Brent-Salamin algorithm

The Brent-Salamin algorithm is an algorithm for computing $\pi$. It was discovered independently by Richard Brent and Eugene Salamin about 1975, and is also known as the Gauss-Legendre algorithm since it depends on some results of Gauss and Legendre (but they did not invent the algorithm, probably because it is not much use for hand computation).

See also

Gauss-Legendre algorithm, Salamin-Brent algorithm, http://wwwmaths.anu.edu.au/~brent/pub/pub028.html