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Take Down Multi-threaded Newton Method
Syntax
`ok = harmonic_takedown(xout)
`
Purpose
This routine does the takedown for splitting the Newton method into sub-intervals.
Thread
It is assumed that this function is called by thread zero, and all the other threads have completed their work and are blocked (waiting).
xout
See multi_newton_run .
Source

    namespace {
    bool multi_newton_takedown(vector<double>& xout)
    {     // number of threads in the calculation
         size_t num_threads  = std::max(num_threads_, size_t(1));

         // remove duplicates and points that are not solutions
         xout.resize(0);
         bool   ok = true;
         ok       &= thread_alloc::thread_num() == 0;

         // initialize as more that sub_length_ / 2 from any possible solution
         double xlast = - sub_length_;
         for(size_t thread_num = 0; thread_num < num_threads; thread_num++)
         {     vector<double>& x = work_all_[thread_num]->x;

              size_t i;
              for(i = 0; i < x.size(); i++)
              {     // check for case where this point is lower limit for this
                   // thread and upper limit for previous thread
                   if( fabs(x[i] - xlast) >= sub_length_ )
                   {     xout.push_back( x[i] );
                        xlast = x[i];
                   }
                   else
                   {     double fcur, flast, df;
                        fun_(x[i],   fcur, df);
                        fun_(xlast, flast, df);
                        if( fabs(fcur) < fabs(flast) )
                        {     xout[ xout.size() - 1] = x[i];
                             xlast                  = x[i];
                        }
                   }
              }
              // check that this thread was ok with the work it did
              ok &= work_all_[thread_num]->ok;
         }

         // go down so free memory for other threads before memory for master
         size_t thread_num = num_threads;
         while(thread_num--)
         {
    # if USE_THREAD_ALLOC_FOR_WORK_ALL
              // call the destructor for vector destructor
              work_all_[thread_num]->x.~vector<double>();
              // delete the raw memory allocation
              void* v_ptr = static_cast<void*>( work_all_[thread_num] );
              thread_alloc::return_memory( v_ptr );
    # else
              delete work_all_[thread_num];
    # endif
              // Note that xout corresponds to memroy that is inuse by master
              // (so we can only chech have freed all their memory).
              if( thread_num > 0 )
              {     // check that there is no longer any memory inuse by this thread
                   ok &= thread_alloc::inuse(thread_num) == 0;
                   // return all memory being held for future use by this thread
                   thread_alloc::free_available(thread_num);
              }
         }
         // now we are done with the work_all_ vector so free its memory
         // (because it is a static variable)
         work_all_.clear();

         return ok;
    }
    }

Input File: example/multi_thread/multi_newton.cpp