typedef uint32_t u32;

// have to a multiply of 2
#define COMMA 8 @\label{comma}@
#define COMMA_FIX (COMMA >> 1)

void heron_sqrt(u32 *mem) {
  int i = mem[0];
  while (i > 0) {
    u32 s = mem[i];
    u32 x = s;
    if (s > 1) {
      // x_0 = (s + 1) / 2
      // without increment to avoid overflow for 0xffffffff
      x = x >> 1;
      u32 old_x = x;

      while(1) {
        // x_{n + 1} = (x_n + (s / x_n)) / 2
        x = (x >> 1) + ((s/x) >> 1);
        if (old_x <= x) {
          break;
        }
        old_x = x;
      }
    }
    mem[i] = x << COMMA_FIX;
    i--;
  }
}