Java Comparing Floating-Point Numbers

Java Comparing Floating-Point Numbers


You want to compare two floating-point numbers for equality.


Based on what we’ve just discussed, you probably won’t just go comparing two
floats or doubles for equality. You might expect the floating-point wrapper classes,

Float and Double , to override the equals( ) method, which they do. The equals( )
method returns true if the two values are the same bit for bit, that is, if and only if
the numbers are the same or are both NaN . It returns false otherwise, including if the
argument passed in is null, or if one object is +0.0 and the other is –0.0.

If this sounds weird, remember that the complexity comes partly from the nature of
doing real number computations in the less-precise floating-point hardware, and
partly from the details of the IEEE Standard 754, which specifies the floating-point
functionality that Java tries to adhere to, so that underlying floating-point processor
hardware can be used even when Java programs are being interpreted.

To actually compare floating-point numbers for equality, it is generally desirable to
compare them within some tiny range of allowable differences; this range is often
regarded as a tolerance or as epsilon. Example shows an equals( ) method you
can use to do this comparison, as well as comparisons on values of NaN . When run, it
prints that the first two numbers are equal within epsilon:

$ java FloatCmp
True within epsilon 1.0E-7

* Floating-point comparisons.
public class FloatCmp {
final static double EPSILON = 0.0000001;
public static void main(String[] argv) {
double da = 3 * .3333333333;
double db = 0.99999992857;
// Compare two numbers that are expected to be close.
if (da == db) {
System.out.println("Java considers " + da + "==" + db);
// else compare with our own equals method
} else if (equals(da, db, 0.0000001)) {
System.out.println("True within epsilon " + EPSILON);
} else {
System.out.println(da + " != " + db);
// Show that comparing two NaNs is not a good idea:
double d1 = Double.NaN;
double d2 = Double.NaN;
if (d1 == d2)
System.err.println("Comparing two NaNs incorrectly returns true.");
if (!new Double(d1).equals(new Double(d2)))
System.err.println("Double(NaN).equal(NaN) incorrectly returns false.");

/** Compare two doubles within a given epsilon */
public static boolean equals(double a, double b, double eps) {
if (a==b) return true;
// If the difference is less than epsilon, treat as equal.
return Math.abs(a - b) < eps;
/** Compare two doubles, using default epsilon */
public static boolean equals(double a, double b) {
if (a==b) return true;
// If the difference is less than epsilon, treat as equal.
return Math.abs(a - b) < EPSILON * Math.max(Math.abs(a), Math.abs(b));

Note that neither of the System.err messages about “incorrect returns” prints. The point of this example with NaN s is that you should always make sure values are not NaN before entrusting them to Double.equals( ).


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