Hello,<br><br>Boost random library implements GRNG (Gaussian Random Number Generator) with Box-Muller transform (<a href="http://www.boost.org/doc/libs/1_39_0/boost/random/normal_distribution.hpp">code here</a>). I want to discuss about this line of code:<br>
<pre>_cached_rho = sqrt(-result_type(2) * log(result_type(1)-_r2));</pre>I don&#39;t know why log is applied to 1-r2, instead of r2 directly, yielding<br><pre>_cached_rho = sqrt(-result_type(2) * log(_r2));</pre>According with [<a href="http://www.cse.cuhk.edu.hk/%7Ephwl/mt/public/archives/papers/grng_acmcs07.pdf">1</a>, <a href="http://mathworld.wolfram.com/Box-MullerTransformation.html">2</a>, <a href="http://en.wikipedia.org/wiki/Box-Muller_transformation">3</a>] the uniform random variable r2 is always used directly (never 1-r2). I&#39;d like to know why 1-r2 is used.<br>
<br clear="all">I&#39;ve tried to compare with other scientific libraries like <a href="http://www.gnu.org/software/gsl/manual/html_node/The-Gaussian-Distribution.html">GSL</a>, <a href="http://scythe.wustl.edu/api/rng_8h-source.html">Scythestat</a> and <a href="http://ltilib.sourceforge.net/doc/html/index.shtml">LTILib</a>, but they use the Box-Muller polar form (or Marsaglia polar method) or even Ziggurat algorithm, which are supposed to be more efficient. Why isn&#39;t polar form implemented? I&#39;d like to know why 1-r2 is used anyway.<br>
<br>Regards,<br>  Enrique<br><br>