Spigot algorithm

Article summary

A spigot algorithm is an algorithm for computing the value of a transcendental number (such as or e) that generates the digits of the number sequentially from left to right providing increasing precision as the algorithm proceeds. Spigot algorithms also aim to minimize the amount of intermediate storage required. The name comes from the sense of the word "spigot" for a tap or valve controlling the flow of a liquid. Spigot algorithms can be contrasted with algorithms that store and process complete numbers to produce successively more accurate approximations to the desired transcendental. Interest in spigot algorithms was spurred in the early days of computational mathematics by extreme constraints on memory, and such an algorithm for calculating the digits of e appeared in a paper by Sale in 1968. In 1970, Abdali presented a more general algorithm to compute the sums of series in which the ratios of successive terms can be expressed as quotients of integer functions of term positions. This algorithm is applicable to many familiar series for trigonometric functions, logarithms, and transcendental numbers because these series satisfy the above condition. The name "spigot algorithm" seems to have been coined by Stanley Rabinowitz and Stan Wagon, whose algorithm for calculating the digits of is sometimes referred to as "the spigot algorithm for ".…

Key claims

No claims recorded.

Discussion questions

1. Summarise the article in your own words. Which single claim would you verify first, and why?
2. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
3. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

Bibliography

No sources recorded.