce, because min(x,y) = -max(-x,-y) (when x
  // and y are signed).  (This lets us combine the min and max into
  // a single all-reduce.)  If each process sets localDist=1 if its
  // number of local elements is strictly less than the number of
  // global elements, and localDist=0 otherwise, then a MAX
  // all-reduce on localDist tells us if the Map is distributed (1
  // if yes, 0 if no).  Thus, we can append localDist onto the end
  // of the data and get the global result from the all-reduce.
  if (std::numeric_limits<GO>::is_signed) {
    // Does my process NOT own all the elements?
    const GO localDist =
        (as<GST>(numLocalElements_) < numGlobalElements_) ? 1 : 0;
 
    GO minMaxInput[3];
    minMaxInput[0] = -minMyGID_;
    minMaxInput[1] = maxMyGID_;
    minMaxInput[2] = localDist;
 
    GO minMaxOutput[3];
    minMaxOutput[0] = 0;
    minMaxOutput[1] = 0;
    minMaxOutput[2] = 0;
    reduceAll<int, GO>(*comm, REDUCE_MAX, 3, minMaxInput, minMaxOutput);
    minAllGID_          = -minMaxOutput[0];
    maxAllGID_          = minMaxOutput[1];
    const GO globalDist = minMaxOutput[2];
    distributed_        = (comm_->getSize() > 1 && globalDist == 1);
  } else {  // unsigned; use two reductions
    // This is always correct, no matter the signedness of GO.
    reduceAll<int, GO>(*comm_, REDUCE_MIN, minMyGID_, outArg(minAllGID_));
    reduceAll<int, GO>(*comm_, REDUCE_MAX, maxMyGID_, outArg(maxAllGID_));
    distributed_ = checkIsDist();
  }
 
  contiguous_ = false;  // "Contiguous" is conservative.
 
  TEUCHOS_TEST_FOR_EXCEPTION(
      minAllGID_ < indexBase_,
      std::invalid_argument,
      "Tpetra::Map constructor (noncontiguous): "
      "Minimum global ID = "
          << minAllGID_ << " over all process(es) is "
                           "less than the given indexBase = "
          << indexBase_ << ".");
 
  // Create the Directory on demand in getRemoteIndexList().
  // setupDirectory ();
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Map<LocalOrdinal, GlobalOrdinal, Node>::
    Map(const global_size_t numGlobalElements,
        const GlobalOrdinal indexList[],
        const LocalOrdinal indexListSize,
        const GlobalOrdinal indexBase,
        const Teuchos::RCP<const Teuchos::Comm<int>>& comm)
  : comm_(comm)
  , uniform_(false)
  , directory_(new Directory<LocalOrdinal, GlobalOrdinal, Node>()) {
  using std::endl;
  const char funcName[] =
      "Map(gblNumInds,indexList,indexListSize,indexBase,comm)";
 
  const bool verbose = Details::Behavior::verbose("Map");
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(
        comm_.getRawPtr(), "Map", funcName);
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    std::cerr << os.str();
  }
  Tpetra::Details::initializeKokkos();
  Tpetra::Details::Behavior::reject_unrecognized_env_vars();
  Tpetra::Details::ProfilingRegion pr(funcName);
  checkMapInputArray("(GST, const GO[], LO, GO, comm)",
                     indexList, static_cast<size_t>(indexListSize),
                     comm.getRawPtr());
  // Not quite sure if I trust all code to behave correctly if the
  // pointer is nonnull but the array length is nonzero, so I'll
  // make sure the raw pointer is null if the length is zero.
  const GlobalOrdinal* const indsRaw = indexListSize == 0 ? NULL : indexList;
  Kokkos::View<const GlobalOrdinal*,
               Kokkos::LayoutLeft,
               Kokkos::HostSpace,
               Kokkos::MemoryUnmanaged>
      inds(indsRaw, indexListSize);
  initWithNonownedHostIndexList(funcName, numGlobalElements, inds,
                                indexBase, comm);
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done" << endl;
    std::cerr << os.str();
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Map<LocalOrdinal, GlobalOrdinal, Node>::
    Map(const global_size_t numGlobalElements,
        const Teuchos::ArrayView<const GlobalOrdinal>& entryList,
        const GlobalOrdinal indexBase,
        const Teuchos::RCP<const Teuchos::Comm<int>>& comm)
  : comm_(comm)
  , uniform_(false)
  , directory_(new Directory<LocalOrdinal, GlobalOrdinal, Node>()) {
  using std::endl;
  const char* funcName = "Map(gblNumInds,entryList(Teuchos::ArrayView),indexBase,comm)";
 
  const bool verbose = Details::Behavior::verbose("Map");
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(
        comm_.getRawPtr(), "Map", funcName);
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    std::cerr << os.str();
  }
  Tpetra::Details::initializeKokkos();
  Tpetra::Details::Behavior::reject_unrecognized_env_vars();
  Tpetra::Details::ProfilingRegion pr(funcName);
  const size_t numLclInds = static_cast<size_t>(entryList.size());
  checkMapInputArray("(GST, ArrayView, GO, comm)",
                     entryList.getRawPtr(), numLclInds,
                     comm.getRawPtr());
  // Not quite sure if I trust both ArrayView and View to behave
  // correctly if the pointer is nonnull but the array length is
  // nonzero, so I'll make sure it's null if the length is zero.
  const GlobalOrdinal* const indsRaw =
      numLclInds == 0 ? NULL : entryList.getRawPtr();
  Kokkos::View<const GlobalOrdinal*,
               Kokkos::LayoutLeft,
               Kokkos::HostSpace,
               Kokkos::MemoryUnmanaged>
      inds(indsRaw, numLclInds);
  initWithNonownedHostIndexList(funcName, numGlobalElements, inds,
                                indexBase, comm);
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done" << endl;
    std::cerr << os.str();
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Map<LocalOrdinal, GlobalOrdinal, Node>::
    Map(const global_size_t numGlobalElements,
        const Kokkos::View<const GlobalOrdinal*, device_type>& entryList,
        const GlobalOrdinal indexBase,
        const Teuchos::RCP<const Teuchos::Comm<int>>& comm)
  : comm_(comm)
  , uniform_(false)
  , directory_(new Directory<LocalOrdinal, GlobalOrdinal, Node>()) {
  using Kokkos::LayoutLeft;
  using Kokkos::subview;
  using Kokkos::View;
  using Kokkos::view_alloc;
  using Kokkos::WithoutInitializing;
  using std::endl;
  using Teuchos::arcp;
  using Teuchos::ArrayView;
  using Teuchos::as;
  using Teuchos::broadcast;
  using Teuchos::outArg;
  using Teuchos::ptr;
  using Teuchos::REDUCE_MAX;
  using Teuchos::REDUCE_MIN;
  using Teuchos::REDUCE_SUM;
  using Teuchos::reduceAll;
  using Teuchos::typeName;
  using LO       = local_ordinal_type;
  using GO       = global_ordinal_type;
  using GST      = global_size_t;
  const GST GSTI = Tpetra::Details::OrdinalTraits<GST>::invalid();
  const char funcName[] =
      "Map(gblNumInds,entryList(Kokkos::View),indexBase,comm)";
 
  const bool verbose = Details::Behavior::verbose("Map");
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(
        comm_.getRawPtr(), "Map", funcName);
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    std::cerr << os.str();
  }
  Tpetra::Details::initializeKokkos();
  Tpetra::Details::Behavior::reject_unrecognized_env_vars();
  Tpetra::Details::ProfilingRegion pr(funcName);
  checkMapInputArray("(GST, Kokkos::View, GO, comm)",
                     entryList.data(),
                     static_cast<size_t>(entryList.extent(0)),
                     comm.getRawPtr());
 
  // The user has specified the distribution of indices over the
  // processes, via the input array of global indices on each
  // process.  The distribution is not necessarily contiguous or
  // equally shared over the processes.
 
  // The length of the input array on this process is the number of
  // local indices to associate with this process, even though the
  // input array contains global indices.  We assume that the number
  // of local indices on a process can be stored in a size_t;
  // numLocalElements_ is a size_t, so this variable and that should
  // have the same type.
  const size_t numLocalElements(entryList.size());
 
  initialNonuniformDebugCheck(funcName, numGlobalElements,
                              numLocalElements, indexBase, comm);
 
  // NOTE (mfh 20 Feb 2013, 10 Oct 2016) In some sense, this global
  // reduction is redundant, since the directory Map will have to do
  // the same thing.  Thus, we could do the scan and broadcast for
  // the directory Map here, and give the computed offsets to the
  // directory Map's constructor.  However, a reduction costs less
  // than a scan and broadcast, so this still saves time if users of
  // this Map don't ever need the Directory (i.e., if they never
  // call getRemoteIndexList on this Map).
  if (numGlobalElements != GSTI) {
    numGlobalElements_ = numGlobalElements;  // Use the user's value.
  } else {                                   // The user wants us to compute the sum.
    reduceAll(*comm, REDUCE_SUM,
              static_cast<GST>(numLocalElements),
              outArg(numGlobalElements_));
  }
 
  // mfh 20 Feb 2013: We've never quite done the right thing for
  // duplicate GIDs here.  Duplicate GIDs have always been counted
  // distinctly in numLocalElements_, and thus should get a
  // different LID.  However, we've always used std::map or a hash
  // table for the GID -> LID lookup table, so distinct GIDs always
  // map to the same LID.  Furthermore, the order of the input GID
  // list matters, so it's not desirable to sort for determining
  // uniqueness.
  //
  // I've chosen for now to write this code as if the input GID list
  // contains no duplicates.  If this is not desired, we could use
  // the lookup table itself to determine uniqueness: If we haven't
  // seen the GID before, it gets a new LID and it's added to the
  // LID -> GID and GID -> LID tables.  If we have seen the GID
  // before, it doesn't get added to either table.  I would
  // implement this, but it would cost more to do the double lookups
  // in the table (one to check, and one to insert).
  //
  // More importantly, since we build the GID -> LID table in (a
  // thread-) parallel (way), the order in which duplicate GIDs may
  // get inserted is not defined.  This would make the assignment of
  // LID to GID nondeterministic.
 
  numLocalElements_ = numLocalElements;
  indexBase_        = indexBase;
 
  minMyGID_ = indexBase_;
  maxMyGID_ = indexBase_;
 
  // NOTE (mfh 27 May 2015): While finding the initial contiguous
  // GID range requires looking at all the GIDs in the range,
  // dismissing an interval of GIDs only requires looking at the
  // first and last GIDs.  Thus, we could do binary search backwards
  // from the end in order to catch the common case of a contiguous
  // interval followed by noncontiguous entries.  On the other hand,
  // we could just expose this case explicitly as yet another Map
  // constructor, and avoid the trouble of detecting it.
  if (numLocalElements_ > 0) {
    // Find contiguous GID range, with the restriction that the
    // beginning of the range starts with the first entry.  While
    // doing so, fill in the LID -> GID table.
    typename decltype(lgMap_)::non_const_type lgMap(view_alloc("lgMap", WithoutInitializing), numLocalElements_);
 
    // Because you can't use lambdas in constructors on CUDA.  Or using private/protected data.
    // DEEP_COPY REVIEW - DEVICE-TO-DEVICE
    Kokkos::deep_copy(typename device_type::execution_space(), lgMap, entryList);
    LO lastContiguousGID_loc;
    computeConstantsOnDevice(entryList, minMyGID_, maxMyGID_, firstContiguousGID_, lastContiguousGID_, lastContiguousGID_loc);
    LO firstNonContiguous_loc = lastContiguousGID_loc + 1;
    auto nonContigGids        = Kokkos::subview(entryList, std::pair<size_t, size_t>(firstNonContiguous_loc, entryList.extent(0)));
 
    // NOTE: We do not fill the glMapHost_ and lgMapHost_ views here.  They will be filled lazily later
    glMap_ = global_to_local_table_type(nonContigGids,
                                        firstNonContiguous_loc);
 
    // "Commit" the local-to-global lookup table we filled in above.
    lgMap_ = lgMap;
 
  } else {
    minMyGID_ = std::numeric_limits<GlobalOrdinal>::max();
    maxMyGID_ = std::numeric_limits<GlobalOrdinal>::lowest();
    // This insures tests for GIDs in the range
    // [firstContiguousGID_, lastContiguousGID_] fail for processes
    // with no local elements.
    firstContiguousGID_ = indexBase_ + 1;
    lastContiguousGID_  = indexBase_;
    // glMap_ was default constructed, so it's already empty.
  }
 
  // Compute the min and max of all processes' GIDs.  If
  // numLocalElements_ == 0 on this process, minMyGID_ and maxMyGID_
  // are both indexBase_.  This is wrong, but fixing it would
  // require either a fancy sparse all-reduce, or a custom reduction
  // operator that ignores invalid values ("invalid" means
  // Tpetra::Details::OrdinalTraits<GO>::invalid()).
  //
  // Also, while we're at it, use the same all-reduce to figure out
  // if the Map is distributed.  "Distributed" means that there is
  // at least one process with a number of local elements less than
  // the number of global elements.
  //
  // We're computing the min and max of all processes' GIDs using a
  // single MAX all-reduce, because min(x,y) = -max(-x,-y) (when x
  // and y are signed).  (This lets us combine the min and max into
  // a single all-reduce.)  If each process sets localDist=1 if its
  // number of local elements is strictly less than the number of
  // global elements, and localDist=0 otherwise, then a MAX
  // all-reduce on localDist tells us if the Map is distributed (1
  // if yes, 0 if no).  Thus, we can append localDist onto the end
  // of the data and get the global result from the all-reduce.
  if (std::numeric_limits<GO>::is_signed) {
    // Does my process NOT own all the elements?
    const GO localDist =
        (as<GST>(numLocalElements_) < numGlobalElements_) ? 1 : 0;
 
    GO minMaxInput[3];
    minMaxInput[0] = -minMyGID_;
    minMaxInput[1] = maxMyGID_;
    minMaxInput[2] = localDist;
 
    GO minMaxOutput[3];
    minMaxOutput[0] = 0;
    minMaxOutput[1] = 0;
    minMaxOutput[2] = 0;
    reduceAll<int, GO>(*comm, REDUCE_MAX, 3, minMaxInput, minMaxOutput);
    minAllGID_          = -minMaxOutput[0];
    maxAllGID_          = minMaxOutput[1];
    const GO globalDist = minMaxOutput[2];
    distributed_        = (comm_->getSize() > 1 && globalDist == 1);
  } else {  // unsigned; use two reductions
    // This is always correct, no matter the signedness of GO.
    reduceAll<int, GO>(*comm_, REDUCE_MIN, minMyGID_, outArg(minAllGID_));
    reduceAll<int, GO>(*comm_, REDUCE_MAX, maxMyGID_, outArg(maxAllGID_));
    distributed_ = checkIsDist();
  }
 
  contiguous_ = false;  // "Contiguous" is conservative.
 
  TEUCHOS_TEST_FOR_EXCEPTION(
      minAllGID_ < indexBase_,
      std::invalid_argument,
      "Tpetra::Map constructor (noncontiguous): "
      "Minimum global ID = "
          << minAllGID_ << " over all process(es) is "
                           "less than the given indexBase = "
          << indexBase_ << ".");
 
  // Create the Directory on demand in getRemoteIndexList().
  // setupDirectory ();
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done" << endl;
    std::cerr << os.str();
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Map<LocalOrdinal, GlobalOrdinal, Node>::~Map() {
  if (!Kokkos::is_initialized()) {
    std::ostringstream os;
    os << "WARNING: Tpetra::Map destructor (~Map()) is being called after "
          "Kokkos::finalize() has been called.  This is user error!  There are "
          "two likely causes: "
       << std::endl
       << "  1. You have a static Tpetra::Map (or RCP or shared_ptr of a Map)"
       << std::endl
       << "  2. You declare and construct a Tpetra::Map (or RCP or shared_ptr "
          "of a Tpetra::Map) at the same scope in main() as Kokkos::finalize() "
          "or Tpetra::finalize()."
       << std::endl
       << std::endl
       << "Don't do either of these!  Please refer to GitHib Issue #2372."
       << std::endl;
    ::Tpetra::Details::printOnce(std::cerr, os.str(),
                                 this->getComm().getRawPtr());
  } else {
    using ::Tpetra::Details::mpiIsFinalized;
    using ::Tpetra::Details::mpiIsInitialized;
    using ::Tpetra::Details::teuchosCommIsAnMpiComm;
 
    Teuchos::RCP<const Teuchos::Comm<int>> comm = this->getComm();
    if (!comm.is_null() && teuchosCommIsAnMpiComm(*comm) &&
        mpiIsInitialized() && mpiIsFinalized()) {
      // Tpetra itself does not require MPI, even if building with
      // MPI.  It is legal to create Tpetra objects that do not use
      // MPI, even in an MPI program.  However, calling Tpetra stuff
      // after MPI_Finalize() has been called is a bad idea, since
      // some Tpetra defaults may use MPI if available.
      std::ostringstream os;
      os << "WARNING: Tpetra::Map destructor (~Map()) is being called after "
            "MPI_Finalize() has been called.  This is user error!  There are "
            "two likely causes: "
         << std::endl
         << "  1. You have a static Tpetra::Map (or RCP or shared_ptr of a Map)"
         << std::endl
         << "  2. You declare and construct a Tpetra::Map (or RCP or shared_ptr "
            "of a Tpetra::Map) at the same scope in main() as MPI_finalize() or "
            "Tpetra::finalize()."
         << std::endl
         << std::endl
         << "Don't do either of these!  Please refer to GitHib Issue #2372."
         << std::endl;
      ::Tpetra::Details::printOnce(std::cerr, os.str(), comm.getRawPtr());
    }
  }
  // mfh 20 Mar 2018: We can't check Tpetra::isInitialized() yet,
  // because Tpetra does not yet require Tpetra::initialize /
  // Tpetra::finalize.
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::isOneToOne() const {
  TEUCHOS_TEST_FOR_EXCEPTION(
      getComm().is_null(), std::logic_error,
      "Tpetra::Map::isOneToOne: "
      "getComm() returns null.  Please report this bug to the Tpetra "
      "developers.");
 
  // This is a collective operation, if it hasn't been called before.
  setupDirectory();
  return directory_->isOneToOne(*this);
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
LocalOrdinal
Map<LocalOrdinal, GlobalOrdinal, Node>::
    getLocalElement(GlobalOrdinal globalIndex) const {
  if (isContiguous()) {
    if (globalIndex < getMinGlobalIndex() ||
        globalIndex > getMaxGlobalIndex()) {
      return Tpetra::Details::OrdinalTraits<LocalOrdinal>::invalid();
    }
    return static_cast<LocalOrdinal>(globalIndex - getMinGlobalIndex());
  } else if (globalIndex >= firstContiguousGID_ &&
             globalIndex <= lastContiguousGID_) {
    return static_cast<LocalOrdinal>(globalIndex - firstContiguousGID_);
  } else {
    // If the given global index is not in the table, this returns
    // the same value as OrdinalTraits<LocalOrdinal>::invalid().
    // glMapHost_ is Host and does not assume UVM
    lazyPushToHost();
    return glMapHost_.get(globalIndex);
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
GlobalOrdinal
Map<LocalOrdinal, GlobalOrdinal, Node>::
    getGlobalElement(LocalOrdinal localIndex) const {
  if (localIndex < getMinLocalIndex() || localIndex > getMaxLocalIndex()) {
    return Tpetra::Details::OrdinalTraits<GlobalOrdinal>::invalid();
  }
  if (isContiguous()) {
    return getMinGlobalIndex() + localIndex;
  } else {
    // This is a host Kokkos::View access, with no RCP or ArrayRCP
    // involvement.  As a result, it is thread safe.
    //
    // lgMapHost_ is a host pointer; this does NOT assume UVM.
    lazyPushToHost();
    return lgMapHost_[localIndex];
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::
    isNodeLocalElement(LocalOrdinal localIndex) const {
  if (localIndex < getMinLocalIndex() || localIndex > getMaxLocalIndex()) {
    return false;
  } else {
    return true;
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::
    isNodeGlobalElement(GlobalOrdinal globalIndex) const {
  return this->getLocalElement(globalIndex) !=
         Tpetra::Details::OrdinalTraits<LocalOrdinal>::invalid();
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::isUniform() const {
  return uniform_;
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::isContiguous() const {
  return contiguous_;
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
typename Map<LocalOrdinal, GlobalOrdinal, Node>::local_map_type
Map<LocalOrdinal, GlobalOrdinal, Node>::
    getLocalMap() const {
  return local_map_type(glMap_, lgMap_, getIndexBase(),
                        getMinGlobalIndex(), getMaxGlobalIndex(),
                        firstContiguousGID_, lastContiguousGID_,
                        getLocalNumElements(), isContiguous());
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::
    isCompatible(const Map<LocalOrdinal, GlobalOrdinal, Node>& map) const {
  using Teuchos::outArg;
  using Teuchos::REDUCE_MIN;
  using Teuchos::reduceAll;
  //
  // Tests that avoid the Boolean all-reduce below by using
  // globally consistent quantities.
  //
  if (this == &map) {
    // Pointer equality on one process always implies pointer
    // equality on all processes, since Map is immutable.
    return true;
  } else if (getComm()->getSize() != map.getComm()->getSize()) {
    // The two communicators have different numbers of processes.
    // It's not correct to call isCompatible() in that case.  This
    // may result in the all-reduce hanging below.
    return false;
  } else if (getGlobalNumElements() != map.getGlobalNumElements()) {
    // Two Maps are definitely NOT compatible if they have different
    // global numbers of indices.
    return false;
  } else if (isContiguous() && isUniform() &&
             map.isContiguous() && map.isUniform()) {
    // Contiguous uniform Maps with the same number of processes in
    // their communicators, and with the same global numbers of
    // indices, are always compatible.
    return true;
  } else if (!isContiguous() && !map.isContiguous() &&
             lgMap_.extent(0) != 0 && map.lgMap_.extent(0) != 0 &&
             lgMap_.data() == map.lgMap_.data()) {
    // Noncontiguous Maps whose global index lists are nonempty and
    // have the same pointer must be the same (and therefore
    // contiguous).
    //
    // Nonempty is important.  For example, consider a communicator
    // with two processes, and two Maps that share this
    // communicator, with zero global indices on the first process,
    // and different nonzero numbers of global indices on the second
    // process.  In that case, on the first process, the pointers
    // would both be NULL.
    return true;
  }
 
  TEUCHOS_TEST_FOR_EXCEPTION(
      getGlobalNumElements() != map.getGlobalNumElements(), std::logic_error,
      "Tpetra::Map::isCompatible: There's a bug in this method.  We've already "
      "checked that this condition is true above, but it's false here.  "
      "Please report this bug to the Tpetra developers.");
 
  // Do both Maps have the same number of indices on each process?
  const int locallyCompat =
      (getLocalNumElements() == map.getLocalNumElements()) ? 1 : 0;
 
  int globallyCompat = 0;
  reduceAll<int, int>(*comm_, REDUCE_MIN, locallyCompat, outArg(globallyCompat));
  return (globallyCompat == 1);
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::
    locallySameAs(const Map<LocalOrdinal, GlobalOrdinal, Node>& map) const {
  using Teuchos::ArrayView;
  using GO        = global_ordinal_type;
  using size_type = typename ArrayView<const GO>::size_type;
 
  // If both Maps are contiguous, we can compare their GID ranges
  // easily by looking at the min and max GID on this process.
  // Otherwise, we'll compare their GID lists.  If only one Map is
  // contiguous, then we only have to call getLocalElementList() on
  // the noncontiguous Map.  (It's best to avoid calling it on a
  // contiguous Map, since it results in unnecessary storage that
  // persists for the lifetime of the Map.)
 
  if (this == &map) {
    // Pointer equality on one process always implies pointer
    // equality on all processes, since Map is immutable.
    return true;
  } else if (getLocalNumElements() != map.getLocalNumElements()) {
    return false;
  } else if (getMinGlobalIndex() != map.getMinGlobalIndex() ||
             getMaxGlobalIndex() != map.getMaxGlobalIndex()) {
    return false;
  } else {
    if (isContiguous()) {
      if (map.isContiguous()) {
        return true;  // min and max match, so the ranges match.
      } else {        // *this is contiguous, but map is not contiguous
        TEUCHOS_TEST_FOR_EXCEPTION(
            !this->isContiguous() || map.isContiguous(), std::logic_error,
            "Tpetra::Map::locallySameAs: BUG");
        ArrayView<const GO> rhsElts = map.getLocalElementList();
        const GO minLhsGid          = this->getMinGlobalIndex();
        const size_type numRhsElts  = rhsElts.size();
        for (size_type k = 0; k < numRhsElts; ++k) {
          const GO curLhsGid = minLhsGid + static_cast<GO>(k);
          if (curLhsGid != rhsElts[k]) {
            return false;  // stop on first mismatch
          }
        }
        return true;
      }
    } else if (map.isContiguous()) {  // *this is not contiguous, but map is
      TEUCHOS_TEST_FOR_EXCEPTION(
          this->isContiguous() || !map.isContiguous(), std::logic_error,
          "Tpetra::Map::locallySameAs: BUG");
      ArrayView<const GO> lhsElts = this->getLocalElementList();
      const GO minRhsGid          = map.getMinGlobalIndex();
      const size_type numLhsElts  = lhsElts.size();
      for (size_type k = 0; k < numLhsElts; ++k) {
        const GO curRhsGid = minRhsGid + static_cast<GO>(k);
        if (curRhsGid != lhsElts[k]) {
          return false;  // stop on first mismatch
        }
      }
      return true;
    } else if (this->lgMap_.data() == map.lgMap_.data()) {
      // Pointers to LID->GID "map" (actually just an array) are the
      // same, and the number of GIDs are the same.
      return this->getLocalNumElements() == map.getLocalNumElements();
    } else {  // we actually have to compare the GIDs
      if (this->getLocalNumElements() != map.getLocalNumElements()) {
        return false;  // We already checked above, but check just in case
      } else {
        using range_type = Kokkos::RangePolicy<LocalOrdinal, typename node_type::execution_space>;
 
        auto lhsLclMap = getLocalMap();
        auto rhsLclMap = map.getLocalMap();
 
        LocalOrdinal numMismatchedElements = 0;
        Kokkos::parallel_reduce(
            "Tpetra::Map::locallySameAs",
            range_type(0, this->getLocalNumElements()),
            KOKKOS_LAMBDA(const LocalOrdinal lid, LocalOrdinal& numMismatches) {
              if (lhsLclMap.getGlobalElement(lid) != rhsLclMap.getGlobalElement(lid))
                ++numMismatches;
            },
            numMismatchedElements);
 
        return (numMismatchedElements == 0);
      }
    }
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::
    isLocallyFitted(const Map<LocalOrdinal, GlobalOrdinal, Node>& map) const {
  if (this == &map)
    return true;
 
  // We are going to check if lmap1 is fitted into lmap2:
  // Is lmap1 (map) a subset of lmap2 (this)?
  // And do the first lmap1.getLocalNumElements() global elements
  // of lmap1,lmap2 owned on each process exactly match?
  auto lmap1 = map.getLocalMap();
  auto lmap2 = this->getLocalMap();
 
  auto numLocalElements1 = lmap1.getLocalNumElements();
  auto numLocalElements2 = lmap2.getLocalNumElements();
 
  if (numLocalElements1 > numLocalElements2) {
    // There are more indices in the first map on this process than in second map.
    return false;
  }
 
  if (lmap1.isContiguous() && lmap2.isContiguous()) {
    // When both Maps are contiguous, just check the interval inclusion.
    return ((lmap1.getMinGlobalIndex() == lmap2.getMinGlobalIndex()) &&
            (lmap1.getMaxGlobalIndex() <= lmap2.getMaxGlobalIndex()));
  }
 
  if (lmap1.getMinGlobalIndex() < lmap2.getMinGlobalIndex() ||
      lmap1.getMaxGlobalIndex() > lmap2.getMaxGlobalIndex()) {
    // The second map does not include the first map bounds, and thus some of
    // the first map global indices are not in the second map.
    return false;
  }
 
  using LO = local_ordinal_type;
  using range_type =
      Kokkos::RangePolicy<LO, typename node_type::execution_space>;
 
  // Check all elements.
  LO numDiff = 0;
  Kokkos::parallel_reduce(
      "isLocallyFitted",
      range_type(0, numLocalElements1),
      KOKKOS_LAMBDA(const LO i, LO& diff) {
        diff += (lmap1.getGlobalElement(i) != lmap2.getGlobalElement(i));
      },
      numDiff);
 
  return (numDiff == 0);
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::
    isSameAs(const Map<LocalOrdinal, GlobalOrdinal, Node>& map) const {
  using Teuchos::outArg;
  using Teuchos::REDUCE_MIN;
  using Teuchos::reduceAll;
  //
  // Tests that avoid the Boolean all-reduce below by using
  // globally consistent quantities.
  //
  if (this == &map) {
    // Pointer equality on one process always implies pointer
    // equality on all processes, since Map is immutable.
    return true;
  } else if (getComm()->getSize() != map.getComm()->getSize()) {
    // The two communicators have different numbers of processes.
    // It's not correct to call isSameAs() in that case.  This
    // may result in the all-reduce hanging below.
    return false;
  } else if (getGlobalNumElements() != map.getGlobalNumElements()) {
    // Two Maps are definitely NOT the same if they have different
    // global numbers of indices.
    return false;
  } else if (getMinAllGlobalIndex() != map.getMinAllGlobalIndex() ||
             getMaxAllGlobalIndex() != map.getMaxAllGlobalIndex() ||
             getIndexBase() != map.getIndexBase()) {
    // If the global min or max global index doesn't match, or if
    // the index base doesn't match, then the Maps aren't the same.
    return false;
  } else if (isDistributed() != map.isDistributed()) {
    // One Map is distributed and the other is not, which means that
    // the Maps aren't the same.
    return false;
  } else if (isContiguous() && isUniform() &&
             map.isContiguous() && map.isUniform()) {
    // Contiguous uniform Maps with the same number of processes in
    // their communicators, with the same global numbers of indices,
    // and with matching index bases and ranges, must be the same.
    return true;
  }
 
  // The two communicators must have the same number of processes,
  // with process ranks occurring in the same order.  This uses
  // MPI_COMM_COMPARE.  The MPI 3.1 standard (Section 6.4) says:
  // "Operations that access communicators are local and their
  // execution does not require interprocess communication."
  // However, just to be sure, I'll put this call after the above
  // tests that don't communicate.
  if (!::Tpetra::Details::congruent(*comm_, *(map.getComm()))) {
    return false;
  }
 
  // If we get this far, we need to check local properties and then
  // communicate local sameness across all processes.
  const int isSame_lcl = locallySameAs(map) ? 1 : 0;
 
  // Return true if and only if all processes report local sameness.
  int isSame_gbl = 0;
  reduceAll<int, int>(*comm_, REDUCE_MIN, isSame_lcl, outArg(isSame_gbl));
  return isSame_gbl == 1;
}
 
namespace {  // (anonymous)
template <class LO, class GO, class DT>
class FillLgMap {
 public:
  FillLgMap(const Kokkos::View<GO*, DT>& lgMap,
            const GO startGid)
    : lgMap_(lgMap)
    , startGid_(startGid) {
    Kokkos::RangePolicy<LO, typename DT::execution_space>
        range(static_cast<LO>(0), static_cast<LO>(lgMap.size()));
    Kokkos::parallel_for(range, *this);
  }
 
  KOKKOS_INLINE_FUNCTION void operator()(const LO& lid) const {
    lgMap_(lid) = startGid_ + static_cast<GO>(lid);
  }
 
 private:
  const Kokkos::View<GO*, DT> lgMap_;
  const GO startGid_;
};
 
}  // namespace
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
typename Map<LocalOrdinal, GlobalOrdinal, Node>::global_indices_array_type
Map<LocalOrdinal, GlobalOrdinal, Node>::getMyGlobalIndices() const {
  using std::endl;
  using LO                 = local_ordinal_type;
  using GO                 = global_ordinal_type;
  using const_lg_view_type = decltype(lgMap_);
  using lg_view_type       = typename const_lg_view_type::non_const_type;
  const bool debug         = Details::Behavior::debug("Map");
  const bool verbose       = Details::Behavior::verbose("Map");
 
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(
        comm_.getRawPtr(), "Map", "getMyGlobalIndices");
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    std::cerr << os.str();
  }
 
  // If the local-to-global mapping doesn't exist yet, and if we
  // have local entries, then create and fill the local-to-global
  // mapping.
  const bool needToCreateLocalToGlobalMapping =
      lgMap_.extent(0) == 0 && numLocalElements_ > 0;
 
  if (needToCreateLocalToGlobalMapping) {
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Need to create lgMap" << endl;
      std::cerr << os.str();
    }
    if (debug) {
      // The local-to-global mapping should have been set up already
      // for a noncontiguous map.
      TEUCHOS_TEST_FOR_EXCEPTION(!isContiguous(), std::logic_error,
                                 "Tpetra::Map::getMyGlobalIndices: The local-to-global "
                                 "mapping (lgMap_) should have been set up already for a "
                                 "noncontiguous Map.  Please report this bug to the Tpetra "
                                 "developers.");
    }
    const LO numElts = static_cast<LO>(getLocalNumElements());
 
    using Kokkos::view_alloc;
    using Kokkos::WithoutInitializing;
    lg_view_type lgMap("lgMap", numElts);
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Fill lgMap" << endl;
      std::cerr << os.str();
    }
    FillLgMap<LO, GO, device_type> fillIt(lgMap, minMyGID_);
 
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Copy lgMap to lgMapHost" << endl;
      std::cerr << os.str();
    }
 
    auto lgMapHost = Kokkos::create_mirror_view(Kokkos::HostSpace(), lgMap);
    // DEEP_COPY REVIEW - DEVICE-TO-HOST
    auto exec_instance = execution_space();
    Kokkos::deep_copy(exec_instance, lgMapHost, lgMap);
 
    // There's a non-trivial chance we'll grab this on the host,
    // so let's make sure the copy finishes
    exec_instance.fence();
 
    // "Commit" the local-to-global lookup table we filled in above.
    lgMap_     = lgMap;
    lgMapHost_ = lgMapHost;
  } else {
    lazyPushToHost();
  }
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done" << endl;
    std::cerr << os.str();
  }
  return lgMapHost_;
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
typename Map<LocalOrdinal, GlobalOrdinal, Node>::global_indices_array_device_type
Map<LocalOrdinal, GlobalOrdinal, Node>::getMyGlobalIndicesDevice() const {
  using std::endl;
  using LO                 = local_ordinal_type;
  using GO                 = global_ordinal_type;
  using const_lg_view_type = decltype(lgMap_);
  using lg_view_type       = typename const_lg_view_type::non_const_type;
  const bool debug         = Details::Behavior::debug("Map");
  const bool verbose       = Details::Behavior::verbose("Map");
 
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(
        comm_.getRawPtr(), "Map", "getMyGlobalIndicesDevice");
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    std::cerr << os.str();
  }
 
  // If the local-to-global mapping doesn't exist yet, and if we
  // have local entries, then create and fill the local-to-global
  // mapping.
  const bool needToCreateLocalToGlobalMapping =
      lgMap_.extent(0) == 0 && numLocalElements_ > 0;
 
  if (needToCreateLocalToGlobalMapping) {
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Need to create lgMap" << endl;
      std::cerr << os.str();
    }
    if (debug) {
      // The local-to-global mapping should have been set up already
      // for a noncontiguous map.
      TEUCHOS_TEST_FOR_EXCEPTION(!isContiguous(), std::logic_error,
                                 "Tpetra::Map::getMyGlobalIndices: The local-to-global "
                                 "mapping (lgMap_) should have been set up already for a "
                                 "noncontiguous Map.  Please report this bug to the Tpetra "
                                 "developers.");
    }
    const LO numElts = static_cast<LO>(getLocalNumElements());
 
    using Kokkos::view_alloc;
    using Kokkos::WithoutInitializing;
    lg_view_type lgMap("lgMap", numElts);
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Fill lgMap" << endl;
      std::cerr << os.str();
    }
    FillLgMap<LO, GO, device_type> fillIt(lgMap, minMyGID_);
 
    // "Commit" the local-to-global lookup table we filled in above.
    lgMap_ = lgMap;
  }
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done" << endl;
    std::cerr << os.str();
  }
  return lgMap_;
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::ArrayView<const GlobalOrdinal>
Map<LocalOrdinal, GlobalOrdinal, Node>::getLocalElementList() const {
  using GO = global_ordinal_type;
 
  // If the local-to-global mapping doesn't exist yet, and if we
  // have local entries, then create and fill the local-to-global
  // mapping.
  (void)this->getMyGlobalIndices();
 
  // This does NOT assume UVM; lgMapHost_ is a host pointer.
  lazyPushToHost();
  const GO* lgMapHostRawPtr = lgMapHost_.data();
  // The third argument forces ArrayView not to try to track memory
  // in a debug build.  We have to use it because the memory does
  // not belong to a Teuchos memory management class.
  return Teuchos::ArrayView<const GO>(
      lgMapHostRawPtr,
      lgMapHost_.extent(0),
      Teuchos::RCP_DISABLE_NODE_LOOKUP);
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::isDistributed() const {
  return distributed_;
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
std::string Map<LocalOrdinal, GlobalOrdinal, Node>::description() const {
  using Teuchos::TypeNameTraits;
  std::ostringstream os;
 
  os << "Tpetra::Map: {"
     << "LocalOrdinalType: " << TypeNameTraits<LocalOrdinal>::name()
     << ", GlobalOrdinalType: " << TypeNameTraits<GlobalOrdinal>::name()
     << ", NodeType: " << TypeNameTraits<Node>::name();
  if (this->getObjectLabel() != "") {
    os << ", Label: \"" << this->getObjectLabel() << "\"";
  }
  os << ", Global number of entries: " << getGlobalNumElements()
     << ", Number of processes: " << getComm()->getSize()
     << ", Uniform: " << (isUniform() ? "true" : "false")
     << ", Contiguous: " << (isContiguous() ? "true" : "false")
     << ", Distributed: " << (isDistributed() ? "true" : "false")
     << "}";
  return os.str();
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
std::string
Map<LocalOrdinal, GlobalOrdinal, Node>::
    localDescribeToString(const Teuchos::EVerbosityLevel vl) const {
  using LO = local_ordinal_type;
  using std::endl;
 
  // This preserves current behavior of Map.
  if (vl < Teuchos::VERB_HIGH) {
    return std::string();
  }
  auto outStringP = Teuchos::rcp(new std::ostringstream());
  Teuchos::RCP<Teuchos::FancyOStream> outp =
      Teuchos::getFancyOStream(outStringP);
  Teuchos::FancyOStream& out = *outp;
 
  auto comm          = this->getComm();
  const int myRank   = comm->getRank();
  const int numProcs = comm->getSize();
  out << "Process " << myRank << " of " << numProcs << ":" << endl;
  Teuchos::OSTab tab1(out);
 
  const LO numEnt = static_cast<LO>(this->getLocalNumElements());
  out << "My number of entries: " << numEnt << endl
      << "My minimum global index: " << this->getMinGlobalIndex() << endl
      << "My maximum global index: " << this->getMaxGlobalIndex() << endl;
 
  if (vl == Teuchos::VERB_EXTREME) {
    out << "My global indices: [";
    const LO minLclInd = this->getMinLocalIndex();
    for (LO k = 0; k < numEnt; ++k) {
      out << minLclInd + this->getGlobalElement(k);
      if (k + 1 < numEnt) {
        out << ", ";
      }
    }
    out << "]" << endl;
  }
 
  out.flush();  // make sure the ostringstream got everything
  return outStringP->str();
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
void Map<LocalOrdinal, GlobalOrdinal, Node>::
    describe(Teuchos::FancyOStream& out,
             const Teuchos::EVerbosityLevel verbLevel) const {
  using std::endl;
  using Teuchos::TypeNameTraits;
  using Teuchos::VERB_DEFAULT;
  using Teuchos::VERB_HIGH;
  using Teuchos::VERB_LOW;
  using Teuchos::VERB_NONE;
  using LO = local_ordinal_type;
  using GO = global_ordinal_type;
  const Teuchos::EVerbosityLevel vl =
      (verbLevel == VERB_DEFAULT) ? VERB_LOW : verbLevel;
 
  if (vl == VERB_NONE) {
    return;  // don't print anything
  }
  // If this Map's Comm is null, then the Map does not participate
  // in collective operations with the other processes.  In that
  // case, it is not even legal to call this method.  The reasonable
  // thing to do in that case is nothing.
  auto comm = this->getComm();
  if (comm.is_null()) {
    return;
  }
  const int myRank   = comm->getRank();
  const int numProcs = comm->getSize();
 
  // Only Process 0 should touch the output stream, but this method
  // in general may need to do communication.  Thus, we may need to
  // preserve the current tab level across multiple "if (myRank ==
  // 0) { ... }" inner scopes.  This is why we sometimes create
  // OSTab instances by pointer, instead of by value.  We only need
  // to create them by pointer if the tab level must persist through
  // multiple inner scopes.
  Teuchos::RCP<Teuchos::OSTab> tab0, tab1;
 
  if (myRank == 0) {
    // At every verbosity level but VERB_NONE, Process 0 prints.
    // By convention, describe() always begins with a tab before
    // printing.
    tab0 = Teuchos::rcp(new Teuchos::OSTab(out));
    out << "\"Tpetra::Map\":" << endl;
    tab1 = Teuchos::rcp(new Teuchos::OSTab(out));
    {
      out << "Template parameters:" << endl;
      Teuchos::OSTab tab2(out);
      out << "LocalOrdinal: " << TypeNameTraits<LO>::name() << endl
          << "GlobalOrdinal: " << TypeNameTraits<GO>::name() << endl
          << "Node: " << TypeNameTraits<Node>::name() << endl;
    }
    const std::string label = this->getObjectLabel();
    if (label != "") {
      out << "Label: \"" << label << "\"" << endl;
    }
    out << "Global number of entries: " << getGlobalNumElements() << endl
        << "Minimum global index: " << getMinAllGlobalIndex() << endl
        << "Maximum global index: " << getMaxAllGlobalIndex() << endl
        << "Index base: " << getIndexBase() << endl
        << "Number of processes: " << numProcs << endl
        << "Uniform: " << (isUniform() ? "true" : "false") << endl
        << "Contiguous: " << (isContiguous() ? "true" : "false") << endl
        << "Distributed: " << (isDistributed() ? "true" : "false") << endl;
  }
 
  // This is collective over the Map's communicator.
  if (vl >= VERB_HIGH) {  // VERB_HIGH or VERB_EXTREME
    const std::string lclStr = this->localDescribeToString(vl);
    Tpetra::Details::gathervPrint(out, lclStr, *comm);
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const Map<LocalOrdinal, GlobalOrdinal, Node>>
Map<LocalOrdinal, GlobalOrdinal, Node>::
    replaceCommWithSubset(const Teuchos::RCP<const Teuchos::Comm<int>>& newComm) const {
  using Teuchos::RCP;
  using Teuchos::rcp;
  using GST      = global_size_t;
  using LO       = local_ordinal_type;
  using GO       = global_ordinal_type;
  using map_type = Map<LO, GO, Node>;
 
  // mfh 26 Mar 2013: The lazy way to do this is simply to recreate
  // the Map by calling its ordinary public constructor, using the
  // original Map's data.  This only involves O(1) all-reduces over
  // the new communicator, which in the common case only includes a
  // small number of processes.
 
  // Create the Map to return.
  if (newComm.is_null() || newComm->getSize() < 1) {
    return Teuchos::null;  // my process does not participate in the new Map
  } else if (newComm->getSize() == 1) {
    lazyPushToHost();
 
    // The case where the new communicator has only one process is
    // easy.  We don't have to communicate to get all the
    // information we need.  Use the default comm to create the new
    // Map, then fill in all the fields directly.
    RCP<map_type> newMap(new map_type());
 
    newMap->comm_ = newComm;
    // mfh 07 Oct 2016: Preserve original behavior, even though the
    // original index base may no longer be the globally min global
    // index.  See #616 for why this doesn't matter so much anymore.
    newMap->indexBase_          = this->indexBase_;
    newMap->numGlobalElements_  = this->numLocalElements_;
    newMap->numLocalElements_   = this->numLocalElements_;
    newMap->minMyGID_           = this->minMyGID_;
    newMap->maxMyGID_           = this->maxMyGID_;
    newMap->minAllGID_          = this->minMyGID_;
    newMap->maxAllGID_          = this->maxMyGID_;
    newMap->firstContiguousGID_ = this->firstContiguousGID_;
    newMap->lastContiguousGID_  = this->lastContiguousGID_;
    // Since the new communicator has only one process, neither
    // uniformity nor contiguity have changed.
    newMap->uniform_    = this->uniform_;
    newMap->contiguous_ = this->contiguous_;
    // The new communicator only has one process, so the new Map is
    // not distributed.
    newMap->distributed_ = false;
    newMap->lgMap_       = this->lgMap_;
    newMap->lgMapHost_   = this->lgMapHost_;
    newMap->glMap_       = this->glMap_;
    newMap->glMapHost_   = this->glMapHost_;
    // It's OK not to initialize the new Map's Directory.
    // This is initialized lazily, on first call to getRemoteIndexList.
 
    return newMap;
  } else {  // newComm->getSize() != 1
    // Even if the original Map is contiguous, the new Map might not
    // be, especially if the excluded processes have ranks != 0 or
    // newComm->getSize()-1.  The common case for this method is to
    // exclude many (possibly even all but one) processes, so it
    // likely doesn't pay to do the global communication (over the
    // original communicator) to figure out whether we can optimize
    // the result Map.  Thus, we just set up the result Map as
    // noncontiguous.
    //
    // TODO (mfh 07 Oct 2016) We don't actually need to reconstruct
    // the global-to-local table, etc.  Optimize this code path to
    // avoid unnecessary local work.
 
    // Make Map (re)compute the global number of elements.
    const GST RECOMPUTE = Tpetra::Details::OrdinalTraits<GST>::invalid();
    // TODO (mfh 07 Oct 2016) If we use any Map constructor, we have
    // to use the noncontiguous Map constructor, since the new Map
    // might not be contiguous.  Even if the old Map was contiguous,
    // some process in the "middle" might have been excluded.  If we
    // want to avoid local work, we either have to do the setup by
    // hand, or write a new Map constructor.
#if 1
    // The disabled code here throws the following exception in
    // Map's replaceCommWithSubset test:
    //
    // Throw test that evaluated to true: static_cast<unsigned long long> (numKeys) > static_cast<unsigned long long> (::Kokkos::ArithTraits<ValueType>::max ())
    // 10:
    // 10:   Tpetra::Details::FixedHashTable: The number of keys -3 is greater than the maximum representable ValueType value 2147483647.  This means that it is not possible to use this constructor.
    // 10:   Process 3: origComm->replaceCommWithSubset(subsetComm) threw an exception: /scratch/prj/Trilinos/Trilinos/packages/tpetra/core/src/Tpetra_Details_FixedHashTable_def.hpp:1044:
 
    auto lgMap = this->getMyGlobalIndices();
    using size_type =
        typename std::decay<decltype(lgMap.extent(0))>::type;
    const size_type lclNumInds =
        static_cast<size_type>(this->getLocalNumElements());
    using Teuchos::TypeNameTraits;
    TEUCHOS_TEST_FOR_EXCEPTION(lgMap.extent(0) != lclNumInds, std::logic_error,
                               "Tpetra::Map::replaceCommWithSubset: Result of getMyGlobalIndices() "
                               "has length "
                                   << lgMap.extent(0) << " (of type " << TypeNameTraits<size_type>::name() << ") != this->getLocalNumElements()"
                                                                                                              " = "
                                   << this->getLocalNumElements() << ".  The latter, upon being "
                                                                     "cast to size_type = "
                                   << TypeNameTraits<size_type>::name() << ", "
                                                                           "becomes "
                                   << lclNumInds << ".  Please report this bug to the Tpetra "
                                                    "developers.");
#else
    Teuchos::ArrayView<const GO> lgMap = this->getLocalElementList();
#endif  // 1
 
    const GO indexBase = this->getIndexBase();
    // map stores HostSpace of CudaSpace but constructor is still CudaUVMSpace
    auto lgMap_device = Kokkos::create_mirror_view_and_copy(device_type(), lgMap);
    return rcp(new map_type(RECOMPUTE, lgMap_device, indexBase, newComm));
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const Map<LocalOrdinal, GlobalOrdinal, Node>>
Map<LocalOrdinal, GlobalOrdinal, Node>::
    removeEmptyProcesses() const {
  using Teuchos::Comm;
  using Teuchos::null;
  using Teuchos::outArg;
  using Teuchos::RCP;
  using Teuchos::rcp;
  using Teuchos::REDUCE_MIN;
  using Teuchos::reduceAll;
 
  // Create the new communicator.  split() returns a valid
  // communicator on all processes.  On processes where color == 0,
  // ignore the result.  Passing key == 0 tells MPI to order the
  // processes in the new communicator by their rank in the old
  // communicator.
  const int color = (numLocalElements_ == 0) ? 0 : 1;
  // MPI_Comm_split must be called collectively over the original
  // communicator.  We can't just call it on processes with color
  // one, even though we will ignore its result on processes with
  // color zero.
  RCP<const Comm<int>> newComm = comm_->split(color, 0);
  if (color == 0) {
    newComm = null;
  }
 
  // Create the Map to return.
  if (newComm.is_null()) {
    return null;  // my process does not participate in the new Map
  } else {
    RCP<Map> map = rcp(new Map());
 
    map->comm_               = newComm;
    map->indexBase_          = indexBase_;
    map->numGlobalElements_  = numGlobalElements_;
    map->numLocalElements_   = numLocalElements_;
    map->minMyGID_           = minMyGID_;
    map->maxMyGID_           = maxMyGID_;
    map->minAllGID_          = minAllGID_;
    map->maxAllGID_          = maxAllGID_;
    map->firstContiguousGID_ = firstContiguousGID_;
    map->lastContiguousGID_  = lastContiguousGID_;
 
    // Uniformity and contiguity have not changed.  The directory
    // has changed, but we've taken care of that above.
    map->uniform_    = uniform_;
    map->contiguous_ = contiguous_;
 
    // If the original Map was NOT distributed, then the new Map
    // cannot be distributed.
    //
    // If the number of processes in the new communicator is 1, then
    // the new Map is not distributed.
    //
    // Otherwise, we have to check the new Map using an all-reduce
    // (over the new communicator).  For example, the original Map
    // may have had some processes with zero elements, and all other
    // processes with the same number of elements as in the whole
    // Map.  That Map is technically distributed, because of the
    // processes with zero elements.  Removing those processes would
    // make the new Map locally replicated.
    if (!distributed_ || newComm->getSize() == 1) {
      map->distributed_ = false;
    } else {
      const int iOwnAllGids  = (numLocalElements_ == numGlobalElements_) ? 1 : 0;
      int allProcsOwnAllGids = 0;
      reduceAll<int, int>(*newComm, REDUCE_MIN, iOwnAllGids, outArg(allProcsOwnAllGids));
      map->distributed_ = (allProcsOwnAllGids == 1) ? false : true;
    }
 
    map->lgMap_     = lgMap_;
    map->lgMapHost_ = lgMapHost_;
    map->glMap_     = glMap_;
    map->glMapHost_ = glMapHost_;
 
    // Map's default constructor creates an uninitialized Directory.
    // The Directory will be initialized on demand in
    // getRemoteIndexList().
    //
    // FIXME (mfh 26 Mar 2013) It should be possible to "filter" the
    // directory more efficiently than just recreating it.  If
    // directory recreation proves a bottleneck, we can always
    // revisit this.  On the other hand, Directory creation is only
    // collective over the new, presumably much smaller
    // communicator, so it may not be worth the effort to optimize.
 
    return map;
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
void Map<LocalOrdinal, GlobalOrdinal, Node>::setupDirectory() const {
  TEUCHOS_TEST_FOR_EXCEPTION(
      directory_.is_null(), std::logic_error,
      "Tpetra::Map::setupDirectory: "
      "The Directory is null.  "
      "Please report this bug to the Tpetra developers.");
 
  // Only create the Directory if it hasn't been created yet.
  // This is a collective operation.
  if (!directory_->initialized()) {
    directory_->initialize(*this);
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
LookupStatus
Map<LocalOrdinal, GlobalOrdinal, Node>::
    getRemoteIndexList(const Teuchos::ArrayView<const GlobalOrdinal>& GIDs,
                       const Teuchos::ArrayView<int>& PIDs,
                       const Teuchos::ArrayView<LocalOrdinal>& LIDs) const {
  using Details::verbosePrintArray;
  using std::endl;
  using Tpetra::Details::OrdinalTraits;
  using size_type = Teuchos::ArrayView<int>::size_type;
 
  const bool verbose         = Details::Behavior::verbose("Map");
  const size_t maxNumToPrint = verbose ? Details::Behavior::verbosePrintCountThreshold() : size_t(0);
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(comm_.getRawPtr(),
                                   "Map", "getRemoteIndexList(GIDs,PIDs,LIDs)");
    std::ostringstream os;
    os << *prefix << "Start: ";
    verbosePrintArray(os, GIDs, "GIDs", maxNumToPrint);
    os << endl;
    std::cerr << os.str();
  }
 
  // Empty Maps (i.e., containing no indices on any processes in the
  // Map's communicator) are perfectly valid.  In that case, if the
  // input GID list is nonempty, we fill the output arrays with
  // invalid values, and return IDNotPresent to notify the caller.
  // It's perfectly valid to give getRemoteIndexList GIDs that the
  // Map doesn't own.  SubmapImport test 2 needs this functionality.
  if (getGlobalNumElements() == 0) {
    if (GIDs.size() == 0) {
      if (verbose) {
        std::ostringstream os;
        os << *prefix << "Done; both Map & input are empty" << endl;
        std::cerr << os.str();
      }
      return AllIDsPresent;  // trivially
    } else {
      if (verbose) {
        std::ostringstream os;
        os << *prefix << "Done: Map is empty on all processes, "
                         "so all output PIDs & LIDs are invalid (-1)."
           << endl;
        std::cerr << os.str();
      }
      for (size_type k = 0; k < PIDs.size(); ++k) {
        PIDs[k] = OrdinalTraits<int>::invalid();
      }
      for (size_type k = 0; k < LIDs.size(); ++k) {
        LIDs[k] = OrdinalTraits<LocalOrdinal>::invalid();
      }
      return IDNotPresent;
    }
  }
 
  // getRemoteIndexList must be called collectively, and Directory
  // initialization is collective too, so it's OK to initialize the
  // Directory on demand.
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Call setupDirectory" << endl;
    std::cerr << os.str();
  }
  setupDirectory();
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Call directory_->getDirectoryEntries" << endl;
    std::cerr << os.str();
  }
  const Tpetra::LookupStatus retVal =
      directory_->getDirectoryEntries(*this, GIDs, PIDs, LIDs);
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done; getDirectoryEntries returned "
       << (retVal == IDNotPresent ? "IDNotPresent" : "AllIDsPresent")
       << "; ";
    verbosePrintArray(os, PIDs, "PIDs", maxNumToPrint);
    os << ", ";
    verbosePrintArray(os, LIDs, "LIDs", maxNumToPrint);
    os << endl;
    std::cerr << os.str();
  }
  return retVal;
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
LookupStatus
Map<LocalOrdinal, GlobalOrdinal, Node>::
    getRemoteIndexList(const Teuchos::ArrayView<const GlobalOrdinal>& GIDs,
                       const Teuchos::ArrayView<int>& PIDs) const {
  using Details::verbosePrintArray;
  using std::endl;
 
  const bool verbose         = Details::Behavior::verbose("Map");
  const size_t maxNumToPrint = verbose ? Details::Behavior::verbosePrintCountThreshold() : size_t(0);
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(comm_.getRawPtr(),
                                   "Map", "getRemoteIndexList(GIDs,PIDs)");
    std::ostringstream os;
    os << *prefix << "Start: ";
    verbosePrintArray(os, GIDs, "GIDs", maxNumToPrint);
    os << endl;
    std::cerr << os.str();
  }
 
  if (getGlobalNumElements() == 0) {
    if (GIDs.size() == 0) {
      if (verbose) {
        std::ostringstream os;
        os << *prefix << "Done; both Map & input are empty" << endl;
        std::cerr << os.str();
      }
      return AllIDsPresent;  // trivially
    } else {
      if (verbose) {
        std::ostringstream os;
        os << *prefix << "Done: Map is empty on all processes, "
                         "so all output PIDs are invalid (-1)."
           << endl;
        std::cerr << os.str();
      }
      for (Teuchos::ArrayView<int>::size_type k = 0; k < PIDs.size(); ++k) {
        PIDs[k] = Tpetra::Details::OrdinalTraits<int>::invalid();
      }
      return IDNotPresent;
    }
  }
 
  // getRemoteIndexList must be called collectively, and Directory
  // initialization is collective too, so it's OK to initialize the
  // Directory on demand.
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Call setupDirectory" << endl;
    std::cerr << os.str();
  }
  setupDirectory();
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Call directory_->getDirectoryEntries" << endl;
    std::cerr << os.str();
  }
  const Tpetra::LookupStatus retVal =
      directory_->getDirectoryEntries(*this, GIDs, PIDs);
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done; getDirectoryEntries returned "
       << (retVal == IDNotPresent ? "IDNotPresent" : "AllIDsPresent")
       << "; ";
    verbosePrintArray(os, PIDs, "PIDs", maxNumToPrint);
    os << endl;
    std::cerr << os.str();
  }
  return retVal;
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
void Map<LocalOrdinal, GlobalOrdinal, Node>::lazyPushToHost() const {
  using exec_space = typename Node::device_type::execution_space;
  if (lgMap_.extent(0) != lgMapHost_.extent(0)) {
    Tpetra::Details::ProfilingRegion pr("Map::lazyPushToHost() - pushing data");
    // NOTE: We check lgMap_ and not glMap_, since the latter can
    // be somewhat error prone for contiguous maps
 
    // create_mirror_view preserves const-ness.  create_mirror does not
    auto lgMap_host = Kokkos::create_mirror(Kokkos::HostSpace(), lgMap_);
 
    // Since this was computed on the default stream, we can copy on the stream and then fence
    // the stream
    Kokkos::deep_copy(exec_space(), lgMap_host, lgMap_);
    exec_space().fence();
    lgMapHost_ = lgMap_host;
 
    // Make host version - when memory spaces match these just do trivial assignment
    glMapHost_ = global_to_local_table_host_type(glMap_);
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const Teuchos::Comm<int>>
Map<LocalOrdinal, GlobalOrdinal, Node>::getComm() const {
  return comm_;
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
bool Map<LocalOrdinal, GlobalOrdinal, Node>::
    checkIsDist() const {
  using std::endl;
  using Teuchos::as;
  using Teuchos::outArg;
  using Teuchos::REDUCE_MIN;
  using Teuchos::reduceAll;
 
  const bool verbose = Details::Behavior::verbose("Map");
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    prefix = Details::createPrefix(
        comm_.getRawPtr(), "Map", "checkIsDist");
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    std::cerr << os.str();
  }
 
  bool global = false;
  if (comm_->getSize() > 1) {
    // The communicator has more than one process, but that doesn't
    // necessarily mean the Map is distributed.
    int localRep = 0;
    if (numGlobalElements_ == as<global_size_t>(numLocalElements_)) {
      // The number of local elements on this process equals the
      // number of global elements.
      //
      // NOTE (mfh 22 Nov 2011) Does this still work if there were
      // duplicates in the global ID list on input (the third Map
      // constructor), so that the number of local elements (which
      // are not duplicated) on this process could be less than the
      // number of global elements, even if this process owns all
      // the elements?
      localRep = 1;
    }
    int allLocalRep;
    reduceAll<int, int>(*comm_, REDUCE_MIN, localRep, outArg(allLocalRep));
    if (allLocalRep != 1) {
      // At least one process does not own all the elements.
      // This makes the Map a distributed Map.
      global = true;
    }
  }
  // If the communicator has only one process, then the Map is not
  // distributed.
 
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done; global=" << (global ? "true" : "false")
       << endl;
    std::cerr << os.str();
  }
  return global;
}
 
}  // namespace Tpetra
 
template <class LocalOrdinal, class GlobalOrdinal>
Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal>>
Tpetra::createLocalMap(const size_t numElements,
                       const Teuchos::RCP<const Teuchos::Comm<int>>& comm) {
  typedef LocalOrdinal LO;
  typedef GlobalOrdinal GO;
  using NT = typename ::Tpetra::Map<LO, GO>::node_type;
  return createLocalMapWithNode<LO, GO, NT>(numElements, comm);
}
 
template <class LocalOrdinal, class GlobalOrdinal>
Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal>>
Tpetra::createUniformContigMap(const global_size_t numElements,
                               const Teuchos::RCP<const Teuchos::Comm<int>>& comm) {
  typedef LocalOrdinal LO;
  typedef GlobalOrdinal GO;
  using NT = typename ::Tpetra::Map<LO, GO>::node_type;
  return createUniformContigMapWithNode<LO, GO, NT>(numElements, comm);
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>>
Tpetra::createUniformContigMapWithNode(const global_size_t numElements,
                                       const Teuchos::RCP<const Teuchos::Comm<int>>& comm) {
  using Teuchos::rcp;
  using map_type                = Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>;
  const GlobalOrdinal indexBase = static_cast<GlobalOrdinal>(0);
 
  return rcp(new map_type(numElements, indexBase, comm, GloballyDistributed));
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>>
Tpetra::createLocalMapWithNode(const size_t numElements,
                               const Teuchos::RCP<const Teuchos::Comm<int>>& comm) {
  using Teuchos::rcp;
  using Tpetra::global_size_t;
  using map_type                    = Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>;
  const GlobalOrdinal indexBase     = 0;
  const global_size_t globalNumElts = static_cast<global_size_t>(numElements);
 
  return rcp(new map_type(globalNumElts, indexBase, comm, LocallyReplicated));
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>>
Tpetra::createContigMapWithNode(const Tpetra::global_size_t numElements,
                                const size_t localNumElements,
                                const Teuchos::RCP<const Teuchos::Comm<int>>& comm) {
  using Teuchos::rcp;
  using map_type                = Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>;
  const GlobalOrdinal indexBase = 0;
 
  return rcp(new map_type(numElements, localNumElements, indexBase, comm));
}
 
template <class LocalOrdinal, class GlobalOrdinal>
Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal>>
Tpetra::createContigMap(const Tpetra::global_size_t numElements,
                        const size_t localNumElements,
                        const Teuchos::RCP<const Teuchos::Comm<int>>& comm) {
  typedef LocalOrdinal LO;
  typedef GlobalOrdinal GO;
  using NT = typename Tpetra::Map<LO, GO>::node_type;
 
  return Tpetra::createContigMapWithNode<LO, GO, NT>(numElements, localNumElements, comm);
}
 
template <class LocalOrdinal, class GlobalOrdinal>
Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal>>
Tpetra::createNonContigMap(const Teuchos::ArrayView<const GlobalOrdinal>& elementList,
                           const Teuchos::RCP<const Teuchos::Comm<int>>& comm) {
  typedef LocalOrdinal LO;
  typedef GlobalOrdinal GO;
  using NT = typename Tpetra::Map<LO, GO>::node_type;
 
  return Tpetra::createNonContigMapWithNode<LO, GO, NT>(elementList, comm);
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>>
Tpetra::createNonContigMapWithNode(const Teuchos::ArrayView<const GlobalOrdinal>& elementList,
                                   const Teuchos::RCP<const Teuchos::Comm<int>>& comm) {
  using Teuchos::rcp;
  using map_type = Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>;
  using GST      = Tpetra::global_size_t;
  const GST INV  = Tpetra::Details::OrdinalTraits<GST>::invalid();
  // FIXME (mfh 22 Jul 2016) This is what I found here, but maybe this
  // shouldn't be zero, given that the index base is supposed to equal
  // the globally min global index?
  const GlobalOrdinal indexBase = 0;
 
  return rcp(new map_type(INV, elementList, indexBase, comm));
}
 
template <class LO, class GO, class NT>
Teuchos::RCP<const Tpetra::Map<LO, GO, NT>>
Tpetra::createOneToOne(const Teuchos::RCP<const Tpetra::Map<LO, GO, NT>>& M) {
  using Details::verbosePrintArray;
  using std::cerr;
  using std::endl;
  using Teuchos::Array;
  using Teuchos::ArrayView;
  using Teuchos::as;
  using Teuchos::rcp;
  using map_type = Tpetra::Map<LO, GO, NT>;
  using GST      = global_size_t;
 
  const bool verbose = Details::Behavior::verbose("Map");
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    auto comm = M.is_null() ? Teuchos::null : M->getComm();
    prefix    = Details::createPrefix(
           comm.getRawPtr(), "createOneToOne(Map)");
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    cerr << os.str();
  }
  const size_t maxNumToPrint = verbose ? Details::Behavior::verbosePrintCountThreshold() : size_t(0);
  const GST GINV             = Tpetra::Details::OrdinalTraits<GST>::invalid();
  const int myRank           = M->getComm()->getRank();
 
  // Bypasses for special cases where either M is known to be
  // one-to-one, or the one-to-one version of M is easy to compute.
  // This is why we take M as an RCP, not as a const reference -- so
  // that we can return M itself if it is 1-to-1.
  if (!M->isDistributed()) {
    // For a locally replicated Map, we assume that users want to push
    // all the GIDs to Process 0.
 
    // mfh 05 Nov 2013: getGlobalNumElements() does indeed return what
    // you think it should return, in this special case of a locally
    // replicated contiguous Map.
    const GST numGlobalEntries = M->getGlobalNumElements();
    if (M->isContiguous()) {
      const size_t numLocalEntries =
          (myRank == 0) ? as<size_t>(numGlobalEntries) : size_t(0);
      if (verbose) {
        std::ostringstream os;
        os << *prefix << "Input is locally replicated & contiguous; "
                         "numLocalEntries="
           << numLocalEntries << endl;
        cerr << os.str();
      }
      auto retMap =
          rcp(new map_type(numGlobalEntries, numLocalEntries,
                           M->getIndexBase(), M->getComm()));
      if (verbose) {
        std::ostringstream os;
        os << *prefix << "Done" << endl;
        cerr << os.str();
      }
      return retMap;
    } else {
      if (verbose) {
        std::ostringstream os;
        os << *prefix << "Input is locally replicated & noncontiguous"
           << endl;
        cerr << os.str();
      }
      ArrayView<const GO> myGids =
          (myRank == 0) ? M->getLocalElementList() : Teuchos::null;
      auto retMap =
          rcp(new map_type(GINV, myGids(), M->getIndexBase(),
                           M->getComm()));
      if (verbose) {
        std::ostringstream os;
        os << *prefix << "Done" << endl;
        cerr << os.str();
      }
      return retMap;
    }
  } else if (M->isContiguous()) {
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Input is distributed & contiguous" << endl;
      cerr << os.str();
    }
    // Contiguous, distributed Maps are one-to-one by construction.
    // (Locally replicated Maps can be contiguous.)
    return M;
  } else {
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Input is distributed & noncontiguous" << endl;
      cerr << os.str();
    }
    Tpetra::Directory<LO, GO, NT> directory;
    const size_t numMyElems     = M->getLocalNumElements();
    ArrayView<const GO> myElems = M->getLocalElementList();
    Array<int> owner_procs_vec(numMyElems);
 
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Call Directory::getDirectoryEntries: ";
      verbosePrintArray(os, myElems, "GIDs", maxNumToPrint);
      os << endl;
      cerr << os.str();
    }
    directory.getDirectoryEntries(*M, myElems, owner_procs_vec());
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "getDirectoryEntries result: ";
      verbosePrintArray(os, owner_procs_vec, "PIDs", maxNumToPrint);
      os << endl;
      cerr << os.str();
    }
 
    Array<GO> myOwned_vec(numMyElems);
    size_t numMyOwnedElems = 0;
    for (size_t i = 0; i < numMyElems; ++i) {
      const GO GID    = myElems[i];
      const int owner = owner_procs_vec[i];
 
      if (myRank == owner) {
        myOwned_vec[numMyOwnedElems++] = GID;
      }
    }
    myOwned_vec.resize(numMyOwnedElems);
 
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Create Map: ";
      verbosePrintArray(os, myOwned_vec, "GIDs", maxNumToPrint);
      os << endl;
      cerr << os.str();
    }
    auto retMap = rcp(new map_type(GINV, myOwned_vec(),
                                   M->getIndexBase(), M->getComm()));
    if (verbose) {
      std::ostringstream os;
      os << *prefix << "Done" << endl;
      cerr << os.str();
    }
    return retMap;
  }
}
 
template <class LocalOrdinal, class GlobalOrdinal, class Node>
Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>>
Tpetra::createOneToOne(const Teuchos::RCP<const Tpetra::Map<LocalOrdinal, GlobalOrdinal, Node>>& M,
                       const Tpetra::Details::TieBreak<LocalOrdinal, GlobalOrdinal>& tie_break) {
  using Details::Behavior;
  using Details::verbosePrintArray;
  using std::cerr;
  using std::endl;
  using Teuchos::Array;
  using Teuchos::ArrayView;
  using Teuchos::RCP;
  using Teuchos::rcp;
  using Teuchos::toString;
  using LO       = LocalOrdinal;
  using GO       = GlobalOrdinal;
  using map_type = Tpetra::Map<LO, GO, Node>;
 
  const bool verbose = Behavior::verbose("Map");
  std::unique_ptr<std::string> prefix;
  if (verbose) {
    auto comm = M.is_null() ? Teuchos::null : M->getComm();
    prefix    = Details::createPrefix(
           comm.getRawPtr(), "createOneToOne(Map,TieBreak)");
    std::ostringstream os;
    os << *prefix << "Start" << endl;
    cerr << os.str();
  }
  const size_t maxNumToPrint = verbose ? Behavior::verbosePrintCountThreshold() : size_t(0);
 
  // FIXME (mfh 20 Feb 2013) We should have a bypass for contiguous
  // Maps (which are 1-to-1 by construction).
 
  Tpetra::Directory<LO, GO, Node> directory;
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Initialize Directory" << endl;
    cerr << os.str();
  }
  directory.initialize(*M, tie_break);
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done initializing Directory" << endl;
    cerr << os.str();
  }
  size_t numMyElems           = M->getLocalNumElements();
  ArrayView<const GO> myElems = M->getLocalElementList();
  Array<int> owner_procs_vec(numMyElems);
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Call Directory::getDirectoryEntries: ";
    verbosePrintArray(os, myElems, "GIDs", maxNumToPrint);
    os << endl;
    cerr << os.str();
  }
  directory.getDirectoryEntries(*M, myElems, owner_procs_vec());
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "getDirectoryEntries result: ";
    verbosePrintArray(os, owner_procs_vec, "PIDs", maxNumToPrint);
    os << endl;
    cerr << os.str();
  }
 
  const int myRank = M->getComm()->getRank();
  Array<GO> myOwned_vec(numMyElems);
  size_t numMyOwnedElems = 0;
  for (size_t i = 0; i < numMyElems; ++i) {
    const GO GID    = myElems[i];
    const int owner = owner_procs_vec[i];
    if (myRank == owner) {
      myOwned_vec[numMyOwnedElems++] = GID;
    }
  }
  myOwned_vec.resize(numMyOwnedElems);
 
  // FIXME (mfh 08 May 2014) The above Directory should be perfectly
  // valid for the new Map.  Why can't we reuse it?
  const global_size_t GINV =
      Tpetra::Details::OrdinalTraits<global_size_t>::invalid();
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Create Map: ";
    verbosePrintArray(os, myOwned_vec, "GIDs", maxNumToPrint);
    os << endl;
    cerr << os.str();
  }
  RCP<const map_type> retMap(new map_type(GINV, myOwned_vec(), M->getIndexBase(),
                                          M->getComm()));
  if (verbose) {
    std::ostringstream os;
    os << *prefix << "Done" << endl;
    cerr << os.str();
  }
  return retMap;
}
 
//
// Explicit instantiation macro
//
// Must be expanded from within the Tpetra namespace!
//
 
 
#define TPETRA_MAP_INSTANT(LO, GO, NODE)                                                            \
                                                                                                    \
  template class Map<LO, GO, NODE>;                                                                 \
                                                                                                    \
  template Teuchos::RCP<const Map<LO, GO, NODE>>                                                    \
  createLocalMapWithNode<LO, GO, NODE>(const size_t numElements,                                    \
                                       const Teuchos::RCP<const Teuchos::Comm<int>>& comm);         \
                                                                                                    \
  template Teuchos::RCP<const Map<LO, GO, NODE>>                                                    \
  createContigMapWithNode<LO, GO, NODE>(const global_size_t numElements,                            \
                                        const size_t localNumElements,                              \
                                        const Teuchos::RCP<const Teuchos::Comm<int>>& comm);        \
                                                                                                    \
  template Teuchos::RCP<const Map<LO, GO, NODE>>                                                    \
  createNonContigMapWithNode(const Teuchos::ArrayView<const GO>& elementList,                       \
                             const Teuchos::RCP<const Teuchos::Comm<int>>& comm);                   \
                                                                                                    \
  template Teuchos::RCP<const Map<LO, GO, NODE>>                                                    \
  createUniformContigMapWithNode<LO, GO, NODE>(const global_size_t numElements,                     \
                                               const Teuchos::RCP<const Teuchos::Comm<int>>& comm); \
                                                                                                    \
  template Teuchos::RCP<const Map<LO, GO, NODE>>                                                    \
  createOneToOne(const Teuchos::RCP<const Map<LO, GO, NODE>>& M);                                   \
                                                                                                    \
  template Teuchos::RCP<const Map<LO, GO, NODE>>                                                    \
  createOneToOne(const Teuchos::RCP<const Map<LO, GO, NODE>>& M,                                    \
                 const Tpetra::Details::TieBreak<LO, GO>& tie_break);
 
#define TPETRA_MAP_INSTANT_DEFAULTNODE(LO, GO)                                         \
  template Teuchos::RCP<const Map<LO, GO>>                                             \
  createLocalMap<LO, GO>(const size_t, const Teuchos::RCP<const Teuchos::Comm<int>>&); \
                                                                                       \
  template Teuchos::RCP<const Map<LO, GO>>                                             \
  createContigMap<LO, GO>(global_size_t, size_t,                                       \
                          const Teuchos::RCP<const Teuchos::Comm<int>>&);              \
                                                                                       \
  template Teuchos::RCP<const Map<LO, GO>>                                             \
  createNonContigMap(const Teuchos::ArrayView<const GO>&,                              \
                     const Teuchos::RCP<const Teuchos::Comm<int>>&);                   \
                                                                                       \
  template Teuchos::RCP<const Map<LO, GO>>                                             \
  createUniformContigMap<LO, GO>(const global_size_t,                                  \
                                 const Teuchos::RCP<const Teuchos::Comm<int>>&);
 
#endif  // TPETRA_MAP_DEF_HPP