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The '''Gauss–Legendre algorithm''' is an [[algorithm]] to compute the digits of [[Pi|π]]. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π. However, the drawback is that it is memory intensive and it is therefore sometimes not used over [[Machin-like formulas]].
The method is based on the individual work of [[Carl Friedrich Gauss]] (1777–1855) and [[Adrien-Marie Legendre]] (1752–1833) combined with modern algorithms for multiplication and [[square root]]s. It repeatedly replaces two numbers by their [[arithmetic mean|arithmetic]] and [[geometric mean]], in order to approximate their [[arithmetic-geometric mean]].
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