Gauss-legendre Algorithm

$a\; =\; 1\backslash qquad\; b\; =\; \backslash frac\{1\}\{\backslash sqrt\{2\}\}\backslash qquad\; t\; =\; \backslash frac\{1\}\{4\}\backslash qquad\; p\; =\; 1$

$x\; =\; \backslash frac\{a\; +\; b\}\{2\}$

$y\; =\; \backslash sqrt\{ab\}$

$t\; =\; t\; -\; p(a-x)^2$

$a\; =\; x$

$b\; =\; y$

$p\; =\; 2p$

$\backslash pi\; \backslash approx\; \backslash frac\{(a+b)^2\}\{4t\}$

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