OpenMP parallel multiplication slower than Sequential multiplication

Question

I'm learning OpenMP and I'm trying to do a simple task: A[r][c] * X[c] = B[r] (matrix vector multiplication). The problem is: the sequential code is faster than parallel and I don't know why! My code:

#include <omp.h>
#include <time.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/wait.h>
#include <sys/time.h>
#include <sys/types.h>


// Defined variables
#define row_matriz_A 80000
#define col_matriz_A 800
#define THREADS_NUM 4

// FUNCAO - GERAR MATRIZES
void gerarMatrizes(int r, int c, int mA[], int vX[], int vB[]){...}

// FUNCAO - SEQUENTIAL MULTIPLICATION
void multSequencial(int r, int c, int mA[], int vX[], int vB[]){
    // Variables
    int i, j, offset, sum;                        
    struct timeval tv1,tv2;  
    double t1, t2;        
    // Begin Time
    gettimeofday(&tv1, NULL);
    t1 = (double)(tv1.tv_sec) + (double)(tv1.tv_usec)/ 1000000.00;
    for(i = 0; i < r; i++){
        sum = 0;
        for(j = 0; j < c; j++){
            offset = i * c + j;
            sum += mA[offset] * vX[j];
        }
        vB[i] = sum;
    }
    // End time
    gettimeofday(&tv2, NULL);
    t2 = (double)(tv2.tv_sec) + (double)(tv2.tv_usec)/ 1000000.00;
    printf("\nO tempo de execucao sequencial foi: %lf segundos.\n", (t2 - t1));
    return;
}

// FUNCAO - MULTIPLICACAO PARALELA COM OpenMP
void matvecHost(int r, int c, int mA[], int vX[], int vB[]){
    // Variaveis
    int tID, i, j, offset, sum;
    struct timeval tv1, tv2;
    double t1, t2;
    // Init vB
    for(i = 0; i < r; i++) vB[i] = 0;
    // BEGIN Time
    gettimeofday(&tv1, NULL);
    t1 = (double)(tv1.tv_sec) + (double)(tv1.tv_usec)/ 1000000.00;
    omp_set_num_threads(THREADS_NUM);
    #pragma omp parallel private(tID, i, j) shared(mA, vB, vX)
    {
        tID = omp_get_thread_num();     
        #pragma omp for
            for(i = 0; i < r; i++){
                sum = 0;
                for(j = 0; j < c; j++){
                    offset = i * c + j;
                    sum += mA[offset] * vX[j];
                }
                vB[i] = sum;
            }
    }
    // End time
    gettimeofday(&tv2, NULL);
    t2 = (double)(tv2.tv_sec) + (double)(tv2.tv_usec)/ 1000000.00;
    printf("\nO tempo de execucao OpenMP foi: %lf segundos.\n", (t2 - t1));
    return;
}

// FUNCAO - PRINCIPAL
int main(int argc, char * argv[]) {
    int row, col;
    row = row_matriz_A;
    col = col_matriz_A;
    int *matrizA = (int *)calloc(row * col, sizeof(int));
    int *vectorX = (int *)calloc(col * 1, sizeof(int));
    int *vectorB = (int *)calloc(row * 1, sizeof(int));
    gerarMatrizes(row, col, matrizA, vectorX, vectorB);                    
    multSequencial(row, col, matrizA, vectorX, vectorB);
    matvecHost(row, col, matrizA, vectorX, vectorB);
    return 0;
}

Previous solutions that did not worked:

• Use collapse in my squared for
• Increse rows and columns size
• Increase thread numbers (A teacher recommend to use thread number == threads physical number)
• Use malloc instead of m[i][j]

EDIT - ANSWER

My parallel block was correctly changed based on the correct answer:

#pragma omp parallel private(i, j, sum) shared(mA, vB, vX)
{
    #pragma omp for
        for(i = 0; i < r; i++){
            sum = 0;
            for(j = 0; j < c; j++){
                sum += mA[i * c + j] * vX[j];
            }
            vB[i] = sum;
        }
}

I still got some a doubt:

• If I define i , j and sum inside my parallel block, they will be set as private automatically? This improve the speed in my code or not?

Answer 1

You have race conditions on sum and offset - those are shared between the threads instead of being thread-private.

This also likely explains the slowdown: On x86, the CPU will actually work hard to make sure accesses to shared variables "work". This involves flushing cache lines after every (!) write to offset and sum - so all the threads are wildly writing into the same variables, but each one has to wait until the write from the previous thread (on a different core) has arrived in the local cache again after having been flushed. And of course it will produce completely nonsensical results.

I don't know why you are declaring all your variables at the start of the function - that's prone to these kind of mistakes. If you declared i , j , sum and offset (and the unused tID ) in the smallest possible scopes instead, you wouldn't ever had this problem because they would be thread-private automatically in that case.