Problem using pragma omp parallel for to compute pi

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I have written the following code to compute the value of pi and it works:

#include <omp.h>
#include <stdio.h>

static long num_steps = 1000000;
double step;
#define NUM_THREADS 16

int main()
{
    int i, nthreads;
    double tdata, pi, sum[NUM_THREADS];
    omp_set_num_threads(NUM_THREADS);
    step = 1.0 / (double)num_steps;

    tdata = omp_get_wtime();

    #pragma omp parallel
    {
        int i, id, nthrds;
        double x;
        id = omp_get_thread_num();
        nthrds = omp_get_num_threads();
        if (id == 0)
            nthreads = nthrds;
        for (i = id, sum[id] = 0.0; i < num_steps; i = i + nthrds)
        {
            x = (i + 0.5) * step;
            sum[id] = sum[id] + 4.0 / (1.0 + x * x);
        }
    }

    tdata = omp_get_wtime() - tdata;
    for (i = 0, pi = 0.0; i < nthreads; i++)
    {
        pi = pi + sum[i] * step;
    }
    printf("pi=%f and it took %f seconds", pi, tdata);
}

Then I learned that I can use #pragma omp parallel for and then I don't have to manually break the computation to different threads. So I wrote this:

#include <omp.h>
#include <stdio.h>

static long num_steps = 1000000;
double step;
#define NUM_THREADS 16

int main()
{
    int i;
    double tdata, pi, x, sum = 0.0;
    omp_set_num_threads(NUM_THREADS);
    step = 1.0 / (double)num_steps;

    tdata = omp_get_wtime();

    #pragma omp parallel for
    {
        for (i = 0; i < num_steps; i++)
        {
            x = (i + 0.5) * step;
            sum = sum + 4.0 / (1.0 + x * x);
        }
    }

    tdata = omp_get_wtime() - tdata;
    pi = sum * step;
    printf("pi = %f and compute time = %f seconds", pi, tdata);
}

This, however, doesn't work and outputs wrong values of pi. What am I doing wrong? Thank you.

openmp parallel-processing thread-safety multithreading c
1 Answers

There are two race conditions in your code that are leading to incorrect results:

  • One was already pointed out in the comments, i.e., the updates of the variable sum (shared among threads), which can be solved with the reduction clause;
  • The other is the updates of the variable x, which is also shared among the threads. This race condition can be solved by simply making that variable private to threads.

Two possible solutions:

  1. Using the OpenMP's private constructor

     #pragma omp parallel for reduction(+:sum) private(x)
 for (i = 0; i < num_steps; i++)
 {
      x = (i + 0.5) * step;
      sum = sum + 4.0 / (1.0 + x * x);
 }

  2. Declaring the variable 'x' within the scope of the parallel for

     #pragma omp parallel for reduction(+:sum)
 for (i = 0; i < num_steps; i++)
 {
      double x = (i + 0.5) * step;
      sum = sum + 4.0 / (1.0 + x * x);
 }

The final code could look like the following:

    #include <omp.h>
    #include <stdio.h>

    static long num_steps = 1000000;
    #define NUM_THREADS 16

    int main()
    {
        double sum = 0.0;
        omp_set_num_threads(NUM_THREADS);
        double step = 1.0 / (double)num_steps;
    
        double tdata = omp_get_wtime();
    
        #pragma omp parallel for reduction(+:sum)
        for (int i = 0; i < num_steps; i++)
        {
             double x = (i + 0.5) * step;
             sum = sum + 4.0 / (1.0 + x * x);
        }
    
        tdata = omp_get_wtime() - tdata;
        double pi = sum * step;
        printf("pi = %f and compute time = %f seconds", pi, tdata);
    }
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