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evaluation of $ \operatorname{Arg}\zeta (1/2+is) $ ??

If we consider

$\arg\zeta\left(\frac{1}{2} + i\text{t}\right) = \text{Im }\log\zeta\left(\frac{1}{2}+i\text{t}\right)$

for big values of '$t$' what is the FASTEST method (numerical method) to evaluate the Argument of the Riemann zeta function along the critical line?

$\arg\zeta\left(\frac{1}{2}+i\text{t}\right) $

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