Generic sum method for a Collection
Choosing between Long/Integer and Float/Decimal

I'd let the user choose.
Not because that's the best way, but because I don't see any other way.

Number itself is not reflective on the presence of decimal digits.
It would need an interface Integer and interface Decimal or something like that in order to deal with this in a single signature.
However, the API is not designed this way.

So, if both is needed, I'd have a sumInt and a sumFloat method, or maybe sumInteger and sumDecimal. (I prefer Float over Decimal because Decimal is simply wrong because it means 1/10ths and that's just the wrong name. BigDecimal is the wrong name.)

Simpler usage of Generics

The type parameter U is redundant. You could directly go for this signature:

public static &lt;T extends Number&gt; BigDecimal sum(Collection&lt;T&gt; numbers)


And given that inside you actually don't need T, Number is sufficient, you could go for this signature:

public static BigDecimal sum(Collection&lt;? extends Number&gt; numbers)


Going via String is a bit "far away" from numbers, and unnecessary. You could use Number.longValue() in case of BigInteger and Number.doubleValue() in case of BigDecimal.

Then the code would look like this:

public static BigInteger sumInt(final Collection&lt;? extends Number&gt; numbers) {
    BigInteger sum = BigInteger.ZERO;
    for (final Number number : numbers)
        sum = sum.add(new BigInteger(number.longValue());
    return sum;
}

public static BigDecimal sumFloat(final Collection&lt;? extends Number&gt; numbers) {
    BigDecimal sum = BigDecimal.ZERO;
    for (final Number number : numbers)
        sum = sum.add(new BigDecimal(number.doubleValue());
    return sum;
}


How it looks like with Java 8 Streams

With Java 8 Streams, the code could look like this:

public static BigDecimal sumFloat(final Collection&lt;? extends Number&gt;  numbers) {
    return numbers
            .parallelStream()
            .mapToDouble(Number::doubleValue)
            .mapToObj(BigDecimal::new)
            .reduce(BigDecimal.ZERO, BigDecimal::add);
}


LSP Violation

However, all these implementations violate the LSP - Liskov Substitution Principle. They will not work correctly for all potential Number types. If the Collection numbers contains BigDecimal or BigInteger objects which exceed the range expressible in double or long, the functions would fail to produce the correct result.

Given the signature, which suggests that any Number would do, and given the fact that class BigInteger extends Number and class BigDecimal extends Number, and given the fact that the signature uses BigInteger resp. BigDecimal as a return value, that would be a pretty unexpected behavior.

The following helper function can fix that problem for the known classes BigDecimal and BigInteger:

public static BigInteger toBigInteger(final Number number) {
    return
        Number instanceof BigInteger ? (BigInteger) number :
        Number instanceof BigDecimal ? ((BigDecimal) number).toBigInteger() :
        new BigInteger(number.longValue());
}


However, if someone creates another subclass of Number which exceeds the range of long, there still would be a problem. This problem could only be solved by fixing the API: class Number should have toBigInteger() and toBigDecimal() methods, which in Number, could be implemented with corresponding defaults. Because the root cause for the LSP violation is not in your code, not in my code, but in the API - in the way how class Number actually is defined.

Using the helper function, the code could look like this:

public class Numbers {

    public static BigInteger sumInt(final Collection&lt;? extends Number&gt; numbers) {
        BigInteger sum = BigInteger.ZERO;
        for (final Number number : numbers)
            sum = sum.add(toBigInteger(number);
        return sum;
    }

    public static BigDecimal sumFloat(final Collection&lt;? extends Number&gt;  numbers) {
        return numbers
                .parallelStream()
                .map(Numbers::toBigDecimal)
                .reduce(BigDecimal.ZERO, BigDecimal::add);
    }


    public static BigInteger toBigInteger(final Number number) {
        return
            Number instanceof BigInteger ? (BigInteger) number :
            Number instanceof BigDecimal ? ((BigDecimal) number).toBigInteger() :
            new BigInteger(number.longValue());
    }
    // ...
}