How to get a number from unsigned long long mask?

Question

I wonder how to reverse something like this. So having a mask where auto mask = 1ULL << 20; how to get 20 out from mask?

Answer 1

Loop-free

Many years ago when I was writing a bit-wise arithmetic for a chess engine, I found a fast implementation which is useful for your requirement, it's loop-free. This method will return the position of the first 1-bit from right-to-left (Least Significant Bit):

inline unsigned int lsb(unsigned long long value)
{
    if (!value)
        return -1;

    value &= -value;
    unsigned int lsb = (unsigned) value | (unsigned) (value >> 32);
    return (((((((((((unsigned) (value >> 32) != 0) << 1)
            + ((lsb & 0xffff0000) != 0)) << 1)
            + ((lsb & 0xff00ff00) != 0)) << 1)
            + ((lsb & 0xf0f0f0f0) != 0)) << 1)
            + ((lsb & 0xcccccccc) != 0)) << 1)
            + ((lsb & 0xaaaaaaaa) != 0);
}

int main()
{
    unsigned long long x = 1ULL<<20;
    cout << lsb(x) << endl;
}

Output

20

I think, I had found it here.

Answer 2

Using log:

#include <iostream>
#include <cmath>
int main() {
    auto mask = 1ULL << 20; 
    std::cout << log2(mask) << std::endl;
    // edit out: std::cout << log(mask) / log(2) << std::endl;
    return 0;
}

or loop and shift:

#include <iostream>
int main() {
    auto mask = 1ULL << 20; 
    for (unsigned int c = 0; c < sizeof(mask) * 8 && mask; c++) {
        mask >>= 1;
        if (mask == 0)
            std::cout << c << std::endl;
    }   
    return 0;
}