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

Generating Random BigInteger Values in Java

In Java, generating random integers within a specified range can be challenging when dealing with large numbers. The issue arises when using conventional methods like nextDouble() for random number generation, as the generated values may not be uniformly distributed beyond the limit of 2⁵³.

Utilizing BigInteger Constructor

To address this, the BigInteger class provides a constructor that enables the creation of random BigInteger values uniformly distributed within a specified bit range.

Constructs the BigInteger Constructor:

<code class="java">public BigInteger(int numBits, Random rnd)</code>

This constructor takes two parameters:

• numBits: Specifies the number of bits for the generated value
• rnd: A Random object used for generating random values

Generating a Random Value Within a Range

To generate a random value within a non-power-of-2 range of 0 to n (inclusive), a loop can be utilized:

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

This loop iterates until a valid random value is obtained. It ensures that the generated value is uniformly distributed within the specified range.

Optimizing Iteration Count

To reduce the number of loop iterations, a more refined solution can be applied.

<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 approach includes a limit on the number of iterations to prevent excessive loop execution. It balances speed and accuracy, reducing the likelihood of an extensive number of iterations.

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