multiplies by 16 to "skim off" the hexadecimal digit at this position (in theory, the next few digits up to the accuracy of the calculations used would also be accurate). This process is similar to performing long multiplication, but only having to perform the summation of some middle columns. While there are some carries that are not counted, computers usually perform arithmetic for many bits (32 or 64) and round, and we are only interested in the most significant digit(s). There is a possibility that a particular computation will be akin to failing to add a small number (e.g. 1) to the number 999999999999999, and that the error will propagate to the most significant digit. BBP compared to other methods of computing This algorithm computes without requiring custom data types having thousands or even millions of digits. The method calculates the nth digit without calculating the first n − 1 digits and can use small, efficient data types. Though the BBP formula can directly calculate the value of any given digit of with less computational effort than formulas that must calculate all intervening digits, BBP remains linearithmic (), whereby successively larger values of n require increasingly more time to calculate; that is, the "further out" a digit is, the longer it takes BBP to calculate it, just like the standard -computing algorithms. Generalizations D. J. Broadhurst provides a generalization of the BBP algorithm that may be used to compute a number of other constants in nearly linear time and logarithmic space. Explicit results are given for Catalan's constant, , , Apéry's constant , , (where is the Riemann zeta function), , , , and various products of powers of and . These results are obtained primarily by the use of polylogarithm ladders. See also Approximations of Experimental mathematics Bellard's formula References Further reading D. J. Broadhurst, "Polylogarithmic ladders, hypergeometric series and the ten millionth digits of ζ(3) and ζ(5)", (1998) arXiv math.CA/9803067 External links Richard J. Lipton, "Making An Algorithm An Algorithm — BBP", weblog post, July 14, 2010. Richard J. Lipton, "Cook’s Class Contains Pi", weblog post, March 15, 2009. David H. Bailey, "BBP Code Directory", web page with links to Bailey's code implementing the BBP algorithm, September 8, 2006. Pi algorithms Experimental mathematics