According to the JLS, [§4.2.3, "Floating-Point Types, Formats, and Values"|http://java.sun.com/docs/books/jls/third_edition/html/typesValues.html#4.2.3] \[[JLS 2005|AA. References#JLS 05]\]: 

NaN (not-a-number) is unordered, so the numerical comparison operators <, <=, >, and >= return false if either or both operands are NaN. The equality operator == returns false if either operand is NaN, and the inequality operator != returns true if either operand is NaN.

Because this unordered property is often unexpected, direct comparisons with NaN must not be performed. Problems can arise when programmers write code that compares floating-point values without considering the semantics of NaN. For example, input validation checks that fail to consider the possibility of a NaN value as input can produce unexpected results. See rule NUM08-J. Check floating-point inputs for exceptional values for additional information.

Noncompliant Code Example

This noncompliant code example attempts a direct comparison with NaN. In accordance with the semantics of NaN, all comparisons with NaN yield false (with the exception of the != operator, which returns true). Consequently, this comparison always return false, and the "result is NaN" message is never printed.

public class NaNComparison {
  public static void main(String[] args) {
    double x = 0.0;
    double result = Math.cos(1/x); // returns NaN if input is infinity
    if (result == Double.NaN) { // comparison is always false!
      System.out.println("result is NaN");
    }
  }
}

Compliant Solution

This compliant solution uses the method Double.isNaN() to check whether the expression corresponds to a NaN value.

public class NaNComparison {
  public static void main(String[] args) {
    double x = 0.0;	  
    double result = Math.cos(1/x); // returns NaN when input is infinity
    if (Double.isNaN(result)) { 
      System.out.println("result is NaN");
    }
  }
}

Risk Assessment

Comparisons with NaN values can lead to unexpected results.

Automated Detection

Automated detection of floating-point comparison operators is straightforward. Sound determination of whether the possibility of an unordered result has been correctly handled is not feasible in the general case. Heuristic checks could be useful.

Bibliography

NUM06-J. Use the strictfp modifier for floating-point calculation consistency across platforms      03. Numeric Types and Operations (NUM)