add_guga_lists Subroutine

    subroutine add_guga_lists(nDets1, nDets2, list1, list2)
        integer, intent(inout) :: nDets1
        integer, intent(in) :: nDets2
        integer(n_int), intent(inout) :: list1(0:, 1:), list2(0:, 1:)

        integer :: i, min_ind, pos, abs_pos, j
        HElement_t(dp) :: tmp_mat

        ! first sort lists to use binary search
        call sort(list1(:, 1:nDets1), ilut_lt, ilut_gt)
        call sort(list2(:, 1:nDets2), ilut_lt, ilut_gt)

        abs_pos = 0
        min_ind = 1

        do i = 1, nDets2

            pos = binary_search_ilut(list1(0:nifd, min_ind:ndets1), list2(0:nifd, i))
            if (pos > 0) then
                ! try new implementation of that without the need of an extra
                ! output list

                ! need the absolute position after binary searches in only
                ! sublists
                abs_pos = abs_pos + pos

                ! when element found just update the matrix element and update
                ! the indices
                tmp_mat = extract_h_element(list1(:, abs_pos)) + &
                          extract_h_element(list2(:, i))

                call encode_matrix_element(list1(:, abs_pos), tmp_mat, 1)

                ! min_ind to search next element is then
                min_ind = min_ind + pos

            else
                ! if the entry is not in list1 i have to move down all
                ! subsequent elements after the found position and insert the
                ! new entry at the indicated absolute position
                abs_pos = abs_pos - pos

                ! is this too big to copy in one go??
                do j = nDets1, abs_pos, -1
                    list1(:, j + 1) = list1(:, j)
                end do
                ! and add the new entry
                list1(:, abs_pos) = list2(:, i)

                ! the minimum index to search from now on should not include
                ! the inserted element, since there should be no repetitions
                ! in both lists
                min_ind = min_ind - pos

                ! and i have to update the number of determinants in list1
                nDets1 = nDets1 + 1

            end if
        end do

    end subroutine add_guga_lists