Question

Given log(a) and log(b), return log(a+b)

double log_sum(double log_a, double log_b){
    double v;
    if(log_a < log_b){
        v=log_b+log(1+exp(log_a-log_b));
    }
    else{
        v=log_a+log(1+exp(log_b-log_a));
    }
    return v;
}

I want to know what are the benefits of the above function?

Answer 1

The primary (brute force) alternative looks like:

v = log(exp(log_a) + exp(log_b));

That has three transcendental function evaluations.

The computation shown uses just two transcendental functions – and should be quicker.

It may also be more stable numerically.