A while back I've played a lot with table based function approximations, especially of exp(x) and log

_{2}(x). What I've found is that there is (IMO) no way around table based methods to get acceptable precision and speed. After taking a quick look to Yeppp's source, I currently have doubts on the efficient of used algorithms, because they use polynomials of 1

*x*th degree.

BTW, a good book on this subject is "Elementary Functions Algorithms and Implementation" by Jean-Michel Muller.

An also interesting paper is "An Accurate Elementary Mathematical Library for the IEEE Floating Point Standard" by S. Gal and B. Bachells. I've used the accurate tables method they descripted for exp(x). After implementing it, I did a compare to the FPU and HPALIB (112 bit precision) with the disillusioning result that the relative error is less than 4E-14 over the whole range (REAL8). However, I've noticed that the MSVCRT use exact the same method (=same error) thus I stay with it

.