C Puzzle #8

This is a very small program as you can see. Whst it will do is: It will just count the number of bits set in a given number.

Input is this	Output is this
0	0(0000000)
5	2(0000101)
7	3(0000111)

int Count_Bits (unsigned int x )

  {

      static unsigned int mask[] = { 0x55555555,

          0x33333333,

          0x0F0F0F0F,

          0x00FF00FF,

          0x0000FFFF

          } ;

          int i ;

          int shift ; /* Number of positions to shift to right*/

          for ( i =0, shift =1; i < 5; i ++, shift *= 2)

                  x = (x & mask[i ])+ ( ( x >> shift) & mask[i]);

          return x;

  }

Can you find out the logic used here?
Its really difficult na!!

It would be worth to check for answer