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copied!<p><strong>Summary</strong></p> <p>In Java 6 (and presumably earlier), <code>round(x)</code> is implemented as <code>floor(x+0.5)</code>.<sup>1</sup> This is a specification bug, for precisely this one pathological case.<sup>2</sup> Java 7 no longer mandates this broken implementation.<sup>3</sup></p> <p><strong>The problem</strong></p> <p>0.5+0.49999999999999994 is exactly 1 in double precision:</p> <pre><code>static void print(double d) { System.out.printf("%016x\n", Double.doubleToLongBits(d)); } public static void main(String args[]) { double a = 0.5; double b = 0.49999999999999994; print(a); // 3fe0000000000000 print(b); // 3fdfffffffffffff print(a+b); // 3ff0000000000000 print(1.0); // 3ff0000000000000 } </code></pre> <p>This is because 0.49999999999999994 has a smaller exponent than 0.5, so when they're added, its mantissa is shifted, and the ULP gets bigger.</p> <p><strong>The solution</strong></p> <p>Since Java 7, OpenJDK (for example) implements it thus:<sup>4</sup></p> <pre><code>public static long round(double a) { if (a != 0x1.fffffffffffffp-2) // greatest double value less than 0.5 return (long)floor(a + 0.5d); else return 0; } </code></pre> <hr> <p><sub> 1. <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Math.html#round%28double%29" rel="noreferrer">http://docs.oracle.com/javase/6/docs/api/java/lang/Math.html#round%28double%29</a> </sub></p> <p><sub> 2. <a href="http://bugs.java.com/bugdatabase/view_bug.do?bug_id=6430675" rel="noreferrer">http://bugs.java.com/bugdatabase/view_bug.do?bug_id=6430675</a> (credits to @SimonNickerson for finding this) </sub></p> <p><sub> 3. <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Math.html#round%28double%29" rel="noreferrer">http://docs.oracle.com/javase/7/docs/api/java/lang/Math.html#round%28double%29</a> </sub></p> <p><sub> 4. <a href="http://grepcode.com/file/repository.grepcode.com/java/root/jdk/openjdk/7u40-b43/java/lang/Math.java#Math.round%28double%29" rel="noreferrer">http://grepcode.com/file/repository.grepcode.com/java/root/jdk/openjdk/7u40-b43/java/lang/Math.java#Math.round%28double%29</a> </sub></p>

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