Question

I am trying to make a loop that loops through all different integers where exactly 10 of the last 40 bits are set high, the rest set low. The reason is that I have a map with 40 different values, and I want to sum all different ways ten of these values can be multiplied. (This is just out of curiosity, so it’s really the “bitmanip”-loop that is of interest, not the sum as such.)

If I were to do this with e.g. 2 out of 4 bits, it would be easy to set all manually,

0011 = 3,
0101 = 5,
1001 = 9,
0110 = 6,
1010 = 10,
1100 = 12,

but with 10 out of 40 I can’t seem to find a method to generate these effectively. I tried, starting with 1023 ( = 1111111111 in binary), finding a good way to manipulate this, but with no success. I’ve been trying to do this in C++, but it’s really the general method(if any) that is of interest. I did some googling, but with little success, if anyone has a good link, that would of course be appreciated too. 🙂

Answer 1

A bit more complicated, but done purely by bit manipulation. Your example:

#define WIDTH 4
#define BITS 2

void printbits(long pattern) {
  long bit;
  for (bit = 1L << WIDTH - 1; bit; bit >>= 1)
    putchar(pattern & bit ? 49 : 48);
  putchar('\n');
}

void movebits(pattern, bit) {
  long mask = 3L << bit;
  while (((pattern ^= mask) & mask) && (mask < 1L << WIDTH)) {
    mask <<= 1;
    printbits(pattern);
    if (bit)
      movebits(pattern, bit - 1);
  }
}

int main() {
  long pattern = (1L << BITS) - 1L, mask;
  printbits(pattern);
  movebits(pattern, BITS - 1);
}

Your real application:

#define WIDTH 40
#define BITS 10

and, as polygenelubricants says, be prepared to wait for bit 🙂 Of course, you will replace printbits with something more useful to you…

(Edited for insufficient testing :/ Damn typos…)