Quick addition of numbers in Fibonacci code (Zeckendorf representation)

fib_add.cpp

// Based on the paper by Donald Knuth - Fibonacci multiplication - 1988
// Test program: https://godbolt.org/z/1Mn1K59xa
size_t fib_add(size_t a, size_t b)
{
    size_t x{(a | b) << 1}, x2{(a & b) << 1}, y, y2;
    do
    {
        y = x & x >> 1 & ~(x >> 2);
        const size_t m1{~(y | y << 1)};
        x &= m1;
        x |= x2 & ~m1;
        x |= y << 2;
        x2 &= m1;
        //
        y2 = x2;
        x &= ~y2;
        x2 = y2 << 1 & y2 >> 2;
        const size_t m2{y2 << 1 | y2 >> 2};
        x2 |= x & m2;
        x |= m2;
    } while (y || y2);
    return (x | x << 1 & 2) >> 1;
}