improved xor performance

[kubikowski]

improved xor performance:

Added a preface to xor, which compares elements in the first 2 sets to create the initial resultSet, and the initial duplicates. Additionally, split implementations of each loop into 2 branches, one which adds elements to duplicates and one which does not.

This implementation saves significant time at scale by not adding elements to the duplicates set on the final set comparison. Indeed, for the xor of only 2 sets: no elements whatsoever are added to duplicates. And 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 xor of 2 sets, we see a performance improvement of anywhere from ~30 to ~70%. And for 3 or more sets, we still see improvements of ~10 to ~30%.

[original] raw data:

	xor(of1)	xor(of1, of1)	xor(of1, of2)	xor(of2, of1)	xor(of1, of1, of1)	xor(of1, of2, of3)	xor(of3, of2, of1)
test 1:	4,289.291ms	12,265.707ms	6,822.403ms	8,812.099ms	13,489.179ms	9,289.335ms	10,066.066ms
test 2:	5,002.647ms	13,373.451ms	7,521.562ms	8,966.832ms	14,557.072ms	9,911.047ms	10,953.452ms
test 3:	4,708.450ms	12,850.578ms	7,378.796ms	8,919.654ms	13,818.081ms	9,836.513ms	11,157.035ms
test 4:	4,123.982ms	12,572.005ms	7,701.330ms	8,939.424ms	13,487.043ms	8,767.213ms	10,390.920ms
test 5:	4,922.881ms	16,788.944ms	7,327.372ms	9,940.865ms	14,577.289ms	9,589.192ms	11,942.640ms
average:	4,609.450ms	13,570.137ms	7,350.293ms	9,115.775ms	13,985.733ms	9,478.660ms	10,902.023ms

	xor(100 Eq)	xor(10k Eq)	xor(100 Dj)	xor(10k Dj)
test 1:	523.303ms	369.874ms	3,031.034ms	3,223.919ms
test 2:	589.087ms	399.620ms	3,334.634ms	3,409.872ms
test 3:	687.281ms	432.568ms	3,224.346ms	3,262.135ms
test 4:	557.071ms	417.389ms	2,984.109ms	3,076.535ms
test 5:	632.142ms	503.307ms	3,337.861ms	3,411.966ms
average:	597.777ms	424.552ms	3,182.397ms	3,276.885ms

	100k ⋅ xor(2 Eq)	100k ⋅ xor(5 Eq)	100k ⋅ xor(2 Dj)	100k ⋅ xor(5 Dj)
test 1:	836.240ms	557.291ms	1,054.668ms	919.818ms
test 2:	784.405ms	662.988ms	1,136.804ms	958.899ms
test 3:	788.272ms	568.934ms	992.142ms	961.228ms
test 4:	753.647ms	534.395ms	1,010.893ms	851.651ms
test 5:	791.815ms	620.453ms	1,332.216ms	1,213.450ms
average:	790.876ms	588.812ms	1,105.345ms	981.009ms

[refactor] raw data:

	xor(of1)	xor(of1, of1)	xor(of1, of2)	xor(of2, of1)	xor(of1, of1, of1)	xor(of1, of2, of3)	xor(of3, of2, of1)
test 1:	4,042.787ms	3,772.797ms	4,686.519ms	4,612.897ms	11,134.199ms	8,434.715ms	8,568.729ms
test 2:	4,093.107ms	3,722.795ms	4,815.067ms	4,335.210ms	11,219.319ms	8,754.869ms	8,344.972ms
test 3:	4,286.660ms	3,693.109ms	4,814.299ms	4,244.118ms	11,156.637ms	8,437.587ms	8,529.338ms
test 4:	4,176.574ms	3,672.280ms	5,093.960ms	4,268.555ms	11,353.890ms	8,516.703ms	8,480.596ms
test 5:	4,249.337ms	3,680.425ms	4,860.920ms	4,282.032ms	11,388.819ms	8,571.650ms	8,595.393ms
average:	4,169.693ms	3,708.281ms	4,854.153ms	4,348.562ms	11,250.573ms	8,543.105ms	8,503.806ms

	xor(100 Eq)	xor(10k Eq)	xor(100 Dj)	xor(10k Dj)
test 1:	533.265ms	311.343ms	3,078.072ms	3,032.642ms
test 2:	490.466ms	315.553ms	3,094.432ms	3,161.461ms
test 3:	487.250ms	302.945ms	3,034.009ms	3,148.477ms
test 4:	490.392ms	313.950ms	3,077.279ms	3,214.733ms
test 5:	493.380ms	304.258ms	3,150.739ms	3,106.725ms
average:	498.951ms	309.610ms	3,086.906ms	3,132.808ms

	100k ⋅ xor(2 Eq)	100k ⋅ xor(5 Eq)	100k ⋅ xor(2 Dj)	100k ⋅ xor(5 Dj)
test 1:	533.170ms	442.016ms	693.439ms	845.515ms
test 2:	261.622ms	494.277ms	743.395ms	972.946ms
test 3:	562.718ms	431.362ms	696.113ms	860.681ms
test 4:	297.686ms	437.088ms	784.171ms	973.658ms
test 5:	554.094ms	439.272ms	742.306ms	857.492ms
average:	441.858ms	448.803ms	731.885ms	902.058ms

[performance improvement] raw data:

	xor(of1)	xor(of1, of1)	xor(of1, of2)	xor(of2, of1)	xor(of1, of1, of1)	xor(of1, of2, of3)	xor(of3, of2, of1)
original:	4,609.450ms	13,570.137ms	7,350.293ms	9,115.775ms	13,985.733ms	9,478.660ms	10,902.023ms
rewrite:	4,169.693ms	3,708.281ms	4,854.153ms	4,348.562ms	11,250.573ms	8,543.105ms	8,503.806ms
improvement:	+9.540%	+72.673%	+33.960%	+52.296%	+19.557%	+9.870%	+21.998%

	xor(100 Eq)	xor(10k Eq)	xor(100 Dj)	xor(10k Dj)
original:	597.777ms	424.552ms	3,182.397ms	3,276.885ms
rewrite:	498.951ms	309.610ms	3,086.906ms	3,132.808ms
improvement:	+16.532%	+4.932%	+27.074%	+4.397%

	100k ⋅ xor(2 Eq)	100k ⋅ xor(5 Eq)	100k ⋅ xor(2 Dj)	100k ⋅ xor(5 Dj)
original:	790.876ms	588.812ms	1,105.345ms	981.009ms
rewrite:	441.858ms	448.803ms	731.885ms	902.058ms
improvement:	+44.131%	+23.778%	+33.787%	+8.048%