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Double your money again

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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.

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.

 

From http://vanillajava.blogspot.com/2011/08/double-your-money-again.html

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