Best way to reduce a pair of integers while maintaining their ratio

I'm running on a platform with no floating-point support, and the largest integer type being 32 bits.

Given a pair of values, I need to ensure that none of them exceeds 16 bits before I continue to process them.

If either one of them does, then I need to reduce both while maintaining their ratio as accurately as possible.

Here is what I've done so far:

#define MAX_VAL 0x0000FFFF

typedef unsigned int uint32;

void func(uint32 x, uint32 y) {
    if (x > MAX_VAL && y <= MAX_VAL) {
        y = y * MAX_VAL / x;
        x = MAX_VAL;
    }

    if (x <= MAX_VAL && y > MAX_VAL) {
        x = x * MAX_VAL / y;
        y = MAX_VAL;
    }

    while (x > MAX_VAL || y > MAX_VAL) {
        x >>= 1;
        y >>= 1;
    }

    ...
}

This seems to work well in terms of accuracy.

However, I would still like to improve performance, specifically with regards to the while loop, while maintaining the level of accuracy of course.

Any ideas how to approach that?