[APPack] Added Max Displacement Metric

[AlexandreSinger]

Added the ability to print the max displacement from the placement reconstruction to the original flat placement.

This metric will help show another dimension to the flat placement reconstruction. Generally, if the average displacement is low, that may not be good if that means that one atom is placed way farther away than where it would like. This can really hurt quality.

I also turned the distance calculation from the Euclidean distance to the Manhattan distance. This should better represent the objective in terms of FPGAs (where the fastest path between two points is not necessarily a straight line).

I reran the results of the flat placement reconstruction on MCNC and VTR-Chain (same testing procedure as the last PR).

MCNC:

iter_num	pack_time(s)	device_util	total_wl	CPD(ns)	percent_cluster_errors	percent_atoms_displaced	average_atom_displacement	max_atom_displacement
0	1.66	0.55	15915.75	5.74	-1.00	-1.00	-1.00	-1.00
1	1.38	0.55	15845.75	5.72	0.06	0.11	1.03	24.90
2	1.36	0.55	15760.75	5.78	0.02	0.05	0.62	23.35
3	1.35	0.55	15741.55	5.75	0.01	0.03	0.50	24.20
4	1.36	0.55	15731.45	5.77	0.00	0.03	0.47	22.10
5	1.37	0.55	15744.25	5.75	0.00	0.03	0.47	22.60
6	1.36	0.55	15738.00	5.70	0.00	0.03	0.46	23.70
7	1.36	0.55	15718.60	5.75	0.00	0.03	0.47	22.40
8	1.37	0.55	15771.60	5.72	0.00	0.03	0.44	22.05
9	1.36	0.55	15771.50	5.72	0.00	0.03	0.46	22.60
10	1.36	0.55	15737.35	5.73	0.00	0.03	0.46	20.75

VTR-Chain:

iter_num	pack_time(s)	device_util	total_wl	CPD(ns)	percent_cluster_errors	percent_atoms_displaced	average_atom_displacement	max_atom_displacement
0	38.35	0.41	181585.10	17.57	-1.00	-1.00	-1.00	-1.00
1	31.37	0.41	180732.90	17.54	0.03	0.09	2.35	74.43
2	31.65	0.41	180024.86	17.50	0.01	0.07	1.67	73.48
3	32.44	0.41	180185.67	17.57	0.00	0.05	1.37	73.81
4	33.79	0.41	179515.57	17.55	0.00	0.05	1.27	73.24
5	32.11	0.41	179527.86	17.42	0.00	0.05	1.17	73.19
6	32.66	0.41	178827.62	17.41	0.00	0.05	1.11	74.24
7	31.22	0.41	178657.33	17.48	0.00	0.05	1.18	73.81
8	32.27	0.41	178222.38	17.46	0.00	0.05	1.14	73.67
9	34.71	0.41	177943.86	17.43	0.00	0.05	1.08	73.81
10	35.68	0.41	177570.81	17.44	0.00	0.05	1.07	73.10

Looking at a single circuit: LU32PEEng from the VTR-Chain benchmark, with a device size of 105x105:

iter_num	pack_time(s)	device_util	total_wl	CPD(ns)	percent_cluster_errors	percent_atoms_displaced	average_atom_displacement	max_atom_displacement
0	250.52	0.79	1286419.00	73.20	-1.00	-1.00	-1.00	-1
1	204.88	0.79	1268451.00	72.93	0.01	0.02	1.27	182
2	210.36	0.79	1274392.00	72.09	0.00	0.01	0.47	188
3	211.24	0.79	1279439.00	72.85	0.00	0.00	0.28	193
4	216.72	0.79	1270402.00	72.35	0.00	0.00	0.32	183
5	209.30	0.79	1268843.00	71.84	0.00	0.00	0.18	190
6	213.68	0.79	1258073.00	71.66	0.00	0.00	0.15	194
7	206.72	0.79	1257779.00	72.79	0.00	0.00	0.22	180
8	211.49	0.79	1255023.00	72.64	0.00	0.00	0.12	189
9	229.91	0.79	1253152.00	72.55	0.00	0.00	0.06	194
10	235.62	0.79	1252555.00	72.55	0.00	0.00	0.05	183

The units for the max atom displacement is the euclidean distance from the flat placement location to the reconstructed clustered placement. For MCNC, the devices range from 11x11 to 22x22. For VTR-Chain, the devices range from 20x20 to 105x105.

These results show a potential problem with the current (basic) reconstruction, where although the cluster errors and average displacement is quite low, we still see a very high maximum displacement! This implies that there is something wrong with how we are placing the clusters. I think the issue may be the fact that if we find that a cluster cannot be placed at the tile it wants, it falls back on the original algorithm; which may be randomly placed on the chip!

Notice, for the LU32PEEng circuit, the largest distance possible on the device is 210. We can see that the current reconstruction is sometimes placing atoms (a few of them) all the way on the other side of the chip!

[AlexandreSinger]

@vaughnbetz This PR is ready for review. I have updated the results above for MCNC to the Manhattan distance; the VTR Chain results with Manhattan distance are currently being collected.

[AlexandreSinger]

I have updated the description of the PR with the Manhattan distance for VTR Chain.

[vaughnbetz]

LGTM!