I beat my head against parallel_scan for a week and never really understood why I was having the problems I did. Now the developers at Intel have provided a better explanation of how parallel_scan works. It turns out that the pre_scan method may never be run at all, so the final_scan method always has to re-do what was done in pre_scan just to be safe. That explains why I had to make my pre_scan and final_scan methods identical in my example program. It would have been nice if one of the developers had mentioned that within a few days of when I submitted my problem to the Intel TBB forum. Or perhaps they should have called the method pre_scan_sometimes_if_we_feel_like_it just to warn TBB-users of the actual behavior.
Anyway, problem solved.
