Matrix multiplication using SSE intrinsics

Question

I am trying to do Matrix multiplication using SSE. I have written a simple program for 4x4 matrices. Everything seems fine but when I print result , its some garbage values. please help to figure out problem/s. Secondly program stops working when I free memory, not a proper end of program.

#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <float.h>
#include <xmmintrin.h>

void main() {
    float **a, **b, **c;
    int a_r = 4, a_c = 4, b_c = 4, b_r = 4;
    int i, j, k;

    /* allocate memory for matrix one */
    a = (float **)malloc(sizeof(float) * a_r);
    for (i = 0; i < a_c; i++) {
        a[i] = (float *)malloc(sizeof(float) * a_c);
    }
    /* allocate memory for matrix two */
    b = (float **)malloc(sizeof(float) * b_r);
    for (i = 0; i < b_c; i++) {
        b[i] = (float *)malloc(sizeof(float) * b_c);
    }
    /* allocate memory for sum matrix */
    c = (float **)malloc(sizeof(float) * a_r);
    for (i = 0; i < b_c; i++) {
        c[i] = (float *)malloc(sizeof(float) * b_c);
    }
    printf("Initializing matrices...\n");

    //initializing first matrix
    for (i = 0; i < a_r; i++) {
        for (j = 0; j < a_c; j++) {
            a[i][j] = 2;
        }
    }
    // initializing second matrix
    for (i = 0; i < b_r; i++) {
        for (j = 0; j < b_c; j++) {
            b[i][j] = 2;
        }
    }
    /* initialize product matrix */
    for (i = 0; i < a_r; i++) {
        for (j = 0; j < b_c; j++) {
            c[i][j] = 0;
        }
    }

    int count = 0;
    /* multiply matrix one and matrix two */
    for (i = 0; i < a_r; i++) {
        for (j = 0; j < a_c; j++) {
            count = 0;
            __m128 result = _mm_setzero_ps();
            for (k = 0; k < 4; k += 4) {
                __m128 row1 = _mm_loadu_ps(&a[i][k]);
                __m128 row2 = _mm_loadu_ps(&b[k][j]);
                result = _mm_mul_ps(row1, row2);

                for (int t = 1; t < 4; t++) {
                    __m128 row3=_mm_loadu_ps(&a[t * 4]);
                    __m128 row4=_mm_loadu_ps(&b[i][t]);
                    __m128 row5 = _mm_mul_ps(row3,row4);
                    result = _mm_add_ps(row5, result);
                }
                _mm_storeu_ps(&c[i][j], result);
            }
        }
    }
    printf("******************************************************\n");
    printf ("Done.\n");

    for (i = 0; i < a_r ; i++) {
        for (j = 0; j < b_c; j++) {
            printf ("%f   ", c[i][j]);   // issue here when I print results.
        }
        printf("\n");
    }     //  Here program stops working.

    /*free memory*/
    for (i = 0; i < a_r; i++) {
        free(a[i]);
    }
    free(a);
    for (i = 0; i < a_c; i++) {
        free(b[i]);
    }
    free(b);
    for (i = 0; i < b_c; i++) {
        free(c[i]);
    }
    free(c);
}

please have look at address printed for output matrix. how to get aligned addresses, I have _aligned_malloc , but still not aligned.

Answer 1

The allocation for the matrix indirect pointers is incorrect. it should read:

a = (float **)malloc(sizeof(float*) * a_r);

A safer way to write these allocations is this:

a = malloc(sizeof(*a) * a_r);

Note that you could allocate 2D matrices directly:

float (*a)[4][4] = malloc(sizeof(*a));

Or better, as Cody Gray suggested:

float (*a)[4][4] = _aligned_malloc(sizeof(*a));

_aligned_malloc is a non standard function that ensures proper alignment for SSE operands.

If fact you probably do not even need to allocate these matrices with malloc() :

float a[4][4];

But with this latter choice, you must ensure proper alignment for the SSE operations to succeed.

The rest of the code has other problems:

• void main() is incorrect. It should be int main(void)

• The second matrix operand should be transposed so you can read multiple values at a time. The second load would become:

   __m128 row2 = _mm_loadu_ps(&b[j][k]); 

• The summation phase seems incorrect too. And the final store is definitely incorrect, should just be:

   c[i][j] = sum;