Re: qsort, once again

>> So at least on randomized data, the swap_cnt thing is a serious loser.
>> Need to run some tests on special-case inputs though.  Anyone have a
>> test suite they like?

> Here is a distribution maker that will create some torture tests for
> sorting programs.

I fleshed out the sort tester that Bentley & McIlroy give pseudocode for
in their paper (attached below in case anyone wants to hack on it).  Not
very surprisingly, it shows the unmodified B&M algorithm as
significantly better than the BSD-lite version:

Our current BSD qsort:
distribution SAWTOOTH: max cratio 12.9259, average 0.870261 over 252 tests
distribution RAND: max cratio 1.07917, average 0.505924 over 252 tests
distribution STAGGER: max cratio 12.9259, average 1.03706 over 252 tests
distribution PLATEAU: max cratio 12.9259, average 0.632514 over 252 tests
distribution SHUFFLE: max cratio 12.9259, average 1.21631 over 252 tests
method COPY: max cratio 3.87533, average 0.666927 over 210 tests
method REVERSE: max cratio 5.6248, average 0.710284 over 210 tests
method FREVERSE: max cratio 12.9259, average 1.58323 over 210 tests
method BREVERSE: max cratio 5.72661, average 1.13674 over 210 tests
method SORT: max cratio 0.758625, average 0.350092 over 210 tests
method DITHER: max cratio 3.13417, average 0.667222 over 210 tests
Overall: average cratio 0.852415 over 1260 tests

without the swap_cnt code:
distribution SAWTOOTH: max cratio 5.6248, average 0.745818 over 252 tests
distribution RAND: max cratio 1.07917, average 0.510097 over 252 tests
distribution STAGGER: max cratio 5.6248, average 1.0494 over 252 tests
distribution PLATEAU: max cratio 3.57655, average 0.411549 over 252 tests
distribution SHUFFLE: max cratio 5.72661, average 1.05988 over 252 tests
method COPY: max cratio 3.87533, average 0.712122 over 210 tests
method REVERSE: max cratio 5.6248, average 0.751011 over 210 tests
method FREVERSE: max cratio 4.80869, average 0.690224 over 210 tests
method BREVERSE: max cratio 5.72661, average 1.13673 over 210 tests
method SORT: max cratio 0.806618, average 0.539829 over 210 tests
method DITHER: max cratio 3.13417, average 0.702174 over 210 tests
Overall: average cratio 0.755348 over 1260 tests

("cratio" is the ratio of the actual number of comparison function calls
to the theoretical expectation of N*lg2(N).)  The insertion sort
switchover is a loser for both average and worst-case measurements.

I tried Dann's distributions too, with N = 100000:

Our current BSD qsort:
dist fib: cratio 0.0694229
dist camel: cratio 0.0903228
dist constant: cratio 0.0602126
dist five: cratio 0.132288
dist ramp: cratio 4.29937
dist random: cratio 1.09286
dist reverse: cratio 0.5663
dist sorted: cratio 0.18062
dist ten: cratio 0.174781
dist twenty: cratio 0.238098
dist two: cratio 0.090365
dist perverse: cratio 0.334503
dist trig: cratio 0.679846
Overall: max cratio 4.29937, average cratio 0.616076 over 13 tests

without the swap_cnt code:
dist fib: cratio 0.0694229
dist camel: cratio 0.0903228
dist constant: cratio 0.0602126
dist five: cratio 0.132288
dist ramp: cratio 4.29937
dist random: cratio 1.09286
dist reverse: cratio 0.89184
dist sorted: cratio 0.884907
dist ten: cratio 0.174781
dist twenty: cratio 0.238098
dist two: cratio 0.090365
dist perverse: cratio 0.334503
dist trig: cratio 0.679846
Overall: max cratio 4.29937, average cratio 0.695293 over 13 tests

In this set of tests the behavior is just about identical, except for
the case of already-sorted input, where the BSD coding runs in O(N)
instead of O(N lg2 N) time.  So that evidently is why some unknown
person put in the special case.

Some further experimentation destroys my original proposal to limit the
size of subfile we'll use the swap_cnt code for: it turns out that that
eliminates the BSD code's advantage for presorted input (at least for
inputs bigger than the limit) without doing anything much in return.

So my feeling is we should just remove the swap_cnt code and return to
the original B&M algorithm.  Being much faster than expected for
presorted input doesn't justify being far slower than expected for
other inputs, IMHO.  In the context of Postgres I doubt that perfectly
sorted input shows up very often anyway.

Comments?

            regards, tom lane