I couldn't figure out any explanation for that constant. If I had to guess, maybe some optimization for the base-2 log/exp CORDIC algorithm, like a polynomial a

I couldn't figure out any explanation for that constant. If I had to guess, maybe some optimization for the base-2 log/exp CORDIC algorithm, like a polynomial approximation of base-2 log for the small remainder from CORDIC. The dividing by 3 might come from the Taylor series.