How to get the average of several chrono::time_points

Question

The formula for getting the average of several numbers is of course well known:

And this formula can easily be used to get the average of chrono::duration s:

template <class Rep0, class Period0>
auto
sum(const std::chrono::duration<Rep0, Period0>& d0)
{
    return d0;
}

template <class Rep0, class Period0, class ...Rep, class ...Period>
auto
sum(const std::chrono::duration<Rep0, Period0>& d0,
    const std::chrono::duration<Rep, Period>& ...d)
{
    return d0 + sum(d...);
}

template <class ...Rep, class ...Period>
auto
avg(const std::chrono::duration<Rep, Period>& ...d)
{
    return sum(d...) / sizeof...(d);
}

But chrono::time_point s can't be added to one another. How can I average time_point s?

Answer 1

It helps to start out with the assumption that you can add time_point s, and then manipulate the formula to eliminate those additions:

First separate out t ₁ from the sum:

Next both add and subtract t ₁ :

Factor and rearrange:

And then, since you are subtracting t ₁ the same number of times as you are summing, you can include that into the sum:

Now you are summing duration s instead of time_point s! As we already have a function to sum duration s, averaging time_point s can easily build on that:

template <class Clock, class Duration0, class ...Duration>
auto
avg(const std::chrono::time_point<Clock, Duration0>& t0,
    const std::chrono::time_point<Clock, Duration>& ...t)
{
    return t0 + sum((t - t0)...) / (1 + sizeof...(t));
}

Averaging a single time_point is a special case since sum of duration s does not handle summing zero duration s (what would be the units?). So an overload for that case is easily added:

template <class Clock, class Duration0>
auto
avg(const std::chrono::time_point<Clock, Duration0>& t0)
{
    return t0;
}

This is written in C++14. It can be coded in C++11, using the trailing return type declaration syntax, which is more verbose, but completely doable.