ARROW-10796: [C++] Implement optimized RecordBatch sorting

[pitrou]

Add two RecordBatch sorting implementations:

• A single-pass left-to-right radix sort that's fast up to ~8 sort keys
• A single-pass multiple-key-comparing sort that gives decent performance for large numbers of sort keys

Both implementations benefit from direct indexed access into the contiguous RecordBatch columns (as opposed to table sorting, which must index into the chunks).

Add some RecordBatch-sorting benchmarks.

Also, add and improve tests; and fix a bug related to sorting of NaNs and nulls.

Benchmarks (changes less than 10% in absolute value not shown):

                                           benchmark            baseline           contender  change %                                                                                                                                                            counters
10   RecordBatchSortIndicesInt64Narrow/1048576/100/8    1.482m items/sec    5.410m items/sec   265.083    {'run_name': 'RecordBatchSortIndicesInt64Narrow/1048576/100/8', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 1}
20     RecordBatchSortIndicesInt64Narrow/1048576/0/8    1.524m items/sec    5.478m items/sec   259.478      {'run_name': 'RecordBatchSortIndicesInt64Narrow/1048576/0/8', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 1}
60   RecordBatchSortIndicesInt64Narrow/1048576/100/2    2.276m items/sec    7.803m items/sec   242.839    {'run_name': 'RecordBatchSortIndicesInt64Narrow/1048576/100/2', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 2}
21     RecordBatchSortIndicesInt64Narrow/1048576/0/2    2.340m items/sec    7.802m items/sec   233.369      {'run_name': 'RecordBatchSortIndicesInt64Narrow/1048576/0/2', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 2}
23     RecordBatchSortIndicesInt64Wide/1048576/100/2    4.673m items/sec    9.867m items/sec   111.164      {'run_name': 'RecordBatchSortIndicesInt64Wide/1048576/100/2', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 3}
61       RecordBatchSortIndicesInt64Wide/1048576/0/2    4.677m items/sec    9.820m items/sec   109.971        {'run_name': 'RecordBatchSortIndicesInt64Wide/1048576/0/2', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 3}
35     RecordBatchSortIndicesInt64Wide/1048576/100/8    4.680m items/sec    9.822m items/sec   109.850      {'run_name': 'RecordBatchSortIndicesInt64Wide/1048576/100/8', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 3}
55       RecordBatchSortIndicesInt64Wide/1048576/0/8    4.755m items/sec    9.933m items/sec   108.895        {'run_name': 'RecordBatchSortIndicesInt64Wide/1048576/0/8', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 3}
59      RecordBatchSortIndicesInt64Wide/1048576/0/16    4.794m items/sec    8.408m items/sec    75.389       {'run_name': 'RecordBatchSortIndicesInt64Wide/1048576/0/16', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 3}
16    RecordBatchSortIndicesInt64Wide/1048576/100/16    4.733m items/sec    8.177m items/sec    72.780     {'run_name': 'RecordBatchSortIndicesInt64Wide/1048576/100/16', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 3}
29    RecordBatchSortIndicesInt64Narrow/1048576/0/16    1.640m items/sec    2.627m items/sec    60.146     {'run_name': 'RecordBatchSortIndicesInt64Narrow/1048576/0/16', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 1}
9   RecordBatchSortIndicesInt64Narrow/1048576/100/16    1.559m items/sec    2.342m items/sec    50.201   {'run_name': 'RecordBatchSortIndicesInt64Narrow/1048576/100/16', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 1}
4          TableSortIndicesInt64Narrow/1048576/0/2/1    2.415m items/sec    2.699m items/sec    11.723          {'run_name': 'TableSortIndicesInt64Narrow/1048576/0/2/1', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 2}
51        TableSortIndicesInt64Narrow/1048576/0/2/32    1.814m items/sec    2.023m items/sec    11.513         {'run_name': 'TableSortIndicesInt64Narrow/1048576/0/2/32', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 1}
49        TableSortIndicesInt64Narrow/1048576/0/16/4    1.542m items/sec    1.717m items/sec    11.361         {'run_name': 'TableSortIndicesInt64Narrow/1048576/0/16/4', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 1}
30         TableSortIndicesInt64Narrow/1048576/0/2/4    2.272m items/sec    2.516m items/sec    10.733          {'run_name': 'TableSortIndicesInt64Narrow/1048576/0/2/4', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 2}
25         TableSortIndicesInt64Narrow/1048576/0/8/4    1.542m items/sec    1.706m items/sec    10.628          {'run_name': 'TableSortIndicesInt64Narrow/1048576/0/8/4', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 1}
11        TableSortIndicesInt64Narrow/1048576/0/16/1    1.691m items/sec    1.866m items/sec    10.316         {'run_name': 'TableSortIndicesInt64Narrow/1048576/0/16/1', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 1}
12         TableSortIndicesInt64Narrow/1048576/0/8/1    1.683m items/sec    1.856m items/sec    10.280          {'run_name': 'TableSortIndicesInt64Narrow/1048576/0/8/1', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 1}
[...]
6      RecordBatchSortIndicesInt64Narrow/1048576/0/1  185.050m items/sec  164.579m items/sec   -11.062    {'run_name': 'RecordBatchSortIndicesInt64Narrow/1048576/0/1', 'run_type': 'iteration', 'repetitions': 0, 'repetition_index': 0, 'threads': 1, 'iterations': 122}

[pitrou]

cc @kou

[github-actions]

https://issues.apache.org/jira/browse/ARROW-10796

[kou]

+1
Great!

left-to-right radix sort

Wow!

[kou]

Like ConcreteRecordBatchColumnSorter's next_column_?
It would work.

[kou]

Can we always do it?
My understanding that each chunked array in a table can have different number of chunks. For example, the table is valid:

a: [[0, 1], [2, 3, 4]]
b: [[10], [11, 12], [13], [14]]

I'm not sure we can split the table into record batches efficiently.

[pitrou]

TableBatchReader can be used for that.