Comparing Doubles in Java

1. Overview

In this tutorial, we'll talk about the different ways of comparing double values in Java. In particular, it isn't as easy as comparing other primitive types. As a matter of fact, it's problematic in many other languages, not only Java.

First, we'll explain why using the simple == operator is inaccurate and might cause difficult to trace bugs in the runtime. Then, we'll show how to compare doubles in plain Java and common third-party libraries correctly.

2. Using the == Operator

Inaccuracy with comparisons using the == operator is caused by the way double values are stored in a computer's memory. We need to remember that there is an infinite number of values that must fit in limited memory space, usually 64 bits. As a result, we can't have an exact representation of most double values in our computers. They must be rounded to be saved.

Because of the rounding inaccuracy, interesting errors might occur:

double d1 = 0;
for (int i = 1; i <= 8; i++) {
    d1 += 0.1;
 }
double d2 = 0.1 * 8;
System.out.println(d1);
System.out.println(d2);

Both variables, d1 and d2, should equal 0.8. However, when we run the code above, we'll see the following results:

0.7999999999999999
0.8

In that case, comparing both values with the == operator would produce a wrong result. For this reason, we must use a more complex comparison algorithm.

If we want to have the best precision and control over the rounding mechanism, we can use java.math.BigDecimal class.

3. Comparing Doubles in Plain Java

The recommended algorithm to compare double values in plain Java is a threshold comparison method. In this case, we need to check whether the difference between both numbers is within the specified tolerance, commonly called epsilon:

double epsilon = 0.000001d;
assertThat(Math.abs(d1 - d2) < epsilon).isTrue();

The smaller the epsilon's value, the greater the comparison accuracy. However, if we specify the tolerance value too small, we'll get the same false result as in the simple == comparison. In general, epsilon's value with 5 and 6 decimals is usually a good place to start.

Unfortunately, there is no utility from the standard JDK that we could use to compare double values in the recommended and precise way. Luckily, we don't need to write it by ourselves. We can use a variety of dedicated methods provided by free and widely known third-party libraries.

4. Using Apache Commons Math

Apache Commons Math is one of the biggest open-source library dedicated to mathematics and statistics components. From the variety of different classes and methods, we'll focus on org.apache.commons.math3.util.Precision class in particular. It contains 2 helpful equals() methods to compare double values correctly:

double epsilon = 0.000001d;
assertThat(Precision.equals(d1, d2, epsilon)).isTrue();
assertThat(Precision.equals(d1, d2)).isTrue();

The epsilon variable used here has the same meaning as in the previous example. It is an amount of allowed absolute error. However, it's not the only similarity to the threshold algorithm. In particular, both equals methods use the same approach under the hood.

The two-argument function version is just a shortcut for the equals(d1, d2, 1) method call. The epsilon's value in that version is quite high. Therefore we shouldn't use it and always specify the tolerance value by ourselves.

5. Using Guava

Google's Guava is a big set of core Java libraries that extend the standard JDK capabilities. It contains a big number of useful math utils in the com.google.common.math package. To compare double values correctly in Guava, let's implement the fuzzyEquals() method from the DoubleMath class:

double epsilon = 0.000001d;
assertThat(DoubleMath.fuzzyEquals(d1, d2, epsilon)).isTrue();

The method name is different than in the Apache Commons Math, but it works practically identically under the hood. The only difference is that there is no overloaded method with the epsilon's default value.

6. Using JUnit

JUnit is one of the most widely used unit testing frameworks for Java. In general, every unit test usually ends with analyzing the difference between expected and actual values. Therefore, the testing framework must have correct and precise comparison algorithms. In fact, JUnit provides a set of comparing methods for common objects, collections, and primitive types, including dedicated methods to check double values equality:

double epsilon = 0.000001d;
assertEquals(d1, d2, epsilon);

As a matter of fact, it works the same as Guava's and Apache Commons's methods previously described.

It's important to point out that there is also a deprecated, two-argument version without the epsilon argument. However, if we want to be sure our results are always correct, we should stick with the three-argument version.

7. Conclusion

In this article, we've explored different ways of comparing double values in Java.

We've explained why simple comparison might cause difficult to trace bugs in the runtime. Then, we've shown how to compare values in plain Java and common libraries correctly.

As always, the source code for the examples can be found over on GitHub.

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