Generate Random(a, b) making calls to Random(0, 1)

Question

There is known Random(0,1) function, it is a uniformed random function, which means, it will give 0 or 1, with probability 50%. Implement Random(a, b)

Answer 1

Your inclination to put the range from 0 to a-b first is correct. However, you cannot do it as you stated. This question asks exactly how to do that, and the answer utilizes unique factorization. Write m=a-b in base 2, keeping track of the largest needed exponent, say e. Then, find the biggest multiple of m that is smaller than 2^e, call it k. Finally, generate e numbers with RANDOM(0,1), take them as the base 2 expansion of some number x, if x < k*m, return x, otherwise try again. The program looks something like this (simple case when m<2^2):

int RANDOM(0,m) {

    // find largest power of n needed to write m in base 2
    int e=0;
    while (m > 2^e) {
        ++e;
    }

    // find largest multiple of m less than 2^e
    int k=1;
    while (k*m < 2^2) {
        ++k
    }
    --k; // we went one too far

    while (1) {
        // generate a random number in base 2
        int x = 0;
        for (int i=0; i

Now you can simply add a to the result to get uniformly distributed numbers between a and b.