Efficient way to compute geometric mean of many numbers

Question

I need to compute the geometric mean of a large set of numbers, whose values are not a priori limited. The naive way would be

double geometric_mean(std::vect         


        

Answer 1

I think I figured out a way to do it, it combined the two routines in the question, similar to Peter's idea. Here is an example code.

double geometric_mean(std::vector const&data)
{
    const double too_large = 1.e64;
    const double too_small = 1.e-64;
    double sum_log = 0.0;
    double product = 1.0;
    for(auto x:data) {
        product *= x;
        if(product > too_large || product < too_small) {
            sum_log+= std::log(product);
            product = 1;      
        }
    }
    return std::exp((sum_log + std::log(product))/data.size());
}

The bad news is: this comes with a branch. The good news: the branch predictor is likely to get this almost always right (the branch should only rarely be triggered).

The branch could be avoided using Peter's idea of a constant number of terms in the product. The problem with that is that overflow/underflow may still occur within only a few terms, depending on the values.