tail_quantile off by 1 error?

[howsiwei]

Consider the following program:

#include <boost/accumulators/accumulators.hpp>
#include <boost/accumulators/statistics.hpp>
#include <cstdio>

using namespace boost::accumulators;

int main() {
    accumulator_set<int, stats<tag::tail_quantile<left>>> acc(tag::tail<left>::cache_size = 3);
    acc(3);
    acc(4);
    acc(5);

    printf("%d\n", quantile(acc, quantile_probability = 0));
    printf("%d\n", quantile(acc, quantile_probability = 0.9));
}

On my machine it outputs

0
terminate called after throwing an instance of 'boost::exception_detail::clone_impl<boost::exception_detail::error_info_injector<std::runtime_error> >'
  what():  index n = 3 is not in valid range [0, 3)
Aborted (core dumped)

Notice that the result for quantile_probability = 0 is wrong too. Digging into https://www.boost.org/doc/libs/1_70_0/boost/accumulators/statistics/tail_quantile.hpp, I found that index -1 is accessed when quantile_probability = 0.

The simplest fix seems to be: Change

if ( n < static_cast<std::size_t>(tail(args).size()))

to

if (1 <= n && n <= static_cast<std::size_t>(tail(args).size()))

with the caveat that exception would be thrown when quantile_probability = 0.