Here is a small piece of program (14 lines of program) which counts the number of bits set in a number.

Input-Output --> 0-->0(0000000), 5-->2(0000101), 7-->3(0000111)

int CountBits (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 someone explain the algorithm used here/why this works?