How can I create a random BigDecimal in Java?

Question

This question: How to generate a random BigInteger describes a way to achieve the same semantics as Random.nextInt(int n) for BigIntegers.

I would like to do the same for BigDecimal and Random.nextDouble().

One answer in the above question suggests creating a random BigInteger and then creating a BigDouble from it with a random scale. A very quick experiment shows this to be a very bad idea :)

My intuition is that using this method would require the integer to be scaled by something like n-log10(R), where n is the number of digits of precision required in the output and R is the random BigInteger. This should allow the correct number of digits to be present so that (for example) 1 -> 10^-64 and 10^64 -> 1.

The scaling value also needs to be chosen correctly for the result to fall in the range [0,1].

Has anyone done this before, and do they know if the results are correctly distributed? Is there a better way to achieve this?

EDIT: Thanks to @biziclop for correcting my understanding of the scale argument. The above isn't necessary, a constant scale factor has the desired effect.

For later reference, my (apparently working code) is:

private static BigDecimal newRandomBigDecimal(Random r, int precision) {
    BigInteger n = BigInteger.TEN.pow(precision);
    return new BigDecimal(newRandomBigInteger(n, r), precision);
}

private static BigInteger newRandomBigInteger(BigInteger n, Random rnd) {
    BigInteger r;
    do {
        r = new BigInteger(n.bitLength(), rnd);
    } while (r.compareTo(n) >= 0);

    return r;
}

Answer 1

It's surely very easy... if I only knew what you want. For a uniformly distributed number in range [0, 1) and precision N decimal digits generate a uniform BigInteger less than 10*N and scale it down by 10*N.

Answer 2

I made a post about generating a random BigInteger Andy Turner's answer about generating a random BigInteger. I don't use this directly for generating a random BigDecimal. Essentially my concern is to use independent instances of Random to generate each digit in a number. One problem I noticed is that with Random there are only so many values of and particular number that you get in a row. Also the generation tries to maintain something of an even distribution of generated values. My solution depends on something storing an array or collection of Random instances and calling these. I think this is a good way of going about it and I am trying to find out, so am interested if anyone has any pointers or criticism of this approach.

/**
 *
 * @param a_Random
 * @param decimalPlaces
 * @param lowerLimit
 * @param upperLimit
 * @return a pseudo randomly constructed BigDecimal in the range from
 * lowerLimit to upperLimit inclusive and that has up to decimalPlaces
 * number of decimal places
 */
public static BigDecimal getRandom(
        Generic_Number a_Generic_Number,
        int decimalPlaces,
        BigDecimal lowerLimit,
        BigDecimal upperLimit) {
    BigDecimal result;
    BigDecimal range = upperLimit.subtract(lowerLimit);
    BigDecimal[] rangeDivideAndRemainder =
            range.divideAndRemainder(BigDecimal.ONE);
    BigInteger rangeInt = rangeDivideAndRemainder[0].toBigIntegerExact();
    BigInteger intComponent_BigInteger = Generic_BigInteger.getRandom(
            a_Generic_Number,
            rangeInt);
    BigDecimal intComponent_BigDecimal =
            new BigDecimal(intComponent_BigInteger);
    BigDecimal fractionalComponent;
    if (intComponent_BigInteger.compareTo(rangeInt) == 0) {
        BigInteger rangeRemainder =
                rangeDivideAndRemainder[1].toBigIntegerExact();
        BigInteger fractionalComponent_BigInteger =
                Generic_BigInteger.getRandom(a_Generic_Number, rangeRemainder);
        String fractionalComponent_String = "0.";
        fractionalComponent_String += fractionalComponent_BigInteger.toString();
        fractionalComponent = new BigDecimal(fractionalComponent_String);
    } else {
        fractionalComponent = getRandom(
                a_Generic_Number, decimalPlaces);
    }
    result = intComponent_BigDecimal.add(fractionalComponent);
    result.add(lowerLimit);
    return result;
}

/**
 * Provided for convenience.
 * @param a_Generic_BigDecimal
 * @param decimalPlaces
 * @return a random BigDecimal between 0 and 1 inclusive which can have up
 * to decimalPlaces number of decimal places
 */
public static BigDecimal getRandom(
        Generic_Number a_Generic_Number,
        int decimalPlaces) {
    //Generic_BigDecimal a_Generic_BigDecimal = new Generic_BigDecimal();
    Random[] random = a_Generic_Number.get_RandomArrayMinLength(
            decimalPlaces);
    //System.out.println("Got Random[] size " + random.length);
    String value = "0.";
    int digit;
    int ten_int = 10;
    for (int i = 0; i < decimalPlaces; i++) {
        digit = random[i].nextInt(ten_int);
        value += digit;
    }
    int length = value.length();
    // Tidy values ending with zero's
    while (value.endsWith("0")) {
        length--;
        value = value.substring(0, length);
    }
    if (value.endsWith(".")) {
        value = "0";
    }
    BigDecimal result = new BigDecimal(value);
    //result.stripTrailingZeros();
    return result;
}