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copied!<p>I have looked at this paper <a href="http://nic.schraudolph.org/pubs/Schraudolph99.pdf" rel="noreferrer">here</a> which describes how to approximate the exponential function for double precision. After a little research on Wikipedia about single precision floating point representation I have worked out the equivalent algorithms. They only implemented the exp function, so I found an inverse function for the log and then simply did</p> <pre><code> POW(a, b) = EXP(LOG(a) * b). </code></pre> <p>compiling this gcc4.6.2 yields a pow function almost 4 times faster than the standard library's implementation (compiling with O2).</p> <p>Note: the code for EXP is copied almost verbatim from the paper I read and the LOG function is copied from <a href="http://martin.ankerl.com/2007/10/04/optimized-pow-approximation-for-java-and-c-c/" rel="noreferrer">here</a>.</p> <p>Here is the relevant code:</p> <pre><code> #define EXP_A 184 #define EXP_C 16249 float EXP(float y) { union { float d; struct { #ifdef LITTLE_ENDIAN short j, i; #else short i, j; #endif } n; } eco; eco.n.i = EXP_A*(y) + (EXP_C); eco.n.j = 0; return eco.d; } float LOG(float y) { int * nTemp = (int*)&y; y = (*nTemp) >> 16; return (y - EXP_C) / EXP_A; } float POW(float b, float p) { return EXP(LOG(b) * p); } </code></pre> <p>There is still some optimization you can do here, or perhaps that is good enough. This is a rough approximation but if you would have been satisfied with the errors introduced using the double representation, I imagine this will be satisfactory.</p>

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