Alf - 3 months ago 21

C Question

I wanted to use OpenMP around a for-loop that basically sums up the array elements. For comparison, I also sum up the array elements in a serial fashion. For large array-sizes,

`array_size>=5795`

This is the OpenMP-parallelized loop:

`#pragma omp parallel for reduction(+:parallel_sum)`

for (i = 0; i < array_size; i++) {

parallel_sum += array[i];

}

And this is the full code:

`#include<stdio.h>`

#include<stdlib.h>

#include<omp.h>

int main() {

float *array, serial_sum, parallel_sum;

size_t array_size, i;

serial_sum = 0.;

parallel_sum = 0.;

#pragma omp parallel

printf( "number of threads used in parallized part: %d\n", omp_get_num_threads());

printf("enter size of array\n");

scanf("%zu", &array_size);

// memory allocation

array = (float *) malloc(sizeof(float) * array_size);

// initialize array

for (i = 0; i < array_size; i++)

array[i] = i;

// calculate the array sums, parallel first, then serial

#pragma omp parallel for reduction(+:parallel_sum)

for (i = 0; i < array_size; i++) {

parallel_sum += array[i];

}

for (i = 0; i < array_size; i++)

serial_sum = serial_sum + array[i];

if (serial_sum == parallel_sum)

printf("\nserial and parallel sums are equal\n");

else

printf("\nserial and Parallel sums are NOT equal\n");

// free memory

free(array);

return 0;

}

Since the sum can be easily calculated by hand using the sum-formula by Gauss, sum = (n^2+n)/2, where n corresponds to

`array_size`

Answer

Since floating-point types have limited precision, addition is not associative (see Are floating point operations in C associative? and Is Floating point addition and multiplication associative?).

So `a + (b + c)`

can evaluate unequal to `(a + b) + c`

.

When parallelizing/vectorizing, the order operations can indeed be different than adding the numbers from lowest to highest sequentially.

If you printed out the computed values, you would likely find them quite close in this case, just not *exactly* equal.