MCL.cpp

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/****************************************************************/
/* Parallel Combinatorial BLAS Library (for Graph Computations) */
/* version 1.6 -------------------------------------------------*/
/* date: 6/15/2017 ---------------------------------------------*/
/* authors: Ariful Azad, Aydin Buluc  --------------------------*/
/****************************************************************/
/*
 Copyright (c) 2010-2017, The Regents of the University of California
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
 in the Software without restriction, including without limitation the rights
 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the Software is
 furnished to do so, subject to the following conditions:
 
 The above copyright notice and this permission notice shall be included in
 all copies or substantial portions of the Software.
 
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 */
 
 
#include <mpi.h>
 
// These macros should be defined before stdint.h is included
#ifndef __STDC_CONSTANT_MACROS
#define __STDC_CONSTANT_MACROS
#endif
#ifndef __STDC_LIMIT_MACROS
#define __STDC_LIMIT_MACROS
#endif
#include <stdint.h>
 
#include <sys/time.h>
#include <iostream>
#include <fstream>
#include <string>
#include <sstream>  // Required for stringstreams
#include <ctime>
#include <cmath>
#include "CombBLAS/CombBLAS.h"
#include "CC.h"
#include "WriteMCLClusters.h"
 
using namespace std;
using namespace combblas;
 
#define EPS 0.0001
 
double mcl_Abcasttime;
double mcl_Bbcasttime;
double mcl_localspgemmtime;
double mcl_multiwaymergetime;
double mcl_kselecttime;
double mcl_prunecolumntime;
double cblas_allgathertime; // for compilation (TODO: fix this dependency)
int64_t mcl_memory;
double tIO;
 
 
 
class Dist
{
    public:
    typedef SpDCCols < int64_t, double > DCCols;
    typedef SpParMat < int64_t, double, DCCols > MPI_DCCols;
    typedef FullyDistVec < int64_t, double> MPI_DenseVec;
};
 
 
 
typedef struct
{
    //Input/Output file
    string ifilename;
    bool isInputMM;
    int base; // only usefule for matrix market files
    
    string ofilename;
    
    //Preprocessing
    int randpermute;
    bool remove_isolated;
    
    //inflation
    double inflation;
    
    //pruning
    double prunelimit;
    int64_t select;
    int64_t recover_num;
    double recover_pct;
    int kselectVersion; // 0: adapt based on k, 1: kselect1, 2: kselect2
    
    //HipMCL optimization
    int phases;
    int perProcessMem;
    bool isDoublePrecision; // true: double, false: float
    bool is64bInt; // true: int64_t, false: int32_t (currently for both local and global indexing)
    
    //debugging
    bool show;
    
    
}HipMCLParam;
 
 
void InitParam(HipMCLParam & param)
{
    //Input/Output file
    param.ifilename = "";
    param.isInputMM = false;
    param.ofilename = "";
    param.base = 1;
    
    //Preprocessing
    // mcl removes isolated vertices by default,
    // we don't do this because it will create different ordering of vertices!
    param.remove_isolated = false;
    param.randpermute = 0;
    
    //inflation
    param.inflation = 0.0;
    
    //pruning
    param.prunelimit = 1.0/10000.0;
    param.select = 1100;
    param.recover_num = 1400;
    param.recover_pct = .9; // we allow both 90 or .9 as input. Internally, we keep it 0.9
    param.kselectVersion = 1;
    
    //HipMCL optimization
    param.phases = 1;
    param.perProcessMem = 0;
    param.isDoublePrecision = true;
    param.is64bInt = true;
    
    //debugging
    param.show = false;
}
 
void ShowParam(HipMCLParam & param)
{
    ostringstream runinfo;
    runinfo << "\n======================================" << endl;
    runinfo << "Running HipMCL with the parameters: " << endl;
    runinfo << "======================================" << endl;
    runinfo << "Input/Output file" << endl;
    runinfo << "    input filename: " << param.ifilename << endl;
    runinfo << "    input file type: " ;
    if(param.isInputMM)
    {
        runinfo << " Matrix Market" << endl;
        runinfo << "    Base of the input matrix: " << param.base << endl;
    }
    else runinfo << " Labeled Triples format" << endl;
    runinfo << "    Output filename: " << param.ofilename << endl;
    
    
    runinfo << "Preprocessing" << endl;
    runinfo << "    Remove isolated vertices? : ";
    if (param.remove_isolated) runinfo << "yes";
    else runinfo << "no" << endl;
    
    runinfo << "    Randomly permute vertices? : ";
    if (param.randpermute) runinfo << "yes";
    else runinfo << "no" << endl;
    
    runinfo << "Inflation: " << param.inflation << endl;
    
    runinfo << "Pruning" << endl;
    runinfo << "    Prunelimit: " << param.prunelimit << endl;
    runinfo << "    Recover number: " << param.recover_num << endl;
    runinfo << "    Recover percent: " << ceil(param.recover_pct*100) << endl;
    runinfo << "    Selection number: " << param.select << endl;
    // do not expose selection option at this moment
    //runinfo << "Selection algorithm: ";
    //if(kselectVersion==1) runinfo << "tournament select" << endl;
    //else if(kselectVersion==2) runinfo << "quickselect" << endl;
    //else runinfo << "adaptive based on k" << endl;
    
    
    
    runinfo << "HipMCL optimization" << endl;
    runinfo << "    Number of phases: " << param.phases << endl;
    runinfo << "    Memory avilable per process: ";
    if(param.perProcessMem>0) runinfo << param.perProcessMem << "GB" << endl;
    else runinfo << "not provided" << endl;
    if(param.isDoublePrecision) runinfo << "Using double precision floating point" << endl;
    else runinfo << "Using single precision floating point" << endl;
    if(param.is64bInt ) runinfo << "Using 64 bit indexing" << endl;
    else runinfo << "Using 32 bit indexing" << endl;
    
    runinfo << "Debugging" << endl;
    runinfo << "    Show matrices after major steps? : ";
    if (param.show) runinfo << "yes";
    else runinfo << "no" << endl;
    runinfo << "======================================" << endl;
    SpParHelper::Print(runinfo.str());
}
 
void ProcessParam(int argc, char* argv[], HipMCLParam & param)
{
    for (int i = 1; i < argc; i++)
    {
        if (strcmp(argv[i],"-M")==0){
            param.ifilename = string(argv[i+1]);
        }
        else if (strcmp(argv[i],"--matrix-market")==0){
            param.isInputMM = true;
        }
        else if (strcmp(argv[i],"-o")==0){
            param.ofilename = string(argv[i+1]);
        }
        else if (strcmp(argv[i],"--show")==0){
            param.show = true;
        }
        else if (strcmp(argv[i],"--remove-isolated")==0){
            param.remove_isolated = true;
        }
        else if (strcmp(argv[i],"--tournament-select")==0){
            param.kselectVersion = 1;
        }
        else if (strcmp(argv[i],"--quick-select")==0){
            param.kselectVersion = 2;
            
        }
        else if (strcmp(argv[i],"-I")==0){
            param.inflation = atof(argv[i + 1]);
            
        } else if (strcmp(argv[i],"-p")==0) {
            param.prunelimit = atof(argv[i + 1]);
            
        } else if (strcmp(argv[i],"-S")==0) {
            param.select = atoi(argv[i + 1]);
            
        } else if (strcmp(argv[i],"-R")==0) {
            param.recover_num = atoi(argv[i + 1]);
            
        } else if (strcmp(argv[i],"-pct")==0)
        {
            param.recover_pct = atof(argv[i + 1]);
            if(param.recover_pct>1) param.recover_pct/=100.00;
        } else if (strcmp(argv[i],"-base")==0) {
            param.base = atoi(argv[i + 1]);
        }
        else if (strcmp(argv[i],"-rand")==0) {
            param.randpermute = atoi(argv[i + 1]);
        }
        else if (strcmp(argv[i],"-phases")==0) {
            param.phases = atoi(argv[i + 1]);
        }
        else if (strcmp(argv[i],"-per-process-mem")==0) {
            param.perProcessMem = atoi(argv[i + 1]);
        }
        else if (strcmp(argv[i],"--single-precision")==0) {
            param.isDoublePrecision = false;
        }
        else if (strcmp(argv[i],"--32bit-index")==0) {
            param.is64bInt = false;
        }
    }
    
    if(param.ofilename=="") // construct output file name if it is not provided
    {
        param.ofilename = param.ifilename + ".hipmcl";
    }
    
}
 
 
void ShowOptions()
{
    ostringstream runinfo;
    
    runinfo << "Usage: ./hipmcl -M <input filename> -I <inlfation> (required)" << endl;
    
    runinfo << "======================================" << endl;
    runinfo << "     Detail parameter options    " << endl;
    runinfo << "======================================" << endl;
    
    
    
    runinfo << "Input/Output file" << endl;
    runinfo << "    -M <input file name (labeled triples format)> (mandatory)" << endl;
    runinfo << "    --matrix-market : if provided, the input file is in the matrix market format (default: the file is in labeled triples format)" << endl;
    runinfo << "    -base <index of the first vertex in the matrix market file, 0|1> (default: 1) " << endl;
    runinfo << "    -o <output filename> (default: input_file_name.hipmcl )" << endl;
    
    runinfo << "Inflation" << endl;
    runinfo << "-I <inflation> (mandatory)\n";
    
    runinfo << "Preprocessing" << endl;
    runinfo << "    -rand <randomly permute vertices> (default:0)\n";
    runinfo << "    --remove-isolated : if provided, remove isolated vertices (default: don't remove isolated vertices)\n";
    
    
    runinfo << "Pruning" << endl;
    runinfo << "    -p <cutoff> (default: 1/10000)\n";
    runinfo << "    -R <recovery number> (default: 1400)\n";
    runinfo << "    -pct <recovery pct> (default: 90)\n";
    runinfo << "    -S <selection number> (default: 1100)\n";
    
    
    runinfo << "HipMCL optimization" << endl;
    runinfo << "    -phases <number of phases> (default:1)\n";
    runinfo << "    -per-process-mem <memory (GB) available per process> (default:0, number of phases is not estimated)\n";
    runinfo << "    --single-precision (if not provided, use double precision floating point numbers)\n" << endl;
    runinfo << "    --32bit-index (if not provided, use 64 bit indexing for vertex ids)\n" << endl;
    
    runinfo << "Debugging" << endl;
    runinfo << "    --show: show information about matrices after major steps (default: do not show matrices)" << endl;
 
 
    
    runinfo << "======================================" << endl;
    runinfo << "     Few examples    " << endl;
    runinfo << "======================================" << endl;
    runinfo << "Example with with a graph in labeled triples format on a laptop with 8GB memory and 8 cores:\nexport OMP_NUM_THREADS=8\nbin/hipmcl -M data/sevenvertexgraph.txt -I 2 -per-process-mem 8" << endl;
    runinfo << "Same as above with 4 processes and 2 theaded per process cores:\nexport OMP_NUM_THREADS=2\nmpirun -np 4 bin/hipmcl -M data/sevenvertexgraph.txt -I 2 -per-process-mem 2" << endl;
    runinfo << "Example with a graph in matrix market format:\nbin/hipmcl -M data/sevenvertex.mtx --matrix-market -base 1 -I 2 -per-process-mem 8" << endl;
    
    runinfo << "Example on the NERSC/Edison system with 16 nodes and 24 threads per node: \nsrun -N 16 -n 16 -c 24  bin/hipmcl -M data/hep-th.mtx --matrix-market -base 1 -per-process-mem 64 -o hep-th.hipmcl" << endl;
    SpParHelper::Print(runinfo.str());
}
 
 
// base: base of items
// clusters are always numbered 0-based
template <typename IT, typename NT, typename DER>
FullyDistVec<IT, IT> Interpret(SpParMat<IT,NT,DER> & A)
{
    IT nCC;
    // A is a directed graph
    // symmetricize A
    
    SpParMat<IT,NT,DER> AT = A;
    AT.Transpose();
    A += AT;
    FullyDistVec<IT, IT> cclabels = CC(A, nCC);
    return cclabels;
}
 
 
template <typename IT, typename NT, typename DER>
void MakeColStochastic(SpParMat<IT,NT,DER> & A)
{
    FullyDistVec<IT, NT> colsums = A.Reduce(Column, plus<NT>(), 0.0);
    colsums.Apply(safemultinv<NT>());
    A.DimApply(Column, colsums, multiplies<NT>());  // scale each "Column" with the given vector
}
 
template <typename IT, typename NT, typename DER>
NT Chaos(SpParMat<IT,NT,DER> & A)
{
    // sums of squares of columns
    FullyDistVec<IT, NT> colssqs = A.Reduce(Column, plus<NT>(), 0.0, bind2nd(exponentiate(), 2));
    // Matrix entries are non-negative, so max() can use zero as identity
    FullyDistVec<IT, NT> colmaxs = A.Reduce(Column, maximum<NT>(), 0.0);
    colmaxs -= colssqs;
    
    // multiplu by number of nonzeros in each column
    FullyDistVec<IT, NT> nnzPerColumn = A.Reduce(Column, plus<NT>(), 0.0, [](NT val){return 1.0;});
    colmaxs.EWiseApply(nnzPerColumn, multiplies<NT>());
    
    return colmaxs.Reduce(maximum<NT>(), 0.0);
}
 
template <typename IT, typename NT, typename DER>
void Inflate(SpParMat<IT,NT,DER> & A, double power)
{
    A.Apply(bind2nd(exponentiate(), power));
}
 
// default adjustloop setting
// 1. Remove loops
// 2. set loops to max of all arc weights
template <typename IT, typename NT, typename DER>
void AdjustLoops(SpParMat<IT,NT,DER> & A)
{
 
    A.RemoveLoops();
    FullyDistVec<IT, NT> colmaxs = A.Reduce(Column, maximum<NT>(), numeric_limits<NT>::min());
    A.Apply([](NT val){return val==numeric_limits<NT>::min() ? 1.0 : val;}); // for isolated vertices
    A.AddLoops(colmaxs);
    ostringstream outs;
    outs << "Adjusting loops" << endl;
    SpParHelper::Print(outs.str());
}
 
template <typename IT, typename NT, typename DER>
void RemoveIsolated(SpParMat<IT,NT,DER> & A, HipMCLParam & param)
{
    ostringstream outs;
    FullyDistVec<IT, NT> ColSums = A.Reduce(Column, plus<NT>(), 0.0);
    FullyDistVec<IT, IT> nonisov = ColSums.FindInds(bind2nd(greater<NT>(), 0));
    IT numIsolated = A.getnrow() - nonisov.TotalLength();
    outs << "Number of isolated vertices: " << numIsolated << endl;
    SpParHelper::Print(outs.str());
    
    A(nonisov, nonisov, true);
    SpParHelper::Print("Removed isolated vertices.\n");
    if(param.show)
    {
        A.PrintInfo();
    }
    
}
 
//TODO: handle reordered cluster ids
template <typename IT, typename NT, typename DER>
void RandPermute(SpParMat<IT,NT,DER> & A, HipMCLParam & param)
{
    // randomly permute for load balance
    if(A.getnrow() == A.getncol())
    {
        FullyDistVec<IT, IT> p( A.getcommgrid());
        p.iota(A.getnrow(), 0);
        p.RandPerm();
        (A)(p,p,true);// in-place permute to save memory
        SpParHelper::Print("Applied symmetric permutation.\n");
    }
    else
    {
        SpParHelper::Print("Rectangular matrix: Can not apply symmetric permutation.\n");
    }
}
 
template <typename IT, typename NT, typename DER>
FullyDistVec<IT, IT> HipMCL(SpParMat<IT,NT,DER> & A, HipMCLParam & param)
{
    if(param.remove_isolated)
        RemoveIsolated(A, param);
    
    if(param.randpermute)
        RandPermute(A, param);
 
    // Adjust self loops
    AdjustLoops(A);
 
    // Make stochastic
    MakeColStochastic(A);
    SpParHelper::Print("Made stochastic\n");
 
    if(param.show)
    {
        A.PrintInfo();
    }
    
 
    // chaos doesn't make sense for non-stochastic matrices
    // it is in the range {0,1} for stochastic matrices
    NT chaos = 1;
    int it=1;
    double tInflate = 0;
    double tExpand = 0;
     typedef PlusTimesSRing<NT, NT> PTFF;
    // while there is an epsilon improvement
    while( chaos > EPS)
    {
        double t1 = MPI_Wtime();
        //A.Square<PTFF>() ;        // expand
        A = MemEfficientSpGEMM<PTFF, NT, DER>(A, A, param.phases, param.prunelimit, (IT)param.select, (IT)param.recover_num, param.recover_pct, param.kselectVersion, param.perProcessMem);
        
        MakeColStochastic(A);
        tExpand += (MPI_Wtime() - t1);
        
        if(param.show)
        {
            SpParHelper::Print("After expansion\n");
            A.PrintInfo();
        }
        chaos = Chaos(A);
        
        double tInflate1 = MPI_Wtime();
        Inflate(A, param.inflation);
        MakeColStochastic(A);
        tInflate += (MPI_Wtime() - tInflate1);
        
        if(param.show)
        {
            SpParHelper::Print("After inflation\n");
            A.PrintInfo();
        }
        
        
        
        double newbalance = A.LoadImbalance();
        double t3=MPI_Wtime();
        stringstream s;
        s << "Iteration# "  << setw(3) << it << " : "  << " chaos: " << setprecision(3) << chaos << "  load-balance: "<< newbalance << " Time: " << (t3-t1) << endl;
        SpParHelper::Print(s.str());
        it++;
        
        
        
    }
    
    
    double tcc1 = MPI_Wtime();
    // bool does not work because A.AddLoops(1) can not create a fullydist vector with Bool?
    // write a promote train for float
    SpParMat<IT,double, SpDCCols < IT, double >> ADouble = A;
    FullyDistVec<IT, IT> cclabels = Interpret(ADouble);
    double tcc = MPI_Wtime() - tcc1;
    
    
#ifdef TIMING
    int myrank;
    MPI_Comm_rank(MPI_COMM_WORLD,&myrank);
    if(myrank==0)
    {
        cout << "================detailed timing==================" << endl;
        
        cout << "Expansion: " << mcl_Abcasttime + mcl_Bbcasttime + mcl_localspgemmtime + mcl_multiwaymergetime << endl;
        cout << "       Abcast= " << mcl_Abcasttime << endl;
        cout << "       Bbcast= " << mcl_Bbcasttime << endl;
        cout << "       localspgemm= " << mcl_localspgemmtime << endl;
        cout << "       multiwaymergetime= "<< mcl_multiwaymergetime << endl;
        cout << "Prune: " << mcl_kselecttime + mcl_prunecolumntime << endl;
        cout << "       kselect= " << mcl_kselecttime << endl;
        cout << "       prunecolumn= " << mcl_prunecolumntime << endl;
        cout << "Inflation " << tInflate << endl;
        cout << "Component: " << tcc << endl;
        cout << "File I/O: " << tIO << endl;
        cout << "=================================================" << endl;
    }
    
#endif
    
    return cclabels;
 
 
}
 
template <typename IT, typename NT, typename DER>
void Symmetricize(SpParMat<IT,NT,DER> & A)
{
    SpParMat<IT,NT,DER> AT = A;
    AT.Transpose();
    if(!(AT == A))
    {
        SpParHelper::Print("Symmatricizing an unsymmetric input matrix.\n");
        A += AT;
    }
}
 
template <typename GIT, typename LIT, typename NT>
void MainBody(HipMCLParam & param)
{
    SpParMat<GIT,NT, SpDCCols < LIT, NT >> A(MPI_COMM_WORLD);    // construct object
    FullyDistVec<GIT, array<char, MAXVERTNAME> > vtxLabels(A.getcommgrid());
    
    // read file
    
    SpParHelper::Print("Reading input file......\n");
    
    double tIO1 = MPI_Wtime();
    if(param.isInputMM)
        A.ParallelReadMM(param.ifilename, param.base, maximum<NT>());    // if base=0, then it is implicitly converted to Boolean false
    else // default labeled triples format
        vtxLabels = A.ReadGeneralizedTuples(param.ifilename,  maximum<NT>());
    
    tIO = MPI_Wtime() - tIO1;
    ostringstream outs;
    outs << " : took " << tIO << " seconds" << endl;
    SpParHelper::Print(outs.str());
    // Symmetricize the matrix only if needed
    Symmetricize(A);
    
    double balance = A.LoadImbalance();
    
    outs.str("");
    outs.clear();
    if(!param.is64bInt) // don't compute nnz because it may overflow
    {
        GIT nnz = A.getnnz();
        GIT nv = A.getnrow();
        outs << "Number of vertices: " << nv << " number of edges: "<< nnz << endl;
    }
    outs << "Load balance: " << balance << endl;
    SpParHelper::Print(outs.str());
    
    if(param.show)
    {
        A.PrintInfo();
    }
    
    
    
#ifdef TIMING
    mcl_Abcasttime = 0;
    mcl_Bbcasttime = 0;
    mcl_localspgemmtime = 0;
    mcl_multiwaymergetime = 0;
    mcl_kselecttime = 0;
    mcl_prunecolumntime = 0;
#endif
    
    
    
    double tstart = MPI_Wtime();
    
    // Run HipMCL
    FullyDistVec<GIT, GIT> culstLabels = HipMCL(A, param);
    //culstLabels.ParallelWrite(param.ofilename, param.base); // clusters are always numbered 0-based
    
    if(param.isInputMM)
        WriteMCLClusters(param.ofilename, culstLabels, param.base);
    else
        WriteMCLClusters(param.ofilename, culstLabels, vtxLabels);
    
    
    
    GIT nclusters = culstLabels.Reduce(maximum<GIT>(), (GIT) 0 ) ;
    nclusters ++; // because of zero based indexing for clusters
    
    double tend = MPI_Wtime();
    stringstream s2;
    s2 << "Number of clusters: " << nclusters << endl;
    s2 << "Total time: " << (tend-tstart) << endl;
    s2 <<  "=================================================\n" << endl ;
    SpParHelper::Print(s2.str());
    
}
 
 
int main(int argc, char* argv[])
{
    int provided;
    MPI_Init_thread(&argc, &argv, MPI_THREAD_SERIALIZED, &provided);
    if (provided < MPI_THREAD_SERIALIZED)
    {
        printf("ERROR: The MPI library does not have MPI_THREAD_SERIALIZED support\n");
        MPI_Abort(MPI_COMM_WORLD, 1);
    }
    
    int nthreads = 1;
#ifdef THREADED
#pragma omp parallel
    {
        nthreads = omp_get_num_threads();
    }
#endif
    
    int nprocs, myrank;
    MPI_Comm_size(MPI_COMM_WORLD,&nprocs);
    MPI_Comm_rank(MPI_COMM_WORLD,&myrank);
    
    HipMCLParam param;
    
    // initialize parameters to default values
    InitParam(param);
    
    // Populate parameters from command line options
    ProcessParam(argc, argv, param);
    
    // check if mandatory arguments are provided
    if(param.ifilename=="" || param.inflation == 0.0)
    {
        SpParHelper::Print("Required options are missing.\n");
        ShowOptions();
        MPI_Finalize();
        return -1;
    }
    
    
    if(myrank == 0)
    {
        cout << "\nProcess Grid used (pr x pc x threads): " << sqrt(nprocs) << " x " << sqrt(nprocs) << " x " << nthreads << endl;
    }
    
    
    // show parameters used to run HipMCL
    ShowParam(param);
    
    if(param.perProcessMem==0)
    {
        if(myrank == 0)
        {
            cout << "******** Number of phases will not be estimated as -per-process-mem option is supplied. It is highly recommended that you provide -per-process-mem option for large-scale runs. *********** " << endl;
        }
    }
    
    {
        if(param.isDoublePrecision)
            if(param.is64bInt) // default case
                MainBody<int64_t, int64_t, double>(param);
            else
                MainBody<int32_t, int32_t, double>(param);
        else if(param.is64bInt)
            MainBody<int64_t, int64_t, float>(param);
        else
            MainBody<int32_t, int32_t, float>(param); // memory effecient case
    }
    
    
    
    // make sure the destructors for all objects are called before MPI::Finalize()
    MPI_Finalize(); 
    return 0;
}