How to Generate Arbitrarily Large Random BigIntegers in a Specific Range in Java?

Generating Random BigIntegers in Java

Question:

How do you generate arbitrarily large random BigInteger values in the range of 0 to n (excluding n), where n is not a power of 2?

Answer:

Utilizing BigInteger's constructor that takes a bit count and an instance of a Random generator, you can create such values:

public BigInteger(int numBits, Random rnd)

However, to obtain values within the desired range, it is necessary to employ a loop:

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

On average, this loop operates in less than two iterations, ensuring uniform distribution.

Edit:

For situations where the Random generator is performance-intensive, you can implement the following approach:

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);

While this method significantly reduces the likelihood of multiple loop iterations (less than one chance in 2^100), it utilizes the computationally expensive mod() operation. Therefore, this approach may be less efficient than the previous one if the supplied Random instance has low performance overhead.

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