id	summary	reporter	owner	description	type	status	milestone	component	version	severity	resolution	keywords	cc
1437	normal_distribution.hpp, improvements to distribution and possibly speed	m.bannerman@…	No-Maintainer	"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"	Patches	closed	To Be Determined	random	Boost 1.34.1	Optimization	wontfix	random normal distribution box muller transform gaussian