Hello, I have adapted the current normal_distribution from the polar form to the outward Cartesian form. See here http://web.mat.bham.ac.uk/marijke/bm/yabm.pdf listing the benefits of the Cartesian form for the distribution of numbers. This also eliminates trigonometric function calls, however, it does reject pairs of random numbers. Most websites (wolfram, wikipedia) state that the inward Cartesian form is faster but this is generator speed dependent. I've found with my tests (mt19937, double datatype, gcc (GCC) 4.1.3 20070929 (prerelease) (Ubuntu 4.1.2-16ubuntu2), -O2) its about 1.5x slower than the polar form. Although with faster generators I expect it to outperform the polar version. I think this is an improvement on the current normal_distribution.hpp in time critical situations (if a fast generator is used) and it gives a better distribution of numbers, (points rather than bands of inaccessible numbers). I have also found that this version doesn't produce the "may be used uninitialised" warning when compiling with optimisations that I get when I use the original. Please let me know if you think of any other improvements or spot any errors. I will use this in my code however I would like to give something back. I'm not sure what to do with the copyright at the top of the file and I'm not sure if this is the correct way to submit this for review. Apologies in advance if I have made a mistake. Marcus Bannerman