how R implement qnorm()

R is a bit confusing as it requires inverse error function (X =
- sqrt(2)* erf-1 (2*P)), while R doesn't have a build in one. The InvErf
function most people use is through qnorm( InvErf=function(x)

I think you are wrong about 'most people': this is the notation used by a small group of non-statisticians (mainly physicists, I think).

Well, he's right in the sense that it is erf/erfc that are commonly documented in collections of special functions (like Abramowitz & Stegun), and also those that appear in common C math libraries. In both cases of course because physicists have dominated in their development. 

Of course "most people" use Excel these days (which has the inverse normal distribution but AFAICS not the inverse error function).

Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com