I've never seen anyone use Newton: there is an optimum to be found w.r.t speed and accuracy (of the density), do you know how it rank against BM and Ziggurat wrt speed and accuracy?

There is no "std" implementation / algorithm!

Each compiler vendor is allowed to do as they wish as long as they adhere to the requirements specified by the C++ commision. There is no required algorithm there, only "A normal_distribution random number distribution produces random numbers x distributed according to the probability density function p(x,mu,sigma) = ..."

Visual Studio e.g. used the n=16 Irwin Hall distribution approximation.

GCC seems to use the polar form of the Box Muller, here is a snippet for the SSE version that does 4 in parallel

https://github.com/gcc-mirror/gcc/blob/ ... t_random.h