Question

I need to generate arbitrarily large random integers in the range 0 (inclusive) to n (exclusive). My initial thought was to call nextDouble and multiply by n, but once n gets to be larger than 2⁵³, the results would no longer be uniformly distributed.

BigInteger has the following constructor available:

public BigInteger(int numBits, Random rnd)

Constructs a randomly generated BigInteger, uniformly distributed over the range 0 to (2^numBits – 1), inclusive.

How can this be used to get a random value in the range 0 – n, where n is not a power of 2?

Answer 1

Use a loop:

BigInteger randomNumber;
do {
    randomNumber = new BigInteger(upperLimit.bitLength(), randomSource);
} while (randomNumber.compareTo(upperLimit) >= 0);

on average, this will require less than two iterations, and the selection will be uniform.

Edit: If your RNG is expensive, you can limit the number of iterations the following way:

int nlen = upperLimit.bitLength();
BigInteger nm1 = upperLimit.subtract(BigInteger.ONE);
BigInteger randomNumber, temp;
do {
    temp = new BigInteger(nlen + 100, randomSource);
    randomNumber = temp.mod(upperLimit);
} while (s.subtract(randomNumber).add(nm1).bitLength() >= nlen + 100);
// result is in 'randomNumber'

With this version, it is highly improbable that the loop is taken more than once (less than one chance in 2^100, i.e. much less than the probability that the host machine spontaneously catches fire in the next following second). On the other hand, the mod() operation is computationally expensive, so this version is probably slower than the previous, unless the randomSource instance is exceptionally slow.