Chapter: Random Numbers

Let's begin by looking at what, for a long time, served as the basis for "random" number generators for programmers. Basically it's the application of a formula to generate a new number from an old number -- over and over again, hoping that the sequence thus produced is unpredictable and uniformly distributed.

pseudorandomexpt.c contains very simple code to generate new seeds by applying a linear transformation and taking the result modulo m. It has been set up so that you can try different values of

• the number m to modulo by
• The multiplier a
• the added constant r
• the initial value s for the seed

For example running it as

pseudorandomexpt 101 17

Exercise 10

If you finish early, do a google search and see what you can find out about pseudo-random number generators. The next program you look at will be a little bit more sophisticated than the one you just played with (but not much).

Here is the code for pseudorandom.c. There's a similar program in the lab1 directory, but it doesn't have a main() method:

#include < stdio.h >
/* close up those angle brackets if you cut and paste! */
const long MM = 2147483647;  /* luckily, this is a Mersenne prime */
const long AA = 48271;
const long QQ = 44488;
const long RR = 3399;

long seed = 4071776L;  
/* This is an initial seed.
   Change it to anything you like to get a different sequence of
   pseudo-random numbers */

void set_seed(long new_seed) {
   seed = new_seed;
}

double prandom ()
/* A pseudorandom number generator due to Donald Knuth
  The Art of Computer Programming Volume 2 Semi-numerical Algorithms
  It uses a modulo technique to generate a fairly unpredictable and
  well-distributed sequence of seeds.  
  It returns a double formed by dividing the seed by MAXINT
*/
{
  long new_seed;
  new_seed = AA * (seed % QQ) - RR * (seed / QQ);
  if (new_seed > 0)
    seed = new_seed;
  else
    seed = new_seed + MM;
  return ( (double) seed / (double) MM );
}


double prandom_range (double lo, double hi)
/* Scale the result so it lies between lo and hi */ 
{
  if (hi > lo)
    return ( lo + (hi-lo) * prandom() );
  else { 
    printf ("ERROR: in prandom.prandom_range(): lo=%lf hi=%lf\n",lo,hi); 
    return 0;
  }
}
main(argc, argv) 
     int argc;
     char *argv[];
{
/* If the optional argument is on the commandline use it to reset the seed */
  if (argc > 1) set_seed(atoi(argv[1]));  
  int top = 100;                       /* default is ints from 0 - 99 */
  if (argc > 2) top = atoi(argv[2]);   /* but can be adjusted by second arg */
  int i;
  char continu = 'g';
  while (continu != 'q') {
    for (i = 0; i < 10; i++) {
      printf("%d ",  (int) prandom_range(0.0,top*1.0));
    }
    printf("\n");
    printf("Hit q to quit, ENTER to continue > ");
    continu = getchar();
  }
  getchar(); /* eat the CR/LF */
}

If you compile this via gcc -o pseudorandom pseudorandom.c and run it by simply typing pseudorandom you will get a sequence of pseudo-random numbers in the range 0-99. It will always be exactly the same sequence because the initial seed is fixed. By using argc and argv and atoi() you can select a new intial seed for each run. Typing pseudorandom 19071961 you will get a different sequence.

Q. 7

What is the point of this?

See if you can figure out what the second commandline argument does. Discuss!

One last exercise. A good idea is to modify the above code.

Exercise 11

.

Just as the given program prompts for "Hit q to quit, ENTER to continue > " so should yours. But each time there should be an output line consisting of two numbers, each between 1 and 6. Rather like this:

: roll
4 3
Hit q to quit, ENTER to continue:
4 7
Hit q to quit, ENTER to continue:
3 3
Hit q to quit, ENTER to continue:q
: