maths.bailey_borwein_plouffe
============================

.. py:module:: maths.bailey_borwein_plouffe


Functions
---------

.. autoapisummary::

   maths.bailey_borwein_plouffe._subsum
   maths.bailey_borwein_plouffe.bailey_borwein_plouffe


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

.. py:function:: _subsum(digit_pos_to_extract: int, denominator_addend: int, precision: int) -> float

   Private helper function to implement the summation
   functionality.
   @param digit_pos_to_extract: digit position to extract
   @param denominator_addend: added to denominator of fractions in the formula
   @param precision: same as precision in main function
   @return: floating-point number whose integer part is not important


.. py:function:: bailey_borwein_plouffe(digit_position: int, precision: int = 1000) -> str

   Implement a popular pi-digit-extraction algorithm known as the
   Bailey-Borwein-Plouffe (BBP) formula to calculate the nth hex digit of pi.
   Wikipedia page:
   https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula
   @param digit_position: a positive integer representing the position of the digit to
   extract.
   The digit immediately after the decimal point is located at position 1.
   @param precision: number of terms in the second summation to calculate.
   A higher number reduces the chance of an error but increases the runtime.
   @return: a hexadecimal digit representing the digit at the nth position
   in pi's decimal expansion.

   >>> "".join(bailey_borwein_plouffe(i) for i in range(1, 11))
   '243f6a8885'
   >>> bailey_borwein_plouffe(5, 10000)
   '6'
   >>> bailey_borwein_plouffe(-10)
   Traceback (most recent call last):
     ...
   ValueError: Digit position must be a positive integer
   >>> bailey_borwein_plouffe(0)
   Traceback (most recent call last):
     ...
   ValueError: Digit position must be a positive integer
   >>> bailey_borwein_plouffe(1.7)
   Traceback (most recent call last):
     ...
   ValueError: Digit position must be a positive integer
   >>> bailey_borwein_plouffe(2, -10)
   Traceback (most recent call last):
     ...
   ValueError: Precision must be a nonnegative integer
   >>> bailey_borwein_plouffe(2, 1.6)
   Traceback (most recent call last):
     ...
   ValueError: Precision must be a nonnegative integer