Inventive aspects include a high-precision log 1p( ) compute logic section of a computing machine to approximate a function F(x)=log 1p(x)=ln(x+1), using an estimation function E(x), and to at least: (i) receive an input x, (ii) compute (x+1) using only native precision, (iii) compute an integer N such that: 4/32N−1≤(x+1)≤ 4/32N, (iv) compute ƒN(x)=Sx+(S−1) where S=2−N, (v) compute E(ƒN(x)), and (vi) return a value v=E(ƒN(x))+N ln(2) as an approximation of F(x)=log 1p(x).