Bug in density calculation std::piecewise_constant_distribution?

It seems that std::piecewise_constant_distribution computes the densities wrongly , at least with GCC and its standard library.

According to http://ift.tt/1B7rpnb: The densities should be computed as:

Checking this manually reveals the bug!

This can be seen here: http://ift.tt/1B7rrLF

The source code related to this is found in /usr/include/c++/4.8/bits/random.tcc (on linux) and the extract of the initialization function _M_initialize called by the constructor shows that there is something incorrect here:

const double __sum = std::accumulate(_M_den.begin(),
                       _M_den.end(), 0.0);

      __detail::__normalize(_M_den.begin(), _M_den.end(), _M_den.begin(),
                __sum);  <----- WRONG

      // THIS is not the cummulative distribution (since the above normalization does not give the probability of the intervalls!)
      _M_cp.reserve(_M_den.size());
      std::partial_sum(_M_den.begin(), _M_den.end(),
               std::back_inserter(_M_cp));


      // Make sure the last cumulative probability is one.
      _M_cp[_M_cp.size() - 1] = 1.0;



      // Dividing here by the interval length is WRONG!!!

      for (size_t __k = 0; __k < _M_den.size(); ++__k)
           _M_den[__k] /= _M_int[__k + 1] - _M_int[__k];