The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic convergence. Let a_(n + 1) | = | 1/2(a_n + b_n) b_(n + 1) | = | sqrt(a_n b_n) c_(n + 1) | = | 1/2(a_n - b_n) d_n | = | a_n^2 - b_n^2, and define the initial conditions to be a_0 = 1, b_0 = 1/sqrt(2).
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