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POHow to efficiently compare the sign of two floating-point values while handling negative zeros
 

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  1. POHow to efficiently compare the sign of two floating-point values while handling negative zeros
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    <p>Given two floating-point numbers, I'm looking for an <em>efficient</em> way to check if they have the same sign, <em>given that if any of the two values is zero (+0.0 or -0.0), they should be considered to have the same sign</em>.</p> <p>For instance, </p> <ul> <li>SameSign(1.0, 2.0) should return true</li> <li>SameSign(-1.0, -2.0) should return true</li> <li>SameSign(-1.0, 2.0) should return false</li> <li><b>SameSign(0.0, 1.0) should return true</b></li> <li><b>SameSign(0.0, -1.0) should return true</b></li> <li><b>SameSign(-0.0, 1.0) should return true</b></li> <li><b>SameSign(-0.0, -1.0) should return true</b></li> </ul> <p>A naive but correct implementation of <code>SameSign</code> in C++ would be:</p> <pre><code>bool SameSign(float a, float b) { if (fabs(a) == 0.0f || fabs(b) == 0.0f) return true; return (a &gt;= 0.0f) == (b &gt;= 0.0f); } </code></pre> <p>Assuming the IEEE floating-point model, here's a variant of <code>SameSign</code> that compiles to branchless code (at least with with Visual C++ 2008):</p> <pre><code>bool SameSign(float a, float b) { int ia = binary_cast&lt;int&gt;(a); int ib = binary_cast&lt;int&gt;(b); int az = (ia &amp; 0x7FFFFFFF) == 0; int bz = (ib &amp; 0x7FFFFFFF) == 0; int ab = (ia ^ ib) &gt;= 0; return (az | bz | ab) != 0; } </code></pre> <p>with <code>binary_cast</code> defined as follow:</p> <pre><code>template &lt;typename Target, typename Source&gt; inline Target binary_cast(Source s) { union { Source m_source; Target m_target; } u; u.m_source = s; return u.m_target; } </code></pre> <p>I'm looking for two things:</p> <ol> <li><p><b>A faster, more efficient implementation of <code>SameSign</code></b>, using bit tricks, FPU tricks or even SSE intrinsics.</p></li> <li><p><b>An efficient extension of <code>SameSign</code> to three values</b>.</p></li> </ol> <p>Edit:</p> <p>I've made some performance measurements on the three variants of <code>SameSign</code> (the two variants described in the original question, plus Stephen's one). Each function was run 200-400 times, on all consecutive pairs of values in an array of 101 floats filled at random with -1.0, -0.0, +0.0 and +1.0. Each measurement was repeated 2000 times and the minimum time was kept (to weed out all cache effects and system-induced slowdowns). The code was compiled with Visual C++ 2008 SP1 with maximum optimization and SSE2 code generation enabled. The measurements were done on a Core 2 Duo P8600 2.4 Ghz.</p> <p>Here are the timings, not counting the overhead of fetching input values from the array, calling the function and retrieving the result (which amount to 6-7 clockticks):</p> <ul> <li>Naive variant: 15 ticks</li> <li>Bit magic variant: 13 ticks</li> <li><b>Stephens's variant: 6 ticks</b></li> </ul>
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    1. USFrançois Beaune
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    1. COAny particular language/platform?
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      1. USMichael Myers
    2. COHey, thanks for the good question :) Preferably C/C++ on x86.
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      1. USFrançois Beaune
    3. COpossible duplicate of [comparing two floats to see if they're both negative, or both positive.](http://stackoverflow.com/questions/2013680/comparing-two-floats-to-see-if-theyre-both-negative-or-both-positive)
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