Question

That is, what is the fastest way to do the test

if( a >= ( b - c > 0 ? b - c : 0 ) &&
    a <= ( b + c < 255 ? b + c : 255 ) )

    ...

if a, b, and c are all unsigned char aka BYTE. I am trying to optimize an image scanning process to find a sub-image, and a comparison such as this is done about 3 million times per scan, so even minor optimizations could be helpful.

Not sure, but maybe some sort of bitwise operation? Maybe adding 1 to c and testing for less-than and greater-than without the or-equal-to part? I don’t know!

Answer 1

Well, first of all let’s see what you are trying to check without all kinds of over/underflow checks:

a >= b - c
a <= b + c
subtract b from both:
a - b >= -c
a - b <= c

Now that is equal to

abs(a - b) <= c

And in code:

(a>b ? a-b : b-a) <= c

Now, this code is a tad faster and doesn’t contain (or need) complicated underflow/overflow checks.

---

I’ve profiled mine and 6502’s code with 1000000000 repitions and there officially was no difference whatsoever. I would suggest to pick the most elegant solution (which is IMO mine, but opinions differ), since performance is not an argument.

---

However, there was a notable difference between my and the asker’s code. This is the profiling code I used:

#include <iostream>

int main(int argc, char *argv[]) {  
    bool prevent_opti;
    for (int ai = 0; ai < 256; ++ai) {
        for (int bi = 0; bi < 256; ++bi) {
            for (int ci = 0; ci < 256; ++ci) {
                unsigned char a = ai;
                unsigned char b = bi;
                unsigned char c = ci;
                if ((a>b ? a-b : b-a) <= c) prevent_opti = true;
            }
        }
    }

    std::cout << prevent_opti << "\n";

    return 0;
}

With my if statement this took 120ms on average and the asker’s if statement took 135ms on average.