A spigot algorithm is a type of algorithm used to compute the value of a mathematical constant such as or e. Spigot algorithms are unique because they do not require the total number of digits to be fixed beforehand, and do not require the computation of several intermediate results which are combined to produce the final result. There are two kinds of spigot algorithms: (1) those that can produce a single, arbitrary digit (also called digit extraction algorithm); and (2) those that produce a sequence of digits, one after the other. The Bailey-Borwein-Plouffe formula is a digit extr...

The Bailey–Borwein–Plouffe formula (BBP formula) provides a spigot algorithm for the computation of the nth binary digit of π. This summation formula was discovered in 1995 by Simon Plouffe. The formula is named after the authors of the paper in which the formula was published, David H. Bailey, Peter Borwein, and Simon Plouffe. Before that paper, it had been published by Plouffe on his own site. The formula is : \pi = \sum_{i = 0}^{\infty}\left[ \frac{1}{16^i} \left( \frac{4}{8i + 1} - \frac{2}{8i + 4} - \frac{1}{8i + 5} - \frac{1}{8i + 6} \right) \right]. The discovery of this formula c...