[Boost-users] [accumulators] Kahan algorithmic variants of sum_impl, mean_impl?

Subject: [Boost-users] [accumulators] Kahan algorithmic variants of sum_impl, mean_impl?
From: Rhys Ulerich (rhys.ulerich_at_[hidden])
Date: 2011-09-30 10:28:44

>From a look at boost::accumulators::impl::sum_impl [1] it appears a
straightforward, fast 'sum += value' is used to accumulate the running
sum.  That can fall prey to numerical errors if the sum is large and
the value is small.  A slower but more precise summation is possible
using the Kahan summation algorithm [2].

Has anyone implemented a Kahan-based variant for either sum_impl or
mean_impl [3]?

Assuming not, other than to mimic existing code, any implementation
suggestions?  One gotcha for Kahan summation is that optimization
levels employing additive associativity can spoil the computation.
Are there other places in the Boost sources where this has become an
issue and where I might look for a portable way around it?

Thanks,
Rhys

[1] http://svn.boost.org/svn/boost/trunk/boost/accumulators/statistics/sum.hpp
[2] http://en.wikipedia.org/wiki/Kahan_summation_algorithm
[3] http://svn.boost.org/svn/boost/trunk/boost/accumulators/statistics/mean.hpp