# Is there an efficient algorithm for calculation of continued fraction expansion from decimal digits?

Suppose to calculate the continued fraction expansion of $$\pi$$, the common-sense algorithm would be to take the decimal part, perform inversion, which will give the next term as integer part, and the process is repeated for the decimal part.

However, this algorithm has the complexity of order $$\mathcal O(n^2\log(n))$$ assuming $$\mathcal O(n \log n)$$ multiplication. What would be an asymptotically faster algorithm?