Why is it more efficient to implement log_sum like this?

Question

According to this thread: To Compute log(a+b)

Sometimes log_sum is implemented like this:

log(a + b) = log(a * (1 + b/a)) = log a + log(1 + b/a)

I'm confused about why this approach is more efficient.. Does anyone have ideas about this?

Answer 1

This approach might be useful, when a is constant (at least for some b values), and b<<a (significantly smaller). In this case log(1 + b/a) could be calculated through Taylor series expansion fast and with good precision (log1p function in some math libraries, another method)