How do I generate random numbers without rand() function?

If you’re after an ultra-simple pseudo-random generator, you can just use a Linear Feedback shift Register.

The wikipedia article has some code snippets for you to look at, but basically the code for a 16-bit generator will look something like this (lightly massaged from that page…)

  unsigned short lfsr = 0xACE1u;
  unsigned bit;

  unsigned rand()
  {
    bit  = ((lfsr >> 0) ^ (lfsr >> 2) ^ (lfsr >> 3) ^ (lfsr >> 5) ) & 1;
    return lfsr =  (lfsr >> 1) | (bit << 15);
  }