Double your money again

Overview

A long time ago I wrote an article on using double for money. However, it is still a common fear for many developers when the solution is fairly simple.

Why not use BigDecimal

@myfear (Markus) asks a good question, doesn't BigDecimal do rounding already, (and with more options)

IMHO, There are two reason you may want to avoid BigDecimal

1. Clarity.  This may be a matter of option but I find x * y / z clearer than x.multiply(y).divide(z, 10, BigDecimal.ROUND_HALF_UP)
2. Performance. BigDecimal is often 100x slower.

Took an average of 6 ns for rounding using cast
Took an average of 17 ns for rounding using Math.round
Took an average of 932 ns for rounding using BigDecimal.setScale

You might like to test the difference on your machine.

The code

RoundingPerformanceMain.java

When to use BigDecimal

The better question is why would you ever use BigDecimal?

1. Arbitary precision. If you want more than 15 decimal places of precision, use BigDecimal.
2. Precise rounding. If you need to have full control over rounding options, it will be simpler using BigDecimal
3. The project standard is to use BigDecimal. Human factors can be more important than technical arguments.

The problem with using double for money

double has two types of errors. It have representation error. i.e. it cannot represent all possible decimal values exactly. Even 0.1 is not exactly this value. It also has rounding error from calculations. i.e. as you perform calculations, the error increases.

double[] ds = {
        0.1,
        0.2,
        -0.3,
        0.1 + 0.2 - 0.3};
for (double d : ds) {
    System.out.println(d + " => " + new BigDecimal(d));
}

prints

0.1 => 0.1000000000000000055511151231257827021181583404541015625
0.2 => 0.200000000000000011102230246251565404236316680908203125
-0.3 => -0.299999999999999988897769753748434595763683319091796875
5.551115123125783E-17 => 5.5511151231257827021181583404541015625E-17

You can see that the representation for 0.1 and 0.2 is slightly higher than those values, and -0.3 is also slightly higher. When you print them, you get the nicer 0.1 instead of the actual value represented 0.1000000000000000055511151231257827021181583404541015625

However, when you add these values together, you get a value which is slightly higher than 0.

The important thing to remember is that these errors are not random errors. They are manageable and bounded.

Correcting for rounding error

Like many data types, such as date, you have an internal representation for a value and how you represent this as a string.

This is true for double. You need to control how the value is represented as a string. This can can be surprise as Java does a small amount of rounding for representation error is not obvious, however once you have rounding error for operations as well, it can some as a shock.

A common reaction is to assume, there is nothing you can do about it, the error is uncontrollable, unknowable and dangerous. Abandon double and use BigDecimal

However, the error is limited in the IEE-754 standards and accumulate slowly.

Round the result

And just like the need to use a TimeZone and Local for dates, you need to determine the precision of the result before converting to a String.

To resolve this issue, you need to provide appropriate rounding. With money this is easy as you know how many decimal places are appropriate and unless you have $70 trillion you won't get a rounding error large enough you cannot correct it.

// uses round half up, or bankers' rounding
public static double roundToTwoPlaces(double d) {
    return Math.round(d * 100) / 100.0;
}
// OR
public static double roundToTwoPlaces(double d) {
    return ((long) (d < 0 ? d * 100 - 0.5 : d * 100 + 0.5)) / 100.0;
}

If you add this into the result, there is still a small representation error, however it is not large enough that the Double.toString(d) cannot correct for it.

double[] ds = {
        0.1,
        0.2,
        -0.3,
        0.1 + 0.2 - 0.3};
for (double d : ds) {
    System.out.println(d + " to two places " + roundToTwoPlaces(d) + " => " + new BigDecimal(roundToTwoPlaces(d)));
}

prints

0.1 to two places 0.1 => 0.1000000000000000055511151231257827021181583404541015625
0.2 to two places 0.2 => 0.200000000000000011102230246251565404236316680908203125
-0.3 to two places -0.3 => -0.299999999999999988897769753748434595763683319091796875
5.551115123125783E-17 to two places 0.0 => 0

Conclusion

If you have a project standard which says you should use BigDecimal or double, that is what you should follow. However, there is not a good technical reason to fear using double for money.

Related Links

Working with Money - In favour of BigDecimal. A comment which has a good suggestion that a generic Money wrapper be used if performance allows it.

JodaMoney