On the exponential integral computation

New high-precision algorithm for exponential integral calculation was developed. It is based on the representation of exponential integral in form of convergent series when $x$-argument is not large and in form of asymptotically convergent continued fraction when $x$ is large. It was shown that the optimal bound between these representations is $x=1$. At the same time using of 18 series members and 220 continued fraction members guarantees relative pre-cision lower than $2\cdot 10^{-15}$, that exceeds practical needs.