Question

Intuitively one might write a random double generator as follows:

double randDouble(double lowerBound, double upperBound)
{
    double range = upperBound - lowerBound;
    return lowerBound + range * rand();
}

Suppose we assume that rand() returns an evenly distributed pseudorandom double on the interval [0, 1).

Is this method guaranteed to return a random double within [lowerBound, upperBound) with a uniform probability distribution? I’m specifically interested in whether the nature of floating point calculations might cause spikes or dips in the final distribution for some ranges.

Answer 1

First, rand() generates pseudo-random numbers and not truly random. Thus, I will assume you are asking if your function generates pseudo-random numbers within the specified range.

Second, like Oli Charlesworth said, many rand implementations return a number between 0 and RAND_MAX, where RAND_MAX is the largest possible value it can take. In these cases, you can obtain a value in [0, 1) with

double r = rand()/((double)RAND_MAX+1);

the +1 is there so that r can’t be 1.

Other languages have a rand that returns a value between 0 and 1, in which case you don’t need to do the above division. Either way, it turns out that your function returns a decent approximation of a random distribution. See the following link for more details: http://www.thinkage.ca/english/gcos/expl/c/lib/rand.html Note that this link gives you slightly different functions which they claim work a bit better, but the one you have probably works good enough.