Given two values $\log(a)$ and $\log(b)$ of complex values $a$ and $b$. Is there a numerically fast way to compute $\log(a + b)$ (on a CPU)?
I'm aware that, $\log(a + b) = \log(a) + \log(1 + \exp(\log(b) - \log(a)))$. If the magnitude $|a| \gg |b|$, then $\log(a + b)$ converges towards $\log(a)$.
Is it possible to avoid computing the exponential and logarithm?