Optimizing naive matrix multiplication algorithm

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I am optimizing native version of matrix multiplication and I want to optimize it with OpenMP, SIMD and loop reordering. The following code is my attempt. My question is how I can modify the code so that I can avoid expensive memory write which is store function in the inner-most loop.

What I have tried:

C++

void mul_matrix(matrix *result, matrix *mat1, matrix *mat2){
    int I = mat1->rows;
    int J = mat2->cols;
    int K = mat2->rows;
    #pragma omp parallel for
    for(int i = 0; i < I; i++){
        for(int k = 0; k < K; k++){
            _m256d vA = _mm256_set1_pd(mat1->data[i * K + k]);
            for(int j = 0; j < J / 4 * 4; j += 4){
                _m256d sum = _mm256_loadu_pd(result->data + i * J + j);
                _m256d vB = _mm256_loadu_pd(mat2->data + k * J + j);
                _m256d intermediate = _mm256_mul_pd(vA, vB);
                sum = _mm256_add_pd(sum, intermediate);
                _mm256_storeu_pd(result->data + i * J + j, sum);
             }
             for(int x = J / 4 * 4; x < J; x++){
                 result->data[i * J + x] += mat1 -> data[i * K + k] * mat2 -> data[k * J + x];
             }
         }
     }
}
typedef struct matrix{
    int rows;
    int cols;
    double* data;
}matrix;

Posted 8-Aug-20 12:28pm

hck007

Updated 9-Aug-20 7:26am

KarstenK

v2

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KarstenK · Accepted Answer · 2020-08-09T07:26:00

check that you only calculate what you need and extract ANY constant value out of the loops and use const where possible.

Like in

C++

for(int x = J / 4 * 4; x < J; x++){
  result->data[i * J + x] += mat1 -> data[i * K + k] * mat2 -> data[k * J + x];
}

the constant

C++

int J4 = J / 4 * 4;
matrix *mr = result->data[i * J];
const matrix *m1 = mat1->data[i * K + k];
const matrix *m2 = mat2 -> data[k * J};

for(int x = J4; x < J; x++){
     mr[x] += m1 * mat2->m3[x];
}

Advanced is to create the assembly code and look if it shows some strange operations like type conversion or data aligments.