How to get a larger random number from the c function rand()

Question

I am in a coding environment where I only have access to some most basic c functions. #include\'ing other lib is not feasible.

In this environment, I can call rand()

Answer 1

Besides the other excellent solutions proposed here, you can also do a power expansion in RAND_MAX, truncate at a user defined MY_RAND_MAX, and discard solutions which would cause uniformity to be destroyed.

int myrand(int MY_RAND_MAX)
{
    int j = 0, num = 0;

    // Generate digits for expansion in powers of RAND_MAX, up to acceptable range.
    while (pow(RAND_MAX + 1, j) <= MY_RAND_MAX){
        num = num + rand() * (int)pow(RAND_MAX + 1, j);
        j++; 
    } 

    //compute remainder to determine truncation 
    int remainder = ((int)pow(RAND_MAX + 1, j)) % (MY_RAND_MAX + 1); 

    // If number is within accepted bounds, mod and return
    if (num <= (  (int)pow(RAND_MAX + 1, j) - remainder ) ){
        return (num % (MY_RAND_MAX + 1)); 

    // Else, if number generated exceeds allowed bounds, rerun method.
    }else if (num > (  (int)pow(RAND_MAX + 1, j) - remainder ) ){
        return myrand(MY_RAND_MAX);

    }else{
        exit(-1);
    }
}

You can check empirically that this method gives you a statistically uniform output in the given range.

I've done so for several trials with different ranges, each with a sample size of 100000, and got an agreement between the variance of the sample and the expected variance to at least 3 sig. fig.s each time.

p.s. I am not a coder, but a mathematician/physicist who has recently learnt to code, so any and all feedback on the quality of my code would be appreciated.