Question

Here is the function that finds the greater of two numbers:

int larger(int a,int b)
{
    int c=a-b;
    int k=c>>31&1;
    int max=a-k*c;
    return max;
 }

To find the greatest of three numbers, call it such as:

larger(a,larger(b,c));

How does this work?

Answer 1

int c=a-b;

cwill be negative if a < b else it will positive. Now a negative number will have its most significant bit(MSB) set.

int k=c>>31&1;

This step assumes that sizeof(int) is 4 bytes and extracts the MSB of c in k. So k is either 0 or 1

int max=a-k*c;

replacing c = a-b in this we get max = a-k*(a-b). So when

k = 0, max = a-0*(a-b)
           = a

k = 1, max = a-1*(a-b)
           = b