MPI calculations are wrong on multicore than on one

Question

I am newbie on MPI and study it as a university course. The task was to numerically find the value of const e using MPI_Send() and MPI_Recv(). The only suitable way I found was

I run it on 2, 3 and 4 cores but get the wrong number while on 1 core everything is fine. Here's my code:

#include <iostream>
#include <fstream>
#include <cmath>
#include "mpi.h"

using namespace std;

const int n = 1e04;
double start_time, _time;
int w_size, w_rank, name_len;
char cpu_name[MPI_MAX_PROCESSOR_NAME];
ofstream fout("exp_result", std::ios_base::app | std::ios_base::out);

long double factorial(int num){
    if (num < 1)
        return 1;
    else
        return num * factorial(num - 1);
}

void e_finder(){
    long double sum = 0.0, e = 0.0;
    if(w_rank == 0)
        start_time = MPI_Wtime();

    for(int i = 0; i < n; i+=w_size)
        sum += 1.0 / factorial(i);
    MPI_Send(&sum, 1, MPI_LONG_DOUBLE, 0, 0, MPI_COMM_WORLD);

    if(w_rank == 0){
        // e += sum;
        for (int i = 0; i < w_size; i++){
            MPI_Recv(&sum, 1, MPI_LONG_DOUBLE, i, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
            e += sum;
        }
        _time = MPI_Wtime() - start_time;
        cout.precision(29);
        cout << "e = "<< e << endl << fixed << "error is " << abs(e - M_E) << endl;
        cout.precision(9);
        cout << "\nwall clock time = " <<_time << " sec\n";
        fout << w_size << "\t" << _time << endl;
    }
}

int main(int argc, char const *argv[]) {
    MPI_Init(NULL, NULL);
    MPI_Comm_size(MPI_COMM_WORLD, &w_size);
    MPI_Comm_rank(MPI_COMM_WORLD, &w_rank);
    MPI_Get_processor_name(cpu_name, &name_len);

    cout<<"calculations started on cpu:" << w_rank << "!\n";
    MPI_Barrier(MPI_COMM_WORLD);

    e_finder();

    MPI_Finalize();
    fout.close();
    return 0;
}

Can someone help me find out and grasp the mistake? Here are the outputs:

$ mpirun -np 1 ./exp1
calculations started on cpu:0!
e = 2.718281828459045235428168108
error is 0.00000000000000014463256980957

wall clock time = 4.370553009 sec



$ mpirun -np 2 ./exp1
calculations started on cpu:0!
calculations started on cpu:1!
e = 3.0861612696304875570925407846
error is 0.36787944117144246629694248618

wall clock time = 2.449338411 sec



$ mpirun -np 3 ./exp1
calculations started on cpu:0!
calculations started on cpu:1!
calculations started on cpu:2!
e = 3.5041749401277555767651727958
error is 0.78589311166871048596957449739

wall clock time = 2.011082204 sec



$ mpirun -np 4 ./exp1
calculations started on cpu:0!
calculations started on cpu:3!
calculations started on cpu:1!
calculations started on cpu:2!
e = 4.1667658813667669917037150729
error is 1.44848405290772190090811677443

wall clock time = 1.617427335 sec

Answer 1

The issue is with how you are dividing up the work. It seems like you want each program to calculate a portion of the fractions. However, they are all starting on the first fraction and then calculating every w_size-th fraction. This results in some fractions being calculated multiple times and some never being calculated at all. This should be fixed by changing the line

for(int i = 0; i < n; i+=w_size)

to

for(int i = w_rank; i < n; i+=w_size)

This makes each program start on a different fraction, and since they are calculating every w_size-th fractions, there shouldn't be any more collisions between calculated fractions.