TITLE: What algorithm is used by computers to calculate logarithms?
QUESTION [78 upvotes]: I would like to know how logarithms are calculated by computers. The GNU C library, for example, uses a call to the fyl2x() assembler instruction, which means that logarithms are calculated directly from the hardware.
So the question is: what algorithm is used by computers to calculate logarithms?

REPLY [23 votes]: All methods I have seen reduce first by dividing by the power of $2$ in the exponent and adding that exponent times $\ln(2)$ to the result.  From there, the two most common methods I have seen are Taylor series for $\ln(1+x)$ and a variant of the CORDIC algorithm.
J. M. also brings up Padé approximants which I have seen used in some calculator implementations.