I know that back in the Stone Age, people used tables on this thing called paper to look up values for functions like $\sin$ and $\ln$. But how did the guys who wrote the tables calculate those values? I know that they could have used Taylor series or the integral definition of $\ln$ with Riemann sums, but did they really do that for each number in the tables? Maybe they used a ruler and a unit circle for the trigonometric ratios?
Also, does anyone know what computers use to do the same?