Optimizing the Chudnovsky Algorithm for Implementations

The Chudnovsky Algorithm is a fast method for calculating the digits of \pi. Here is the definition:

\displaystyle\frac{1}{\pi}=12\sum_{k=0}^{\infty}\frac{(-1)^k(6k)!(545140134k+13591409)}{(3k)!(k!)^3640320^{3k+\frac{3}{2}}}

The complexity of the algorithm is very high. It involves multiple factorials, exponents and calculations with large numbers. You should not directly implement the it as its definition, since the program will be pretty slow. Here shows some optimization of the algorithm for computations.

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