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POgcc rounding difference between versions
 

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    <p>I'm looking into <a href="https://github.com/imageworks/OpenColorIO/issues/168">why a test case is failing</a></p> <p>The problematic test can be reduced to doing <code>(4.0/9.0) ** (1.0/2.6)</code>, rounding this to 6 digits and checking against a known value (as a string):</p> <pre><code>#include&lt;stdio.h&gt; #include&lt;math.h&gt; int main(){ printf("%.06f\n", powf(4.0/9.0, (1.0/2.6))); } </code></pre> <p>If I compile and run this in gcc 4.1.2 on Linux, I get:</p> <pre><code>0.732057 </code></pre> <p>Python agrees, as does <a href="http://www.wolframalpha.com/input/?i=%284.0%2F9.0%29%2a%2a%281%2F2.6%29">Wolfram|Alpha</a>:</p> <pre><code>$ python2.7 -c 'print "%.06f" % (4.0/9.0)**(1/2.6)' 0.732057 </code></pre> <p>However I get the following result on gcc 4.4.0 on Linux, and 4.2.1 on OS X:</p> <pre><code>0.732058 </code></pre> <p>A <code>double</code> acts identically (although I didn't test this extensively)</p> <p>I'm not sure how to narrow this down any further.. Is this a gcc regression? A change in rounding algorithm? Me doing something silly?</p> <p><strong>Edit:</strong> Printing the result to 12 digits, the digit at the 7th place is 4 vs 5, which explains the rounding difference, but not the value difference:</p> <p>gcc 4.1.2:</p> <pre><code>0.732057452202 </code></pre> <p>gcc 4.4.0:</p> <pre><code>0.732057511806 </code></pre> <p>Here's the <code>gcc -S</code> output from both versions: <a href="https://gist.github.com/1588729">https://gist.github.com/1588729</a></p>
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    1. COTo remove `printf()` behaving differently as a variable, print or inspect the bits of the memory holding the value, so you remove the "convert to string" part of the story.
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    2. COThe difference between those two is exactly the [machine epsilon](http://en.wikipedia.org/wiki/Machine_epsilon) of a 32 bit processor. Also gcc4.4's result is closer to the actual value of the expression.
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