maths.bailey_borwein_plouffe

Functions

_subsum(→ float)	Private helper function to implement the summation
bailey_borwein_plouffe(→ str)	Implement a popular pi-digit-extraction algorithm known as the

Module Contents

maths.bailey_borwein_plouffe._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

maths.bailey_borwein_plouffe.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