improved intersection performance

[kubikowski]

improved intersection performance:

Added a preface to intersection, which compares elements in the first 2 sets to create the initial resultSet.

This improves the intersection function significantly at scale, when comparing sets with few shared elements. Because, there is no time wasted adding elements to the resultSet which are immediately removed, on the first comparison.

The scale tests show that when taking the intersection of disjoint sets, we see a performance improvement of ~50 - 80%. And, somewhat surprisingly, even when taking the intersection of equivalent sets we see a performance improvement of ~10 - 30%.

[original] raw data:

	inter(of1)	inter(of1, of1)	inter(of1, of2)	inter(of2, of1)	inter(of1, of1, of1)	inter(of1, of2, of3)	inter(of3, of2, of1)
test 1:	4,377.426ms	6,735.451ms	8,102.382ms	2,913.327ms	7,875.956ms	9,478.669ms	2,816.633ms
test 2:	4,281.930ms	6,344.667ms	7,768.613ms	2,867.852ms	7,897.943ms	10,456.894ms	2,791.657ms
test 3:	4,439.299ms	6,545.934ms	7,942.739ms	2,960.505ms	8,127.316ms	9,678.294ms	2,755.021ms
test 4:	4,585.612ms	6,886.564ms	8,257.826ms	3,006.955ms	8,258.781ms	10,307.772ms	2,880.205ms
test 5:	4,440.268ms	6,535.332ms	8,888.246ms	3,106.456ms	8,594.005ms	9,494.206ms	2,872.221ms
average:	4,424.907ms	6,609.590ms	8,191.961ms	2,971.019ms	8,150.800ms	9,883.167ms	2,823.147ms

	inter(100 Eq)	inter(10k Eq)	inter(100 Dj)	inter(10k Dj)
test 1:	410.190ms	247.237ms	22.539ms	0.340ms
test 2:	403.356ms	247.404ms	30.472ms	0.407ms
test 3:	430.968ms	252.189ms	21.216ms	0.294ms
test 4:	418.326ms	278.742ms	37.885ms	0.447ms
test 5:	418.847ms	239.853ms	21.692ms	0.370ms
average:	416.337ms	253.085ms	26.761ms	0.372ms

	100k ⋅ inter(2 Eq)	100k ⋅ inter(5 Eq)	100k ⋅ inter(2 Dj)	100k ⋅ inter(5 Dj)
test 1:	527.243ms	402.482ms	568.494ms	419.922ms
test 2:	751.326ms	414.826ms	618.579ms	354.918ms
test 3:	569.956ms	480.491ms	583.028ms	357.983ms
test 4:	632.521ms	430.562ms	588.263ms	351.663ms
test 5:	498.057ms	400.427ms	607.304ms	382.176ms
average:	595.821ms	425.758ms	593.134ms	373.332ms

[refactor] raw data:

	inter(of1)	inter(of1, of1)	inter(of1, of2)	inter(of2, of1)	inter(of1, of1, of1)	inter(of1, of2, of3)	inter(of3, of2, of1)
test 1:	4,322.983ms	5,693.015ms	3,602.305ms	2,501.756ms	7,228.035ms	5,554.182ms	1,537.629ms
test 2:	4,449.666ms	5,507.669ms	3,856.591ms	2,646.234ms	7,721.171ms	5,962.953ms	1,574.496ms
test 3:	4,405.531ms	5,541.553ms	3,593.993ms	2,537.991ms	7,086.961ms	5,502.272ms	1,567.400ms
test 4:	4,341.720ms	5,423.862ms	3,671.896ms	2,690.478ms	7,159.097ms	5,619.187ms	1,498.521ms
test 5:	4,420.132ms	5,601.589ms	3,666.507ms	2,515.135ms	8,065.955ms	5,737.136ms	1,552.612ms
average:	4,388.006ms	5,553.538ms	3,678.258ms	2,578.319ms	7,452.244ms	5,675.146ms	1,546.132ms

	inter(100 Eq)	inter(10k Eq)	inter(100 Dj)	inter(10k Dj)
test 1:	417.502ms	243.087ms	6.382ms	0.197ms
test 2:	404.111ms	244.578ms	5.169ms	0.200ms
test 3:	423.238ms	254.373ms	6.403ms	0.276ms
test 4:	411.891ms	244.098ms	5.380ms	0.284ms
test 5:	420.107ms	262.649ms	6.121ms	0.266ms
average:	415.370ms	249.757ms	5.891ms	0.245ms

	100k ⋅ inter(2 Eq)	100k ⋅ inter(5 Eq)	100k ⋅ inter(2 Dj)	100k ⋅ inter(5 Dj)
test 1:	402.210ms	356.343ms	179.164ms	154.761ms
test 2:	402.460ms	361.023ms	183.592ms	154.682ms
test 3:	418.264ms	380.176ms	185.116ms	167.811ms
test 4:	398.838ms	361.441ms	174.396ms	158.667ms
test 5:	396.364ms	351.970ms	223.328ms	263.549ms
average:	403.627ms	362.191ms	189.119ms	179.894ms

[performance improvement] raw data:

	inter(of1)	inter(of1, of1)	inter(of1, of2)	inter(of2, of1)	inter(of1, of1, of1)	inter(of1, of2, of3)	inter(of3, of2, of1)
original:	4,424.907ms	6,609.590ms	8,191.961ms	2,971.019ms	8,150.800ms	9,883.167ms	2,823.147ms
rewrite:	4,388.006ms	5,553.538ms	3,678.258ms	2,578.319ms	7,452.244ms	5,675.146ms	1,546.132ms
improvement:	+0.834%	+15.978%	+55.099%	+13.218%	+8.571%	+42.578%	+45.234%

	inter(100 Eq)	inter(10k Eq)	inter(100 Dj)	inter(10k Dj)
original:	416.337ms	253.085ms	26.761ms	0.372ms
rewrite:	415.370ms	249.757ms	5.891ms	0.245ms
improvement:	+0.232%	+1.315%	+77.987%	+34.140%

	100k ⋅ inter(2 Eq)	100k ⋅ inter(5 Eq)	100k ⋅ inter(2 Dj)	100k ⋅ inter(5 Dj)
original:	595.821ms	425.758ms	593.134ms	373.332ms
rewrite:	403.627ms	362.191ms	189.119ms	179.894ms
improvement:	+32.257%	+14.930%	+68.115%	+51.814%