maths.chudnovsky_algorithm
==========================

.. py:module:: maths.chudnovsky_algorithm


Attributes
----------

.. autoapisummary::

   maths.chudnovsky_algorithm.n


Functions
---------

.. autoapisummary::

   maths.chudnovsky_algorithm.pi


Module Contents
---------------

.. py:function:: pi(precision: int) -> str

   The Chudnovsky algorithm is a fast method for calculating the digits of PI,
   based on Ramanujan's PI formulae.

   https://en.wikipedia.org/wiki/Chudnovsky_algorithm

   PI = constant_term / ((multinomial_term * linear_term) / exponential_term)
       where constant_term = 426880 * sqrt(10005)

   The linear_term and the exponential_term can be defined iteratively as follows:
       L_k+1 = L_k + 545140134            where L_0 = 13591409
       X_k+1 = X_k * -262537412640768000  where X_0 = 1

   The multinomial_term is defined as follows:
       6k! / ((3k)! * (k!) ^ 3)
           where k is the k_th iteration.

   This algorithm correctly calculates around 14 digits of PI per iteration

   >>> pi(10)
   '3.14159265'
   >>> pi(100)
   '3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706'
   >>> pi('hello')
   Traceback (most recent call last):
       ...
   TypeError: Undefined for non-integers
   >>> pi(-1)
   Traceback (most recent call last):
       ...
   ValueError: Undefined for non-natural numbers


.. py:data:: n
   :value: 50