Openmp - for's inside for's - c++

Question

I'm trying to parallelize a "for" with openmp.
However the result, parallel code vs nonparallel, is different. I believe that it is related with the definition of the sum variable outside of the loop, but I don't know how to solve the problem.
What I want is to parallelize the first "for" loop.
Edit: 1
Here is the simplest example I could find.
//g++ -o test2 test2.cpp -fopenmp
//
//
#include <cmath>
#include <iostream>
using namespace std;
double f(double i, double j)
{
return i + j;
}
int main()
{
const int size = 256;
double sum = 0;
//will use openmp
#pragma omp parallel for
for(int i = 0; i < size; i = i + 1)
{
for(int j = 0; j < size; j=j+1)
{
if(i != j)
{
sum = sum + f(i,j);
}
}
}
cout << "sum = " << sum << endl;
//not using openmp
sum = 0;
for(int i = 0; i < size; i = i + 1)
{
for(int j = 0; j < size; j=j+1)
{
if(i != j)
{
sum = sum + f(i,j);
}
}
}
cout << "sum = " << sum << endl;
}

Answer 1

Your problem is the access to sum being performed by several threads. I.e. when the first thread reaches
sum=sum+f(i,j);
it grabs sum, does the calculations, writes the result to sum. When another thread in the meantime arrived at that line, it grabs the old value of sum and dumps its result, overwriting the first threads results.
A solution would be to set
double increment=f(i,j);
#pragma omp critical
sum+=increment;
Also note that your code's results are not predictable and change when you run it several times.

Answer 2

Thank you for your answer, it finally works.
The following code is a working code with Christoph Solution.
//g++ -o test2 test2.cpp -fopenmp
#include <cmath>
#include <iostream>
using namespace std;
double f(double i, double j)
{
return i + j;
}
int main()
{
const int size = 256;
double sum = 0;
//will use openmp
#pragma omp parallel for
for(int i = 0; i < size; i = i + 1)
{
for(int j = 0; j < size; j=j+1)
{
if(i != j)
{
double increment = f(i,j);
#pragma omp critical
sum = sum + increment;
}
}
}
cout << "sum = " << sum << endl;
//not using openmp
sum = 0;
for(int i = 0; i < size; i = i + 1)
{
for(int j = 0; j < size; j=j+1)
{
if(i != j)
{
sum = sum + f(i,j);
}
}
}
cout << "sum = " << sum << endl;
}