How to Generate Random BigInteger Values within a Specific Range in Java?

Generating Random BigInteger Values within a Specific Range in Java

In Java programming, generating random BigInteger values within a prescribed range requires careful consideration to ensure uniform distribution and computational efficiency. One might initially resort to multiplying the result of nextDouble by the upper limit, but this approach becomes problematic when dealing with values beyond the limits of double precision (2⁵³).

To address this issue, the BigInteger class provides a suitable constructor:

public BigInteger(int numBits, Random rnd)

This constructor generates a random BigInteger within the range 0 to (2^numBits - 1), ensuring uniform distribution. However, the challenge remains in obtaining values within the desired range (0 to n), where n is not necessarily a power of 2.

Solution:

An effective solution is to employ a loop:

<code class="java">BigInteger randomNumber;
do {
    randomNumber = new BigInteger(upperLimit.bitLength(), randomSource);
} while (randomNumber.compareTo(upperLimit) >= 0);</code>

On average, this loop will execute less than twice, ensuring uniform distribution.

Optimization for Expensive RNGs:

If the chosen RNG is computationally intensive, the number of iterations can be limited:

<code class="java">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);</code>

This version significantly reduces the likelihood of the loop being traversed more than once (less than 1 in 2¹⁰⁰). However, the mod() operation is computationally expensive, so this optimization may only be beneficial if the RNG instance is particularly slow.

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