improved pairwiseDisjoint performance

[kubikowski]

improved pairwiseDisjoint performance:

Added a preface to pairwiseDisjoint, which evaluates the first 2 sets against each other, before creating an allElements set. Thereby, we can evaluate for equivalent values immediately, without wasting time copying. And only after those first 2 sets are shown to be disjoint do we create a disjoint union, and continue evaluating.

This improves the pairwiseDisjoint function tremendously at scale, when rendering false results. The scale tests show that when evaluating low numbers of input sets, and expecting a false result, pairwiseDisjoint's performance improved by at least 60% for all cases. And all of the worst case scenario tests put it well past a 99% time reduction.

Meanwhile, for the expected true cases, where the input sets are all indeed pairwise disjoint, the timing remains consistent to within 2% of the original code.

[original] raw data:

	pwdj(of1)	pwdj(of1, of1)	pwdj(of1, of2)	pwdj(of2, of1)	pwdj(of1, of1, of1)	pwdj(of1, of2, of3)	pwdj(of3, of2, of1)
test 1:	0.121ms	4616.321ms	5212.080ms	2191.888ms	4752.401ms	4857.238ms	1499.582ms
test 2:	0.121ms	4616.217ms	4754.881ms	2043.206ms	4283.293ms	4695.374ms	1418.194ms
test 3:	0.076ms	4870.573ms	4523.984ms	2188.633ms	4534.958ms	4699.525ms	1462.781ms
test 4:	0.068ms	4779.581ms	4251.215ms	2215.621ms	4407.859ms	4284.716ms	1456.211ms
test 5:	0.073ms	4647.334ms	4738.660ms	2171.088ms	4615.125ms	4688.970ms	1413.700ms
average:	0.092ms	4706.005ms	4696.164ms	2162.087ms	4518.727ms	4645.165ms	1450.094ms

	pwdj(100 Eq)	pwdj(10k Eq)	pwdj(100 Dj)	pwdj(10k Dj)
test 1:	11.581ms	0.139ms	3192.462ms	3441.889ms
test 2:	11.584ms	0.139ms	3309.798ms	3682.435ms
test 3:	11.493ms	0.155ms	3333.312ms	3430.862ms
test 4:	11.748ms	0.133ms	3073.472ms	3421.060ms
test 5:	11.749ms	0.157ms	3238.370ms	3416.453ms
average:	11.631ms	0.145ms	3229.483ms	3478.540ms

	100k ⋅ pwdj(2 Eq)	100k ⋅ pwdj(5 Eq)	100k ⋅ pwdj(2 Dj)	100k ⋅ pwdj(5 Dj)
test 1:	402.260ms	297.228ms	633.365ms	656.887ms
test 2:	530.508ms	312.616ms	647.248ms	724.051ms
test 3:	384.281ms	248.461ms	606.952ms	632.758ms
test 4:	380.817ms	247.602ms	602.667ms	624.096ms
test 5:	393.395ms	252.512ms	618.183ms	764.189ms
average:	418.252ms	271.684ms	621.683ms	680.396ms

[refactor] raw data:

	pwdj(of1)	pwdj(of1, of1)	pwdj(of1, of2)	pwdj(of2, of1)	pwdj(of1, of1, of1)	pwdj(of1, of2, of3)	pwdj(of3, of2, of1)
test 1:	0.111ms	0.045ms	0.073ms	0.037ms	0.038ms	0.036ms	0.038ms
test 2:	0.095ms	0.028ms	0.041ms	0.040ms	0.040ms	0.027ms	0.024ms
test 3:	0.095ms	0.042ms	0.023ms	0.022ms	0.024ms	0.022ms	0.044ms
test 4:	0.093ms	0.028ms	0.032ms	0.023ms	0.025ms	0.022ms	0.025ms
test 5:	0.094ms	0.046ms	0.025ms	0.021ms	0.024ms	0.022ms	0.024ms
average:	0.098ms	0.038ms	0.039ms	0.029ms	0.030ms	0.026ms	0.031ms

	pwdj(100 Eq)	pwdj(10k Eq)	pwdj(100 Dj)	pwdj(10k Dj)
test 1:	0.039ms	0.098ms	3339.116ms	3518.037ms
test 2:	0.026ms	0.071ms	3204.100ms	3455.223ms
test 3:	0.037ms	0.095ms	3331.485ms	3578.823ms
test 4:	0.022ms	0.065ms	3274.879ms	3607.102ms
test 5:	0.023ms	0.083ms	3401.351ms	3444.900ms
average:	0.029ms	0.082ms	3310.186ms	3520.817ms

	100k ⋅ pwdj(2 Eq)	100k ⋅ pwdj(5 Eq)	100k ⋅ pwdj(2 Dj)	100k ⋅ pwdj(5 Dj)
test 1:	79.831ms	107.261ms	156.064ms	639.600ms
test 2:	75.213ms	110.701ms	161.179ms	647.508ms
test 3:	82.847ms	113.090ms	144.679ms	630.964ms
test 4:	76.478ms	103.787ms	247.077ms	650.319ms
test 5:	73.818ms	103.084ms	172.667ms	647.936ms
average:	77.637ms	107.585ms	176.333ms	643.265ms

[performance improvement] raw data:

	pwdj(of1)	pwdj(of1, of1)	pwdj(of1, of2)	pwdj(of2, of1)	pwdj(of1, of1, of1)	pwdj(of1, of2, of3)	pwdj(of3, of2, of1)
original:	0.092ms	4706.005ms	4696.164ms	2162.087ms	4518.727ms	4645.165ms	1450.094ms
rewrite:	0.098ms	0.038ms	0.039ms	0.029ms	0.030ms	0.026ms	0.031ms
improvement:	-6.521%	+99.999%	+99.999%	+99.999%	+99.999%	+99.999%	+99.998%

	pwdj(100 Eq)	pwdj(10k Eq)	pwdj(100 Dj)	pwdj(10k Dj)
original:	11.631ms	0.145ms	3229.483ms	3478.540ms
rewrite:	0.029ms	0.082ms	3310.186ms	3520.817ms
improvement:	+99.751%	+43.448%	-2.499%	-1.215%

	100k ⋅ pwdj(2 Eq)	100k ⋅ pwdj(5 Eq)	100k ⋅ pwdj(2 Dj)	100k ⋅ pwdj(5 Dj)
original:	418.252ms	271.684ms	621.683ms	680.396ms
rewrite:	77.637ms	107.585ms	176.333ms	643.265ms
improvement:	+81.438%	+60.401%	+71.636%	+5.457%