How to generate integers within a range from random bits

Question

I have a source of random bits that I would like to massage into integers of various sizes, roughly correlating with the size of popular dice (1-4, 1-6, etc.)

The code I am writing is PHP, so a response in that language is ideal. However, an algorithmic generic response would be totally fine as well.

I would prefer an answer more sophisticated than simply seeding PHP's random() function with chunks of my random data.

Answer 1

If you have an arbitrary number of bits available, you might choose to use a rejection method, along the lines of Java's Random.nextInt(int) . The pseudocode taken from there is:

public int nextInt(int n) {
     if (n<=0)
         new IllegalArgumentException("n must be positive");

     if ((n & -n) == n)  // i.e., n is a power of 2
         return (int)((n * (long)next(31)) >> 31);

     int bits, val;
     do {
         bits = next(31);
         val = bits % n;
     } while(bits - val + (n-1) < 0);
     return val;
 }

next() is a function that returns a specified number of random bits, concatenated into an int . You could replace this with your random bit source.