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copied!<p>From all the questions from under <code>floating-accuracy</code> tag on this site any discussion should probably start with a reference to this question: <a href="https://stackoverflow.com/q/10334688/1328439">How dangerous is it to compare floating point values?</a></p> <p>And a reference thereof to "<a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html" rel="nofollow noreferrer">What Every Computer Scientist Should Know About Floating Point Arithmetic</a>" by David Goldberg. Here is a short summary.</p> <p><strong>1. Exact floating point results are not portable</strong></p> <p>Floating point arithmetic is neither commutative nor associative. IEEE 754 standard that most compilers and platforms follow does not guarantee exact <em>reproducibility</em> of results. Also results will vary on different processors.</p> <p><strong>2. Floating point comparison does not agree with mathematics</strong></p> <p>Consider the following statement</p> <pre><code> int i = 0; double x = 1.0; while (x != 0.0) { x = x/2 ; i++;} </code></pre> <p>In real numbers this computation should never complete however in floating point it will terminate. The value of <code>i</code> depends on the underlying hardware. Using floating point comparison will make it more difficult to analyze the code.</p> <p><strong>3. Why then is floating point comparison implemented in hardware?</strong></p> <p>There are places where exact floating point equality is necessary. One is normalization of floating point numbers.</p>

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