To draw a comparison between this Normal generator (that I will consider as von Neumann’s) and the Box-Müller polar generator,

#Box-Müller bm=function(N){ a=sqrt(-2*log(runif(N/2))) b=2*pi*runif(N/2) return(c(a*sin(b),a*cos(b))) } #vonNeumann vn=function(N){ u=-log(runif(2.64*N)) v=-2*log(runif(2.64*N))>(u-1)^2 w=(runif(2.64*N)<.5)-2 return((w*u)[v]) }

here are the relative computing times

> system.time(bm(1e8)) utilisateur système écoulé 7.015 0.649 7.674 > system.time(vn(1e8)) utilisateur système écoulé 42.483 5.713 48.222