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I read How to figure out the log of a number without a calculator? but what is actually used to compute the basic tables themselves, Newton's method or Taylor series?

  1. If Taylor series is used then how is it done?
  2. Does a calculator use the Taylor series? Is it fast and the recommended way over Newton's method?
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reori
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  • They use an algorithm called CORDIC that involves bitshifting. Here is a link: http://www.qc.cuny.edu/Academics/Degrees/DMNS/Faculty%20Documents/Sultan1.pdf – ncmathsadist Jul 31 '16 at 19:44
  • i didnt ask about trignometry, i asked for logarithms which is much simpler, so do they use newtons method or taylor serious – reori Jul 31 '16 at 19:49
  • It would be nice if you would show some example rather than just give a link. The taylor series is helpful : $\ln(x+1)=x-\frac{x^2}{2}+O(x^3)$ – Peter Jul 31 '16 at 20:55
  • Which kind of logarithm is to figure out ? $\log_{10}$ ot $\ln$ ? – Peter Jul 31 '16 at 20:58
  • Calculators usually use taylor series for $\sin$ , $\cos$ , $\exp$ , etc. – Peter Jul 31 '16 at 20:59
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    @reori: ncmathsadist is quite right. CORDIC is not limited to trigonometry. –  Jul 31 '16 at 21:51
  • Newton's method isn't used to compute logarithms. Because that would mean solving an equation such as $x-e^y=0$, requiring to evaluate exponentials for several iterates, which would be unacceptably inefficient. For direct evaluation, least-squares or least-deviation polynomials can be preferred over Taylor. –  Jul 31 '16 at 21:55

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