Implementing semaphore by using mutex operations and primitives

Question

Some time ago had an interview and was asked to implement Semaphore by using mutex operations and primitives only (he allowed int to be considered as atomic). I came with solution below. He did not like busy/wait part -- while (count >= size) {} -- and asked to implement locking instead by using more primitive types and mutexes. I did not manage to come with improved solution. Any ideas how it could be done?

struct Semaphore {
int size;
atomic<int> count;
mutex updateMutex;

Semaphore(int n) : size(n) { count.store(0); }

void aquire() {
    while (1) {
        while (count >= size) {}
        updateMutex.lock();
        if (count >= size) {
            updateMutex.unlock();
            continue;
        }
        ++count;
        updateMutex.unlock();
        break;
    }
}

void release() {
    updateMutex.lock();
    if (count > 0) {
        --count;
    } // else log err
    updateMutex.unlock();
}
};

Answer 1

I'd wager this is not possible to implement without a busy-loop using mutexes only.

If not busy-looping, you have to block somewhere. The only blocking primitive you've got is a mutex. Hence, you have to block on some mutex, when the semaphore counter is zero. You can be woken up only by the single owner of that mutex. However, you should woken up whenever an arbitrary thread returns a counter to the semaphore.

Now, if you are allowed condition variables, it's an entirely different story.