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, and 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 5-1 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 

Example 5-1.

/** * Floating-point comparisons. ...

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