normal_distribution.hpp, improvements to distribution and possibly speed

[m.bannerman@…]

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.

Posted to boost.developers 2007-11-11

[m.bannerman@…]

Improved normal_distribution.hpp

[m.bannerman@…]

I forgot to mention that this also has a smaller memory footprint than the previous version.

[Steven Watanabe]

I've completely re-written normal_distribution since this ticket was created.