I used several atmospheric density calculators on the net - they give different answers! It seemed that, in 2011, it is not clear how to compute the density of air! I know now also why people mention pressure, temperature and humidity and not density - it is not trivial to compute. I researched more and found an article called

"Revised formula for the density of moist air (CIPM-2007), Metrologia 45 (2008) 149–155"

I have a prototype implementation of it. Soon I will release a BfX function that calculates the air density and expand BfX_c to include humidity as an option. (humidity effects, however are very very small).

(CIPM = International Committee for Weights and Measures)

The calculations confirm the earlier calculations menitionned in this thread for the density for which Ingalls tables are valid, as well as its relative density to icao.