[AP][Solver] Per-Connection Timing Optimization

[AlexandreSinger]

The B2B solver originally used a simple net weighting model to incorperate timing into the objective. This works well, but a more direct approach to timing should provide a better solution.

Added extra edges to the B2B formulation which encode per-connection delays into the objective.

Simply, these edges incentivice the solver to shrink the distance between driver and sinks where shrinking that distance would improve the delay the most (focusing more on currently critical edges).

To encode this objective, I compute the instantaneuous derivative of the delay of an connection with respect to the distance (normalized such that the units are not in seconds) and use that as a weight for a pin to pin connection between each driver and its sinks.

More tuning is likely need to find good factors for each term. For now this was what worked well on the VTR benchmarks.

[AlexandreSinger]

Result on Titan, timing driven with no fixed blocks:

Metric	Value normalized to AP baseline
post_fl_hpwl	1.04
post_dp_hpwl	1.00
total_wirelength	1.00
post_gp_cpd	1.01
post_fl_cpd	1.02
post_dp_cpd	0.98
crit_path_delay	0.98

Wintermute was loaded yesterday, so I do not really trust the runtime results; but locally, I have found that GP runtime increased by around 10-20%.

These results match what I have been seeing on VTR. The post-GP and post-FL results appear to get a bit worse; however overall the result gets better. I believe what is causing this behavior is that the timing analysis and wirelength analysis I am performing during GP is so early that it is more of a guide than truth. Since my timing objective that I added is focused more on the router lookahead than the criticalities that I compute, it appears to do worse in GP but actually does better overall.

Much more tuning is needed. but I think this is good enough to replace the net weighting approach for now. I want to continue to tune and prod this over time.

[AlexandreSinger]

@vaughnbetz This is the code for the timing slides I presented to you on Monday. I was able to focus the objective entirely on the derivative formulation for timing. After my recent updates to the solver, that objective formulation began winning out. Still lots of noise, but I agree with you that its very intuitive.

@amin1377 FYI. Your review would also be appreciated. Also I think you will find this interesting.