Does sharing memory between threads makes them slower? - c++

Question

I'm trying to implement a naive threaded matrix multiplication, I'm creating multiple threads for each linear combination using a manually allocated result array and writing to the respective position on each thread, however my code run slower than on it's single threaded version, is it the use of memory that slows down the code?
I used heap allocation to avoid any memory copying but could it be the problem?
#define rows first
#define columns second
void linear_combination(double const *arr_1,std::pair<int, int> sp_1,
double const *arr_2, std::pair<int, int> sp_2,
double *arr_3, std::pair<int, int> sp_3,
int base_row,int base_col){
double sum = 0;
for (int i = 0; i < sp_1.columns; i++){
int idx_1 = base_row * sp_1.columns + i;
int idx_2 = i * sp_2.columns + base_col;
sum += arr_1[idx_1] * arr_2[idx_2];
}
int idx_3 = base_row * sp_3.columns + base_col;
arr_3[idx_3] = sum;
}
auto matmul(double *m1, std::pair<int, int> sp_1, double *m2, std::pair<int, int> sp_2){
// "sp_n" stands for shape for n-th matrix
if (sp_1.second == sp_2.first){
auto *m3 = (double *) malloc(sp_1.first*sp_2.second* sizeof(double));
std::pair sp_3 = {sp_1.first, sp_2.second};
for (int k = 0; k < sp_3.rows; k++){
std::vector<std::thread> thread_list(sp_2.columns);
for (int j = 0; j < sp_2.columns; j++){
// will automatically save linear combination sum into m3
thread_list[j] = ( std::thread(linear_combination,
m1, sp_1,
m2, sp_2,
m3, sp_3,
k, j) );
}
// join threads and use calculation
std::for_each(thread_list.begin(), thread_list.end(), std::mem_fn(&std::thread::join));
}
return std::make_tuple(m3, sp_3);
} else{
puts("Size mismatch");
printf("%d %d\n", sp_1.second, sp_2.first);
double m3 = 0;
return std::make_tuple(&m3, std::make_pair(0, 0));
}
}