Question

I’m trying to address the issue of odd matrices for strassen’s algorithm. My implementation truncates the recursion at a certain point, call it Q, and switches over to the standard implementation. Therefore in doing static padding, I don’t actually need to pad up to the next power of 2. I just need to pad up to the least m*2^k greater than the input matrix dimension such that m < Q.

I’m having some trouble implementing this – mainly because I’m not sure what would be most efficient. Do I need to loop through all possible m values, or do I increment from each given input, testing if they fulfill the criteria?

Answer 1

You are correct. Padding up to m * 2^k should perform much better than padding up to next power of 2.

I think you should pad up to value calculated by this function:

int get_best_pud_up_value(int actual_size, int Q) {
    int cnt = 0;
    int n = actual_size;
    while(n > Q) {
        cnt++;
        n /= 2;
    }

    // result should be smallest value such that:
    // result >= actual_size AND
    // result % (1<<cnt) == 0

    if (actual_size % (1<<cnt) == 0) {
        return actual_size;
    } else {
        return actual_size + (1<<cnt) - actual_size % (1<<cnt);
    }
}