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    <p>The best approach I think is to compare <a href="http://en.wikipedia.org/wiki/Unit_in_the_last_place" rel="noreferrer">ULPs</a>.</p> <pre><code>bool is_nan(float f) { return (*reinterpret_cast&lt;unsigned __int32*&gt;(&amp;f) &amp; 0x7f800000) == 0x7f800000 &amp;&amp; (*reinterpret_cast&lt;unsigned __int32*&gt;(&amp;f) &amp; 0x007fffff) != 0; } bool is_finite(float f) { return (*reinterpret_cast&lt;unsigned __int32*&gt;(&amp;f) &amp; 0x7f800000) != 0x7f800000; } // if this symbol is defined, NaNs are never equal to anything (as is normal in IEEE floating point) // if this symbol is not defined, NaNs are hugely different from regular numbers, but might be equal to each other #define UNEQUAL_NANS 1 // if this symbol is defined, infinites are never equal to finite numbers (as they're unimaginably greater) // if this symbol is not defined, infinities are 1 ULP away from +/- FLT_MAX #define INFINITE_INFINITIES 1 // test whether two IEEE floats are within a specified number of representable values of each other // This depends on the fact that IEEE floats are properly ordered when treated as signed magnitude integers bool equal_float(float lhs, float rhs, unsigned __int32 max_ulp_difference) { #ifdef UNEQUAL_NANS if(is_nan(lhs) || is_nan(rhs)) { return false; } #endif #ifdef INFINITE_INFINITIES if((is_finite(lhs) &amp;&amp; !is_finite(rhs)) || (!is_finite(lhs) &amp;&amp; is_finite(rhs))) { return false; } #endif signed __int32 left(*reinterpret_cast&lt;signed __int32*&gt;(&amp;lhs)); // transform signed magnitude ints into 2s complement signed ints if(left &lt; 0) { left = 0x80000000 - left; } signed __int32 right(*reinterpret_cast&lt;signed __int32*&gt;(&amp;rhs)); // transform signed magnitude ints into 2s complement signed ints if(right &lt; 0) { right = 0x80000000 - right; } if(static_cast&lt;unsigned __int32&gt;(std::abs(left - right)) &lt;= max_ulp_difference) { return true; } return false; } </code></pre> <p>A similar technique can be used for doubles. The trick is to convert the floats so that they're ordered (as if integers) and then just see how different they are.</p> <p>I have no idea why this damn thing is screwing up my underscores. Edit: Oh, perhaps that is just an artefact of the preview. That's OK then.</p>
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    1. POComparing IEEE floats and doubles for equality
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    1. COThis wins hands-down for precision. But for performance... you'd have to trade off a bit of that accuracy for a speed improvement. Agreed?
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    2. COIf you need doubles or portability: I found a great cross-platform implementation of this that can deal with both doubles and floats in Google Test and posted it here: http://stackoverflow.com/questions/17333/most-effective-way-for-float-and-double-comparison/3423299#3423299
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